### 12th Standard Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 12 Session 2019 - 2020 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 12th Standard English Medium Maths Reduced Syllabus Annual Exam Model Question Paper With Answer Key - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right]$ and AT = A−1 , then the value of x is

• 2)

Which of the following is not an elementary transformation?

• 3)

$\frac { 1+e^{ -i\theta } }{ 1+{ e }^{ i\theta } }$ =

• 4)

The number of positive zeros of the polynomial $\sum_{j=0}^{n}{ }^{n} C_{r}(-1)^{r} x^{r}$ is

• 5)

Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

#### 12th Standard English Medium Maths Reduced Syllabus Annual Exam Model Question Paper - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right]$, then 9I - A =

• 2)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 3)

If AT is the transpose of a square matrix A, then

• 4)

If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

• 5)

The product of all four values of $\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }$ is

#### 12th Standard English Medium Maths Reduced Syllabus Public Exam Model Question Paper With Answer Key - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

• 2)

If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 3)

The solution of the equation |z|-z=1+2i is

• 4)

If $\omega \neq 1$ is a cubic root of unity and $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 } & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 2 } \end{matrix} \right|$ =3k, then k is equal to

• 5)

If sin−1x = 2sin−1 $\alpha$ has a solution, then

#### 12th Standard English Medium Maths Reduced Syllabus Public Exam Model Question Paper - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If |adj(adj A)| = |A|9, then the order of the square matrix A is

• 2)

If A = $\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right]$ and AT = A−1 , then the value of x is

• 3)

The complex number z which satisfies the condition $\left| \frac { 1+z }{ 1-z } \right|$ =1 lies on

• 4)

The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

• 5)

The domain of the function defined by f(x)=sin−1$\sqrt{x-1}$ is

#### 12th Standard English Medium Maths Reduced Syllabus Creative Three Mark Questions with Answer key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Solve: 2x + 3y = 10, x + 6y = 4 using Cramer's rule.

• 2)

Verify that (A-1)T = (AT)-1 for A=$\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right]$.

• 3)

If the rank of the matrix $\left[ \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right]$ is 2, then find ⋋.

• 4)

Show that the complex numbers 3 + 2i, 5i, -3 + 2i and -i form a square.

• 5)

Find the locus of z if Re$\\ \left( \frac { \bar { z } +1 }{ \bar { z } -i } \right)$ =0.

#### 12th Standard English Medium Maths Reduced Syllabus Creative Two Mark Questions with Answer key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

For the matrix A, if A3 = I, then find A-1.

• 2)

Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

• 3)

Find the rank of the matrix A =$\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 5 \\ -3 \end{matrix}\begin{matrix} -6 \\ 0 \end{matrix}\begin{matrix} 1 \\ 8 \end{matrix} \right]$.

• 4)

Find k if the equations x + 2y + 2z = 0, x - 3y - 3z = 0, 2x + y + kz = 0 have only the trivial solution.

• 5)

Find Re (z) and im (z) if z = 5i11 + 7i3

#### 12th Standard English Medium Maths Reduced Syllabus Creative one Mark Questions with Answer key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

• 2)

If $\rho$(A) = $\rho$([A/B]) = number of unknowns, then the system is

• 3)

If $\rho$(A) = r then which of the following is correct?

• 4)

If $\rho$(A) ≠ $\rho$([AIB]), then the system is

• 5)

If z=cos$\frac { \pi }{ 4 }$+i sin$\frac { \pi }{ 6 }$, then

#### 12th Standard English Medium Maths Reduced Syllabus Five Mark Important Questions With Answer Key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Show that the equations -2x + y + z = a, x - 2y + z = b, x + y -2z = c are consistent only if a + b + c =0.

• 2)

If a1, a2, a3, ... an is an arithmetic progression with common difference d, prove that tan $x = {-b \pm \sqrt{b^2-4ac} \over 2a}\quad \left[ tan^{ -1 }\left( \frac { d }{ 1+{ a }_{ 1 }{ a }_{ 2 } } \right) +tan^{ -1 }\left( \frac { d }{ 1+{ a }_{ 2 }{ a }_{ 3 } } \right) +....tan^{ -1 }\left( \frac { d }{ 1+{ a }_{ n }{ a }_{ n-1 } } \right) \right] =\frac { { a }_{ n }-{ a }_{ 1 } }{ 1+{ a }_{ 1 }{ a }_{ n } }$

• 3)

Provethat ${ tan }^{ -1 }\left( \cfrac { 1-x }{ 1+x } \right) -{ tan }^{ -1 }\left( \cfrac { 1-y }{ 1+y } \right) ={ sin }^{ -1 }\left( \cfrac { y-x }{ \sqrt { 1+{ x }^{ 2 } } .\sqrt { 1+{ y }^{ 2 } } } \right) \\$

• 4)

Find the equation of the ellipse whose eccentricity is $\frac { 1 }{ 2 }$, one of the foci is(2,3) and a directrix is x = 7 . Also find the length of the major and minor axes of the ellipse.

• 5)

Certain telescopes contain both parabolic mirror and a hyperbolic mirror. In the telescope shown in figure the parabola and hyperbola share focus F1 which is 14mabove the vertex of the parabola. The hyperbola’s second focus F2 is 2m above the parabola’s vertex. The vertex of the hyperbolic mirror is 1m below F1. Position a coordinate system with the origin at the centre of the hyperbola and with the foci on the y-axis. Then find the equation of the hyperbola.

#### 12th Standard English Medium Maths Reduced Syllabus Five Mark Important Questions - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Solve the following system of equations, using matrix inversion method:
2x1 + 3x2 + 3x3 = 5, x1 - 2x2 + x3 = -4, 3x1 - x2 - 2x3 = 3.

• 2)

If A = $\left[ \begin{matrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{matrix} \right]$, find the productsAB and BAand hence solve the system of equations x - y + z = 4, x - 2y - 2z = 9, 2x + y + 3z = 1.

• 3)

Test for consistency and if possible, solve the following systems of equations by rank method.
i) x - y + 2z = 2, 2x + y + 4z = 7, 4x - y + z = 4
ii) 3x + y + z = 2, x - 3y + 2z = 1, 7x - y + 4z = 5
iii) 2x + 2y + z = 5, x - y + z = 1, 3x + y + 2z = 4
iv) 2x - y + z = 2, 6x - 3y + 3z = 6, 4x - 2y + 2z = 4

• 4)

Find the value of k for which the equations kx - 2y + z = 1, x - 2ky + z = -2, x - 2y + kz = 1 have
(i) no solution
(ii) unique solution
(iii) infinitely many solution

• 5)

Solve the equation z3+27=0 .

#### 12th Standard English Medium Maths Reduced Syllabus Three Mark Important Questions With Answer Key- 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the rank of the matrix $\left[ \begin{matrix} 2 \\ \begin{matrix} -3 \\ 6 \end{matrix} \end{matrix}\begin{matrix} -2 \\ \begin{matrix} 4 \\ 2 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} -2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} -1 \\ 7 \end{matrix} \end{matrix} \right]$ by reducing it to an echelon form.

• 2)

Find the adjoint of the following:
$\left[ \begin{matrix} 2 & 3 & 1 \\ 3 & 4 & 1 \\ 3 & 7 & 2 \end{matrix} \right]$

• 3)

If zi =2− i and z2=-4+3i , find the inverse of z1z2 and $\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }$

• 4)

If $cos\alpha +cos\beta +cos\gamma =sin\alpha +sin\beta +sin\gamma =0$ then show that
(i) $cos3\alpha +cos3\beta +cos3\gamma =3cos(\alpha +\beta +\gamma )$
(ii) $sin3\alpha +sin3\beta +sin3\gamma +sin3\gamma =3sin\left( \alpha +\beta +\gamma \right)$

• 5)

Show that $\left( \cfrac { 19-7i }{ 9+i } \right) ^{ 12 }+\left( \cfrac { 20-5i }{ 7-6i } \right) ^{ 12 }$ is real

#### 12th Standard English Medium Maths Reduced Syllabus Three Mark Important Questions - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Given A = $\left[ \begin{matrix} 1 & -1 \\ 2 & 0 \end{matrix} \right]$, B = $\left[ \begin{matrix} 3 & -2 \\ 1 & 1 \end{matrix} \right]$ and C = $\left[ \begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix} \right]$, find a matrix X such that AXB = C.

• 2)

Find the rank of the following matrices by row reduction method:
$\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ 5 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} -1 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 3 \\ 7 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 4 \\ 11 \end{matrix} \end{matrix} \right]$

• 3)

A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution ? (Use Cramer’s rule to solve the problem).

• 4)

Find the adjoint of the following:
$\frac { 1 }{ 3 } \left[ \begin{matrix} 2 & 2 & 1 \\ -2 & 1 & 2 \\ 1 & -2 & 2 \end{matrix} \right]$

• 5)

The complex numbers u,v, and w are related by $\cfrac { 1 }{ u } =\cfrac { 1 }{ v } +\cfrac { 1 }{ w }$ If v=3−4i and w=4+3i, find u in rectangular form.

#### 12th Standard English Medium Maths Reduced Syllabus Two Mark Important Questions with Answer key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find a matrix A if adj(A) = $\left[ \begin{matrix} 7 & 7 & -7 \\ -1 & 11 & 7 \\ 11 & 5 & 7 \end{matrix} \right]$.

• 2)

Find the rank of the following matrices by minor method:
$\left[ \begin{matrix} 1 \\ 3 \end{matrix}\begin{matrix} -2 \\ -6 \end{matrix}\begin{matrix} -1 \\ -3 \end{matrix}\begin{matrix} 0 \\ 1 \end{matrix} \right]$

• 3)

Find the rank of the following matrices by minor method:
$\left[ \begin{matrix} 1 & -2 & 3 \\ 2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right]$

• 4)

Find the following $\left| \cfrac { 2+i }{ -1+2i } \right|$

• 5)

Which one of the points i,−2+i , and 3 is farthest from the origin?

#### 12th Standard English medium Maths Reduced Syllabus Two Mark Important Questions - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the inverse (if it exists) of the following:
$\left[ \begin{matrix} -2 & 4 \\ 1 & -3 \end{matrix} \right]$

• 2)

Find the rank of the following matrices by minor method:
$\left[ \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right]$

• 3)

Show that the equations 3x + y + 9z = 0, 3x + 2y + 12z = 0 and 2x + y + 7z = 0 have nontrivial solutions also.

• 4)

Solve 6x - 7y = 16, 9x - 5y = 35 using (Cramer's rule).

• 5)

If z1=1-3i,z2=4i, and z3 = 5 , show that (z1+z2)+z3=z1+(z2+z3)

#### 12th Standard English Medium Maths Reduced syllabus One Mark Important Questions With Answer Key - 2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right]$, then 9I - A =

• 2)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 3)

If (AB)-1 = $\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right]$, then B-1 =

• 4)

If xayb = em, xcyd = en, Δ1 = $\left| \begin{matrix} m & b \\ n & d \end{matrix} \right|$, Δ2 = $\left| \begin{matrix} a & m \\ c & n \end{matrix} \right|$, Δ3 = $\left| \begin{matrix} a & b \\ c & d \end{matrix} \right|$, then the values of x and y are respectively,

• 5)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

#### 12th Standard English Medium Maths Reduced syllabus One Mark Important Questions -2021(Public Exam ) - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

• 2)

If A = $\left[ \begin{matrix} \cos { \theta } & \sin { \theta } \\ -\sin { \theta } & \cos { \theta } \end{matrix} \right]$ and A(adj A) =  $\left[ \begin{matrix} k & 0 \\ 0 & k \end{matrix} \right]$, then k =

• 3)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

• 4)

The principal argument of (sin 40°+i cos40°)5 is

• 5)

The complex number z which satisfies the condition $\left| \frac { 1+z }{ 1-z } \right|$ =1 lies on

#### 12th Standard Maths English Medium Discrete Mathematics Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The operation * defined by a*b =$\frac{ab}{7}$ is not a binary operation on

• 2)

In the set Q define a⊙b= a+b+ab. For what value of y, 3⊙(y⊙5)=7?

• 3)

Which one of the following statements has the truth value T?

• 4)

In the last column of the truth table for ¬( p ∨ ¬q) the number of final outcomes of the truth value 'F' are

• 5)

The proposition p ∧ (¬p ∨ q) is

#### 12th Standard Maths English Medium Discrete Mathematics Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A binary operation on a set S is a function from

• 2)

Which one of the following is a binary operation on N?

• 3)

Which one of the following statements has the truth value T?

• 4)

If a compound statement involves 3 simple statements, then the number of rows in the truth table is

• 5)

The truth table for (p ∧ q) ∨ ¬q is given below

 p q (p ∧ q) ∨ (¬q) T T (a) T F (b) F T (c) F F (d)

Which one of the following is true?

#### 12th Standard Maths English Medium Probability Distributions Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

• 2)

On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

• 3)

If P(X = 0) = 1 - P(X = I). If E(X) = 3 Var(X), then P(X = 0) is

• 4)

If X is a binomial random variable with expected value 6 and variance 2.4, then P(X = 5) is

• 5)

The random variable X has the probability density function

and $E(X)=\cfrac { 7 }{ 12 }$ then a and b are respectively.

#### 12th Standard Maths English Medium Probability Distributions Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is

The mean and variance of the shorter of the two pieces are respectively.

• 2)

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

• 3)

A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

• 4)

Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus.
Then E(X) and E(Y) respectively are

• 5)

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with probability 0.5. Assume that the results of the flips are independent, and let X equal the total number of heads that result The value of E(X) is

#### 12th Standard Maths English Medium Ordinary Differential Equations Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

• 2)

The integrating factor of the differential equation $\frac{dy}{dx}$+P(x)y=Q(x)is x, then P(x)

• 3)

The degree of the differential equation y $y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....$ is

• 4)

If p and q are the order and degree of the differential equation $y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,$When

• 5)

The solution of $\frac { dy }{ dx } ={ 2 }^{ y-x }$is

#### 12th Standard Maths English Medium Ordinary Differential Equations Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The order and degree of the differential equation $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0$are respectively

• 2)

The solution of $\frac{dy}{dx}+$p(x)y=0 is

• 3)

The integrating factor of the differential equation $\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda }$ is

• 4)

The integrating factor of the differential equation $\frac{dy}{dx}$+P(x)y=Q(x)is x, then P(x)

• 5)

The degree of the differential equation y $y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....$ is

#### 12th Standard Maths English Medium Applications of Integration Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of $\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ \left( \frac { { 2x }^{ 7 }-{ 3x }^{ 5 }+{ 7x }^{ 3 }-x+1 }{ { cos }^{ 2 }x } \right) dx }$ is

• 2)

The value of $\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx }$

• 3)

The value of  $\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx }$ is

• 4)

The volume of solid of revolution of the region bounded by y2 = x(a − x) about x-axis is

• 5)

The value of $\int _{ 0 }^{ a }{ { (\sqrt { { a }^{ 2 }-{ x }^{ 2 } } ) }^{ 3 } } dx$

#### 12th Standard Maths English Medium Applications of Integration Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of $\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx }$ is

• 2)

The value of  $\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx }$ is

• 3)

The value of $\int _{ 0 }^{ \infty }{ { e }^{ -3x }{ x }^{ 2 }dx } \\$ is

• 4)

The value of $\int _{ 0 }^{ a }{ { (\sqrt { { a }^{ 2 }-{ x }^{ 2 } } ) }^{ 3 } } dx$

• 5)

For any value of $n \in \mathbb{Z}, \int_{0}^{\pi} e^{\cos ^{2} x} \cos ^{3}[(2 n+1) x] d x$ is

#### 12th Standard Maths English Medium Differentials and Partial Derivatives Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

• 2)

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

• 3)

If $g(x, y)=3 x^{2}-5 y+2 y^{2}, x(t)=e^{t}$ and y(t) = cos t, then $\frac{dg}{dt}$ is equal to

• 4)

If f(x) = $\frac{x}{x+1}$ then its differential is given by

• 5)

If w (x, y, z) = x2 (y - z) + y2 (z - x) + z2(x - y), then $\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z }$ is

#### 12th Standard Maths English Medium Differentials and Partial Derivatives Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If f (x, y) = exy then $\frac { { \partial }^{ 2 }f }{ \partial x\partial y }$ is equal to

• 2)

If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

• 3)

The change in the surface area S = 6x2 of a cube when the edge length varies from xo to xo+ dx is

• 4)

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

• 5)

If (x,y, z) = xy +yz +zx, then fx - fz is equal to

#### 12th Standard Maths English Medium Applications Of Differential Calculus Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t -16t2. The stone reaches the maximum height in time t seconds is given by

• 2)

The tangent to the curve y2 - xy + 9 = 0 is vertical when

• 3)

The value of the limit $\\ \\ \\ \underset { x\rightarrow 0 }{ lim } \left( cotx-\cfrac { 1 }{ x } \right)$

• 4)

The function sin4 x + cos4 x is increasing in the interval

• 5)

The number given by the Mean value theorem for the function $\cfrac { 1 }{ x }$,x∈[1,9] is

#### 12th Standard Maths English Medium Applications Of Differential Calculus Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is $\cfrac { 1 }{ 2 }$ cm

• 2)

The abscissa of the point on the curve $f\left( x \right) =\sqrt { 8-2x }$ at which the slope of the tangent is -0.25 ?

• 3)

The slope of the line normal to the curve f(x) = 2cos 4x at $x=\cfrac { \pi }{ 12 }$

• 4)

Angle between y2 = x and.x2= y at the origin is

• 5)

The value of the limit $\\ \\ \\ \underset { x\rightarrow 0 }{ lim } \left( cotx-\cfrac { 1 }{ x } \right)$

#### 12th Standard Maths English Medium Applications of Vector Algebra Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If a vector $\vec { \alpha }$ lies in the plane of $\vec { \beta }$ and $\vec { \gamma }$ , then

• 2)

$\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0$ , then the value of $[\vec { a } ,\vec { b } ,\vec { c } ]$ is

• 3)

If $\vec { a } ,\vec { b } ,\vec { c }$ are non-coplanar, non-zero vectors such that $[\vec { a } ,\vec { b } ,\vec { c } ]$ = 3, then ${ \{ [\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a } }]\} ^{ 2 }$ is equal to

• 4)

If $\vec { a } ,\vec { b } ,\vec { c }$ are three non-coplanar vectors such that $\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } }$, then the angle between $\vec { a } \ and \ \vec { b }$is

• 5)

If the volume of the parallelepiped with $\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a }$  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with $(\vec { a } \times \vec { b } )\times (\vec { b } \times \vec { c } ),(\vec { b } \times \vec { c } )\times (\vec { c } \times \vec { a } )$ and $(\vec { c } \times \vec { a } )\times (\vec { a } \times \vec { b } )$as coterminous edges is,

#### 12th Standard Maths English Medium Applications of Vector Algebra Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If $\vec{a}$ and $\vec{b}$ are parallel vectors, then $[\vec { a } ,\vec { c } ,\vec { b } ]$ is equal to

• 2)

The volume of the parallelepiped with its edges represented by the vectors $\hat { i } +\hat { j } ,\hat { i } +2\hat { j } ,\hat { i } +\hat { j } +\pi \hat { k }$ is

• 3)

If $\vec { a }$ and $\vec { b }$ are unit vectors such that $[\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 }$, then the angle between $\vec { a }$ and $\vec { b }$ is

• 4)

Consider the vectors $\vec { a } ,\vec { b } ,\vec { c } ,\vec { d}$ such that $(\vec { a } \times \vec { b } )\times (\vec { c } \times \vec { d } )$ = $\vec { 0 }$ Let ${ P }_{ 1 }$ and ${ P }_{ 2 }$ be the planes determined by the pairs of vectors $\vec { a } ,\vec { b }$ and $\vec { c } ,\vec { d }$ respectively. Then the angle between ${ P }_{ 1 }$ and ${ P }_{ 2 }$ is

• 5)

If $\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c }$ where $\vec { a } ,\vec { b } ,\vec { c }$ are any three vectors such that $\vec{b} \cdot \vec{c} \neq 0 \text { and } \vec{a} \cdot \vec{b} \neq 0$, then $\vec { a }$ and $\vec { c }$ are

#### 12th Standard Maths English Medium Two Dimensional Analytical Geometry-II Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

• 2)

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

• 3)

The area of quadrilateral formed with foci of the hyperbolas $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\$ and $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1$

• 4)

If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

• 5)

If x+y=k is a normal to the parabola y2 =12x, then the value of k is

#### 12th Standard Maths English Medium Two Dimensional Analytical Geometry-II Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

• 2)

The circle x2+y= 4x + 8y +5 intersects the line 3x−4y=m at two distinct points if

• 3)

The area of quadrilateral formed with foci of the hyperbolas $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\$ and $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1$

• 4)

Tangents are drawn to the hyperbola  $\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 4 } =1$ parallel to the straight line 2x − y = 1. One of the points of contact of tangents on the hyperbola is

• 5)

An ellipse hasOB as semi minor axes, F and F′ its foci and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

#### 12th Standard Maths English Medium Inverse Trigonometric Functions Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of sin-1 (cos x), 0$\le x\le\pi$ is

• 2)

If x=$\frac{1}{5}$, the valur of cos (cos-1x+2sin-1x) is

• 3)

If sin-1 x+cot-1$(\frac{1}{2})=\frac{\pi}{2}$, then x is equal to

• 4)

The number of solutions of the equation ${ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 }$

• 5)

If $\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right)$ and $\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right)$ then

#### 12th Standard Maths English Medium Inverse Trigonometric Functions Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If cot−1x=$\frac{2\pi}{5}$ for some x$\in$R, the value of tan-1 x is

• 2)

The domain of the function defined by f(x)=sin−1$\sqrt{x-1}$ is

• 3)

If |x|$\le$1, then 2tan-1 x-sin-1 $\frac{2x}{1+x^2}$ is equal to

• 4)

The equation tan-1 x-cot-1 x=tan-1$\left( \frac { 1 }{ \sqrt { 3 } } \right)$has

• 5)

If ${ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha$ then x2 =

#### 12th Standard Maths English Medium Theory of Equations Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A zero of x3 + 64 is

• 2)

A polynomial equation in x of degree n always has

• 3)

If α,β and γ are the roots of x3+px2+qx+r, then $\Sigma \frac { 1 }{ \alpha }$ is

• 4)

If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

• 5)

The polynomial x+ 2x + 3 has

#### 12th Standard Maths English Medium Theory of Equations Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A zero of x3 + 64 is

• 2)

If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

• 3)

The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

• 4)

If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

• 5)

The number of positive zeros of the polynomial $\sum_{j=0}^{n}{ }^{n} C_{r}(-1)^{r} x^{r}$ is

#### 12th Standard Maths English Medium Complex Numbers Reduced Syllabus Important Questions With Answer Key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If z is a non zero complex number, such that 2iz2=$\bar { z }$ then |z| is

• 2)

If |z-2+i|≤2, then the greatest value of |z| is

• 3)

If $\alpha$ and $\beta$ are the roots of x2+x+1=0, then ${ \alpha }^{ 2020 }+{ \beta }^{ 2020 }$ is

• 4)

The product of all four values of $\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }$ is

• 5)

The least positive integer n such that $\left( \frac { 2i }{ 1+i } \right) ^{ n }$  is a positive integer is

#### 12th Standard Maths English Medium Complex Numbers Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

in+in+1+in+2+in+3 is

• 2)

If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

• 3)

If z is a non zero complex number, such that 2iz2=$\bar { z }$ then |z| is

• 4)

If |z-2+i|≤2, then the greatest value of |z| is

• 5)

If |z|=1, then the value of $\cfrac { 1+z }{ 1+\overline { z } }$ is

#### 12th Standard Maths English Medium Application of Matrices and Determinants Reduced Syllabus Important Questions With Answer key 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If P = $\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right]$ is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

• 2)

If A = $\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right]$ then the value of a23 is

• 3)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 4)

If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 5)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

#### 12th Standard Maths English Medium Application of Matrices and Determinants Reduced Syllabus Important Questions 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If |adj(adj A)| = |A|9, then the order of the square matrix A is

• 2)

If A = $\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right]$ then the value of a23 is

• 3)

If xayb = em, xcyd = en, Δ1 = $\left| \begin{matrix} m & b \\ n & d \end{matrix} \right|$, Δ2 = $\left| \begin{matrix} a & m \\ c & n \end{matrix} \right|$, Δ3 = $\left| \begin{matrix} a & b \\ c & d \end{matrix} \right|$, then the values of x and y are respectively,

• 4)

Let A = $\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right]$ and 4B = $\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right]$. If B is the inverse of A, then the value of x is

• 5)

If A is a square matrix of order n, then |adj A| =

#### 12th Standard Maths English Medium Reduced Syllabus Model Question paper with answer key - 2021 Part - 2 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 2)

Cramer's rule is applicable only when ______

• 3)

In a homogeneous system if $\rho$ (A) =$\rho$([A|0]) < the number of unknouns then the system has ________

• 4)

• 5)

If $\omega \neq 1$ is a cubic root of unity and $\left( 1+\omega \right) ^{ 7 }=A+B\omega$ ,then (A,B) equals

#### 12th Standard Maths English Medium Reduced Syllabus Model Question paper with answer key - 2021 Part - 1 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a 3 x 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 2)

If (AB)-1 = $\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right]$, then B-1 =

• 3)

If ATA−1 is symmetric, then A2 =

• 4)

If adj A = $\left[ \begin{matrix} 2 & 3 \\ 4 & -1 \end{matrix} \right]$ and adj B = $\left[ \begin{matrix} 1 & -2 \\ -3 & 1 \end{matrix} \right]$ then adj (AB) is

• 5)

Let A = $\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right]$ and 4B = $\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right]$. If B is the inverse of A, then the value of x is

#### 12th Standard Maths English Medium Reduced Syllabus Model Question paper - 2021 Part - 1 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If P = $\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right]$ is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

• 2)

If ATA−1 is symmetric, then A2 =

• 3)

If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

• 4)

The value of tan $\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right)$ is ______

• 5)

Equation of tangent at (-4, -4) on x2 = -4y is

#### 12th Standard Maths English Medium Reduced Syllabus Model Question paper - 2021 Part - 2 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right]$, B = adj A and C = 3A, then $\frac { \left| adjB \right| }{ \left| C \right| }$

• 2)

The rank of the matrix $\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right]$ is

• 3)

If xayb = em, xcyd = en, Δ1 = $\left| \begin{matrix} m & b \\ n & d \end{matrix} \right|$, Δ2 = $\left| \begin{matrix} a & m \\ c & n \end{matrix} \right|$, Δ3 = $\left| \begin{matrix} a & b \\ c & d \end{matrix} \right|$, then the values of x and y are respectively,

• 4)

If |z-2+i|≤2, then the greatest value of |z| is

• 5)

If $\left| z-\cfrac { 3 }{ z } \right| =2$ then the least value |z| is

#### 12th Standard Maths English Medium Reduced Syllabus Important Questions with Answer key - 2021 Part - 2 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

• 2)

If ATA−1 is symmetric, then A2 =

• 3)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

• 4)

The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

• 5)

The conjugate of a complex number is $\cfrac { 1 }{ i-2 }$/Then the complex number is

#### 12th Standard Maths English Medium Reduced Syllabus Important Questions with Answer key - 2021 Part - 1 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let A = $\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right]$ and 4B = $\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right]$. If B is the inverse of A, then the value of x is

• 2)

Which of the following is not an elementary transformation?

• 3)

If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

• 4)

The number of normals to the hyperbola $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 from an external point is

• 5)

The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are

#### 12th Standard Maths English Medium Reduced Syllabus Important Questions - 2021 Part - 2 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

• 2)

If P = $\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right]$ is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

• 3)

The rank of the matrix $\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right]$ is

• 4)

z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

• 5)

If $\cfrac { z-1 }{ z+1 }$ is purely imaginary, then |z| is

#### 12th Standard Maths English Medium Reduced Syllabus Important Questions - 2021 Part - 1 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

• 2)

The curve y = ex is ________

• 3)

If y = sin x and x changes from $\frac{\pi}{2}$ to ㅠ the approximate change in y is ..............

• 4)

If u = y sin x then $\frac { { \partial }^{ 2 }u }{ \partial x\partial y }$ = ..........

• 5)

The value of $\int _{ -\pi }^{ \pi }{ { sin }^{ 3 }x \ { cos }^{ 3 }x \ } dx$ is

#### Seventh Standard Social Science CIV - Market and Consumer Protection English Medium Free Online Test 1 Mark Questions with Answer Key 2020 - 2021 - by NALLAMAYAN T - View & Read

• 1)

In which case a consumer cannot complain against the manufacturer for a defective product?

• 2)

Consumer’s face various problems from the producer’s end due

• 3)

Consumers must be provided with adequate information about a product to make

• 4)

The system of consumer courts at the national, state, and district levels, looking into consumers grievances against unfair trade practices of businessmen and providing necessary compensation, is called.

• 5)

Mixing other extraneous material of inferior quality with a superior quality material is called

#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If |adj(adj A)| = |A|9, then the order of the square matrix A is

• 2)

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

• 3)

in+in+1+in+2+in+3 is

• 4)

A zero of x3 + 64 is

• 5)

For real x, the equation $\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| }$ has

#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a 3 x 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 2)

If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then

• 3)

If A is a non-singular matrix then IA-1|= ______

• 4)

• 5)

The principal value of the amplitude of (1+i) is

#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right]$, B = adj A and C = 3A, then $\frac { \left| adjB \right| }{ \left| C \right| }$

• 2)

The rank of the matrix $\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right]$ is

• 3)

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

• 4)

In a homogeneous system if $\rho$ (A) =$\rho$([A|0]) < the number of unknouns then the system has ________

• 5)

If |z-2+i|≤2, then the greatest value of |z| is

#### 12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If |adj(adj A)| = |A|9, then the order of the square matrix A is

• 2)

If A = $\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right]$, then 9I - A =

• 3)

If P = $\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right]$ is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

• 4)

If A = $\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right]$ and AT = A−1 , then the value of x is

• 5)

The conjugate of a complex number is $\cfrac { 1 }{ i-2 }$/Then the complex number is

#### 12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A$\left[ \begin{matrix} 1 & -2 \\ 1 & 4 \end{matrix} \right] =\left[ \begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \right]$, then A =

• 2)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

• 3)

The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

• 4)

${ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 9 } \right)$is equal to

• 5)

The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

#### 12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right]$ then |adj (AB)| =

• 2)

If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

• 3)

The polynomial x+ 2x + 3 has

• 4)

The domain of the function defined by f(x)=sin−1$\sqrt{x-1}$ is

• 5)

The length of the diameter of the circle which touches the x - axis at the point (1,0) and passes through the point (2,3) .

#### 12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If sin-1 x+cot-1$(\frac{1}{2})=\frac{\pi}{2}$, then x is equal to

• 2)

The eccentricity of the ellipse (x−3)2 +(y−4)2 =$\frac { { y }^{ 2 } }{ 9 }$ is

• 3)

The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

• 4)

The maximum value of the function $x^{2} e^{-2 x}, x>0$ is

• 5)

If w (x, y, z) = x2 (y - z) + y2 (z - x) + z2(x - y), then $\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z }$ is

#### 12th Standard Maths English Medium Free Online Test Book Back One Mark Questions - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let C be the circle with centre at(1,1) and radius =1. If T is the circle centered at (0, y) passing through the origin and touching the circle C externally, then the radius of T is equal to

• 2)

If $\vec { a } ,\vec { b } ,\vec { c }$ are three unit vectors such that $\vec { a }$ is perpendicular to $\vec { b }$ and is parallel to $\vec { c }$ then $\vec { a } \times (\vec { b } \times \vec { c } )$ is equal to

• 3)

If the distance of the point (1,1,1) from the origin is half of its distance from the plane x + y + z + k =0, then the values of k are

• 4)

One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

• 5)

If u(x, y) = x2+ 3xy + y - 2019, then $\frac { \partial u }{ \partial x }$(4, -5) is equal to

#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is

• 2)

The principal value of the amplitude of (1+i) is

• 3)

If xr=$cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right)$ then x1, x2 ... x is

• 4)

The equation $\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 }$ has

• 5)

If $\alpha ={ tan }^{ -1 }\left( tan\cfrac { 5\pi }{ 4 } \right)$ and $\beta ={ tan }^{ -1 }\left( -tan\cfrac { 2\pi }{ 3 } \right)$ then

#### 12th Standard Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 2)

If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then $2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right)$ is

• 3)

According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

• 4)

If |x|$\le$1, then 2tan-1 x-sin-1 $\frac{2x}{1+x^2}$ is equal to

• 5)

If P(x, y) be any point on 16x+ 25y= 400 with foci F1 (3,0) and F2 (-3,0) then PF1 PFis

#### 12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 2)

If A = $\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right]$ be such that λA−1 =A, then λ is

• 3)

According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

• 4)

If sin-1 x+sin-1 y+sin-1 z=$\frac{3\pi}{2}$, the value of x2017+y2018+z2019$-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } }$is

• 5)

The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A =$\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right)$ and A(adj A) =$\lambda$ $\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$ then $\lambda$ is

• 2)

If a = 1+i, then a2 equals

• 3)

Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

• 4)

·If $\alpha ={ tan }^{ -1 }\left( \cfrac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \cfrac { 2x-y }{ \sqrt { 3y } } \right)$ then $\alpha -\beta$

• 5)

y2 - 2x - 2y + 5 = 0 is a

#### 12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2. is inconsistent then k is

• 2)

If a=cosθ + i sinθ, then $\frac { 1+a }{ 1-a }$ =

• 3)

(1+i)3 = ______

• 4)

Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

• 5)

If u = yx then $\frac { \partial u }{ \partial y }$ = ............

#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if

• 2)

The principal value of the amplitude of (1+i) is

• 3)

The equation $\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 }$ has

• 4)

If tan-1(3)+tan-1(x)=tan-1(8)then x=

• 5)

The director circle of the ellipse $\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1$ is

#### 12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Which of the following is not an elementary transformation?

• 2)

If z=$\frac { 1 }{ 1-cos\theta -isin\theta }$, the Re(z) =

• 3)

If z1, z2, z3 are the vertices of a parallelogram, then the fourth vertex z4 opposite to z2 is _____

• 4)

If ∝, β,૪ are the roots of 9x3-7x+6=0, then ∝ β ૪ is __________

• 5)

If ${ tan }^{ -1 }\left( \cfrac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \cfrac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right)$ then x Is

#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Four - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A =$\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right)$ and A(adj A) =$\lambda$ $\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$ then $\lambda$ is

• 2)

If a = 1+i, then a2 equals

• 3)

If x is real and $\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 }$ then

• 4)

The number of real solutions of the equation $\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi <x<\pi$ is

• 5)

Equation of tangent at (-4, -4) on x2 = -4y is

#### 12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Four - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If ATA−1 is symmetric, then A2 =

• 2)

Every homogeneous system ______

• 3)

If A is a non-singular matrix then IA-1|= ______

• 4)

If x+iy =$\frac { 3+5i }{ 7-6i }$, they y =

• 5)

If x + y = 8, then the maximum value of xy is _________

#### 12th Standard Maths English Medium Free Online Test Creative 1 Mark Questions - Part Five - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If $\rho$(A) = $\rho$([A/B]) = number of unknowns, then the system is

• 2)

If z = $\frac { 1 }{ (2+3i)^{ 2 } }$ then |z| =

• 3)

The equation $\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 }$ has

• 4)

${ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right)$ =

• 5)

The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

#### 12th Standard Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Five - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a square matrix that IAI = 2, than for any positive integer n, |An| =

• 2)

If $\rho$(A) = r then which of the following is correct?

• 3)

If z=$\frac { 1 }{ 1-cos\theta -isin\theta }$, the Re(z) =

• 4)

Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

• 5)

Equation of tangent at (-4, -4) on x2 = -4y is

#### 12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 2)

If A =$\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right)$ and A(adj A) =$\lambda$ $\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$ then $\lambda$ is

• 3)

In the non - homogeneous system of equations with 3 unknowns if $\rho$(A) = $\rho$([AIB]) = 2, then the system has _______

• 4)

If A = [2 0 1] then the rank of AAT is ______

• 5)

The conjugate of a complex number is $\cfrac { 1 }{ i-2 }$/Then the complex number is

#### 12th Standard Maths English Medium Free Online Test Volume 1 One Mark Questions with Answer Key 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

• 2)

If A =$\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right)$ and A(adj A) =$\lambda$ $\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right)$ then $\lambda$ is

• 3)

If A is a non-singular matrix then IA-1|= ______

• 4)

The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

• 5)

If $\omega \neq 1$ is a cubic root of unity and $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 } & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 2 } \end{matrix} \right|$ =3k, then k is equal to

#### 12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The abscissa of the point on the curve $f\left( x \right) =\sqrt { 8-2x }$ at which the slope of the tangent is -0.25 ?

• 2)

The equation of the tangent to the curve y=x2-4x+2 at (4,2) is

• 3)

In LMV theorem, we have f'(x1) =$\frac { f(b)-f(a) }{ b-a }$ then a < x1 _________

• 4)

If the curves y = 2ex and y =ae-x intersect orthogonally, then a = _________

• 5)

If w (x, y) = xy, x > 0, then $\frac { \partial w }{ \partial x }$ is equal to

#### 12th Standard Maths English Medium Free Online Test Volume 2 One Mark Questions with Answer Key 2020 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The abscissa of the point on the curve $f\left( x \right) =\sqrt { 8-2x }$ at which the slope of the tangent is -0.25 ?

• 2)

The value of the limit $\\ \\ \\ \underset { x\rightarrow 0 }{ lim } \left( cotx-\cfrac { 1 }{ x } \right)$

• 3)

The equation of the tangent to the curve y=x2-4x+2 at (4,2) is

• 4)

If$u(x, y)=e^{x^{2}+y^{2}}$, then $\frac { \partial u }{ \partial x }$ is equal to

• 5)

If loge4 = 1.3868, then loge4.01 =

#### 12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If |adj(adj A)| = |A|9, then the order of the square matrix A is

• 2)

If A = $\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right]$, then 9I - A =

• 3)

If P = $\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right]$ is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

• 4)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 5)

If adj A = $\left[ \begin{matrix} 2 & 3 \\ 4 & -1 \end{matrix} \right]$ and adj B = $\left[ \begin{matrix} 1 & -2 \\ -3 & 1 \end{matrix} \right]$ then adj (AB) is

#### 12th Standard Maths Application of Matrices and Determinants English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a 3 x 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 2)

If A = $\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right]$ then the value of a23 is

• 3)

If (AB)-1 = $\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right]$, then B-1 =

• 4)

If A = $\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right]$ be such that λA−1 =A, then λ is

• 5)

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj(A).

#### 12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

in+in+1+in+2+in+3 is

• 2)

If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

• 3)

If |z-2+i|≤2, then the greatest value of |z| is

• 4)

z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

• 5)

The principal argument of (sin 40°+i cos40°)5 is

#### 12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

• 2)

If z is a non zero complex number, such that 2iz2=$\bar { z }$ then |z| is

• 3)

The solution of the equation |z|-z=1+2i is

• 4)

If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then $2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right)$ is

• 5)

The value of $\left( \cfrac { 1+3\sqrt { i } }{ 1-\sqrt { 3i } } \right) ^{ 10 }$

#### 12th Standard Maths Theory of Equations English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A zero of x3 + 64 is

• 2)

According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

• 3)

The number of real numbers in [0,2π] satisfying sin4x-2sin2x+1 is

• 4)

The polynomial x+ 2x + 3 has

• 5)

Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

#### 12th Standard Maths Theory of Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If f and g are polynomials of degrees m and n respectively, and if h(x) =(f 0 g)(x), then the degree of h is

• 2)

The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

• 3)

If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

• 4)

The number of positive zeros of the polynomial $\sum_{j=0}^{n}{ }^{n} C_{r}(-1)^{r} x^{r}$ is

• 5)

The quadratic equation whose roots are ∝ and β is

#### 12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of sin-1 (cos x), 0$\le x\le\pi$ is

• 2)

If cot−1x=$\frac{2\pi}{5}$ for some x$\in$R, the value of tan-1 x is

• 3)

If x=$\frac{1}{5}$, the valur of cos (cos-1x+2sin-1x) is

• 4)

${ sin }^{ -1 }\left( tan\frac { \pi }{ 4 } \right) -{ sin }^{ -1 }\left( \sqrt { \frac { 3 }{ x } } \right) =\frac { \pi }{ 6 }$.Then x is a root of the equation

• 5)

If sin-1 $\frac{x}{5}+ cosec^{-1}\frac{5}{4}=\frac{\pi}{2}$, then the value of x is

#### 12th Standard Maths Inverse Trigonometric Functions English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If sin-1 x+sin-1 y=$\frac{2\pi}{3};$then cos-1x+cos-1 y is equal to

• 2)

If sin-1 x+sin-1 y+sin-1 z=$\frac{3\pi}{2}$, the value of x2017+y2018+z2019$-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } }$is

• 3)

The domain of the function defined by f(x)=sin−1$\sqrt{x-1}$ is

• 4)

${ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 9 } \right)$is equal to

• 5)

sin-1(2cos2x-1)+cos-1(1-2sin2x)=

#### 12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

• 2)

The radius of the circle3x2+by2+4bx−6by+b2 =0 is

• 3)

The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

• 4)

If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

• 5)

The equation of the circle passing through the foci of the ellipse  $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$ having centre at (0,3) is

#### 12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

• 2)

The area of quadrilateral formed with foci of the hyperbolas $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\$ and $\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1$

• 3)

Tangents are drawn to the hyperbola  $\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 4 } =1$ parallel to the straight line 2x − y = 1. One of the points of contact of tangents on the hyperbola is

• 4)

Area of the greatest rectangle inscribed in the ellipse $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.$ is

• 5)

The values of m for which the line y=mx+ $2\sqrt { 5 }$ touches the hyperbola 16x2−9y2=144 are the roots of x2−(a+b)x−4=0, then the value of (a+b) is

#### 12th Standard Maths Applications of Vector Algebra English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If $\vec{a}$ and $\vec{b}$ are parallel vectors, then $[\vec { a } ,\vec { c } ,\vec { b } ]$ is equal to

• 2)

If $\vec { a }$ and $\vec { b }$ are unit vectors such that $[\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 }$, then the angle between $\vec { a }$ and $\vec { b }$ is

• 3)

If the volume of the parallelepiped with $\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a }$  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with $(\vec { a } \times \vec { b } )\times (\vec { b } \times \vec { c } ),(\vec { b } \times \vec { c } )\times (\vec { c } \times \vec { a } )$ and $(\vec { c } \times \vec { a } )\times (\vec { a } \times \vec { b } )$as coterminous edges is,

• 4)

If $\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c }$ where $\vec { a } ,\vec { b } ,\vec { c }$ are any three vectors such that $\vec{b} \cdot \vec{c} \neq 0 \text { and } \vec{a} \cdot \vec{b} \neq 0$, then $\vec { a }$ and $\vec { c }$ are

• 5)

The angle between the line $\vec { r } =(\hat { i } +2\hat { j } -3\hat { k } )+t(2\hat { i } +\hat { j } -2\hat { k } )$ and the plane $\vec { r } .(\hat { i } +\hat { j } )+4=0$ is

#### 12th Standard Maths Differentials and Partial Derivatives English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If v (x, y) = log (ex + ey), then $\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y }$ is equal to

• 2)

If f (x, y) = exy then $\frac { { \partial }^{ 2 }f }{ \partial x\partial y }$ is equal to

• 3)

If u(x, y) = x2+ 3xy + y - 2019, then $\frac { \partial u }{ \partial x }$(4, -5) is equal to

• 4)

If the radius of the sphere is measured as 9 em with an error of 0.03 cm, the approximate error in calculating its volume is

• 5)

If u = log $\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$, then $\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } }$ is

#### 12th Standard Maths Applications of Vector Algebra English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If a vector $\vec { \alpha }$ lies in the plane of $\vec { \beta }$ and $\vec { \gamma }$ , then

• 2)

If $\vec { a } ,\vec { b } ,\vec { c }$ are three non-coplanar vectors such that $\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } }$, then the angle between $\vec { a } \ and \ \vec { b }$is

• 3)

If the line $\frac { x-2 }{ 3 } =\frac { y-1 }{ -5 }= \frac {z+2 }{ 2 }$ lies in the plane x + 3y + - αz + β = 0, then (α, β) is

• 4)

The vector equation $\vec { r } =(\hat { i } -2\hat { j } -\hat { k } )+t(6\hat { i } -\hat { k) }$ represents a straight line passing through the points

• 5)

Let $\overset { \rightarrow }{ a }$,$\overset { \rightarrow }{ b }$ and $\overset { \rightarrow }{ c }$ be three non- coplanar vectors and let $\overset { \rightarrow }{ p } ,\overset { \rightarrow }{ q } ,\overset { \rightarrow }{ r }$ be the vectors defined by the relations $\overset { \rightarrow }{ P } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ q } =\frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ r } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] }$ Then the value of  $\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r }$=

#### 12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is $\cfrac { 1 }{ 2 }$ cm

• 2)

The slope of the line normal to the curve f(x) = 2cos 4x at $x=\cfrac { \pi }{ 12 }$

• 3)

The number given by the Rolle's theorem for the functlon x3-3x2, x∈[0,3] is

• 4)

One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

• 5)

If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

#### 12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. Find the rate of change of the balloon's angle of elevation in radian per second when the balloon is 30 metres above the ground.

• 2)

The tangent to the curve y2 - xy + 9 = 0 is vertical when

• 3)

The minimum value ofthe function |3-x|+9 is

• 4)

The point of inflection of the curve y = (x - 1)3 is

• 5)

The point on the curve y=x2 is the tangent parallel to X-axis is

#### 12th Standard Maths Differentials and Partial Derivatives English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

• 2)

If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

• 3)

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

• 4)

If w (x, y, z) = x2 (y - z) + y2 (z - x) + z2(x - y), then $\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z }$ is

• 5)

If y = x4 - 10 and if x changes from 2 to 1.99, the approximate change in y is

#### 12th Standard Maths Applications of Integration English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of $\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx }$ is

• 2)

The value of $\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx }$ is

• 3)

The value of  $\int _{ 0 }^{ \pi }{ { sin }^{ 4 }xdx }$ is

• 4)

If $\int _{ 0 }^{ a }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx=\frac { \pi }{ 8 } }$ then a is

• 5)

#### 12th Standard Maths Applications of Integration English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The area between y2 = 4x and its latus rectum is

• 2)

The value of $\int _{ 0 }^{ \pi }{ \frac { dx }{ 1+{ 5 }^{ cos\ x } } }$ is

• 3)

The volume of solid of revolution of the region bounded by y2 = x(a − x) about x-axis is

• 4)

The value of $\int _{ -1 }^{ 2 }{ |x|dx }$

• 5)

The value of $\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }xcosxdx }$ is

#### 12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The order and degree of the differential equation $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +{ \left( \frac { dy }{ dx } \right) }^{ 1/3 }+{ x }^{ 1/4 }=0$are respectively

• 2)

The differential equation of the family of curves y = Aex + Be−x, where A and B are arbitrary constants is

• 3)

The solution of the differential equation 2x$\frac{dy}{dx}-y=3$represents

• 4)

The degree of the differential equation y $y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....$ is

• 5)

The solution of the differential equation $\frac { dy }{ dx } +\frac { 1 }{ \sqrt { 1-{ x }^{ 2 } } } =0$

#### 12th Standard Maths Ordinary Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

• 2)

The general solution of the differential equation $\frac { dy }{ dx } =\frac { y }{ x }$ is

• 3)

The solution of $\frac{dy}{dx}+$p(x)y=0 is

• 4)

If p and q are the order and degree of the differential equation $y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,$When

• 5)

If sin x is the integrating factor of the linear differential equation $\frac { dy }{ dx } +Py=Q,$ then P is

#### 12th Standard Maths Probability Distributions English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let X be random variable with probability density function
$f(x)=\left\{\begin{array}{ll} \frac{2}{x^{3}} & x \geq 1 \\ 0 & x<1 \end{array}\right.$
Which of the following statement is correct

• 2)

A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

• 3)

If the function  $f(x)=\cfrac { 1 }{ 12 }$ for a < x < b, represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?

• 4)

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with probability 0.5. Assume that the results of the flips are independent, and let X equal the total number of heads that result The value of E(X) is

• 5)

If P(X = 0) = 1 - P(X = I). If E(X) = 3 Var(X), then P(X = 0) is

#### 12th Standard Maths Probability Distributions Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is

The mean and variance of the shorter of the two pieces are respectively.

• 2)

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

• 3)

Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus.
Then E(X) and E(Y) respectively are

• 4)

On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

• 5)

If X is a binomial random variable with expected value 6 and variance 2.4, then P(X = 5) is

#### 12th Standard Maths Discrete Mathematics English Medium Free Online Test One Mark Questions 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A binary operation on a set S is a function from

• 2)

The operation * defined by a*b =$\frac{ab}{7}$ is not a binary operation on

• 3)

If a*b=$\sqrt { { a }^{ 2 }+{ b }^{ 2 } }$ on the real numbers then * is

• 4)

Which one is the inverse of the statement (PVq)➝(pΛq)?

• 5)

Which one of the following is incorrect? For any two propositions p and q, we have

#### 12th Standard Maths Discrete Mathematics Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Subtraction is not a binary operation in

• 2)

If a compound statement involves 3 simple statements, then the number of rows in the truth table is

• 3)

Which one is the contrapositive of the statement (pVq)⟶r?

• 4)

The proposition p ∧ (¬p ∨ q) is

• 5)

If * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is

#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If $4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi$ then x is

• 2)

The domain of cos-1(x2 - 4) is______

• 3)

The auxiliary circle of the ellipse $\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 }$ = 1 is

• 4)

The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

• 5)

The angle between the vector $3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k }$ and the z-axis is

#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Two - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right]$ and AB = I , then B =

• 2)

If $\rho$(A) = r then which of the following is correct?

• 3)

In the system of liner equations with 3 unknowns If $\rho$(A) = $\rho$([A|B]) =1, the system has ________

• 4)

The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

• 5)

If z = a + ib lies in quadrant then $\frac { \bar { z } }{ z }$ also lies in the III quadrant if

#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Three - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A is a 3 x 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 2)

If A, B and C are invertible matrices of some order, then which one of the following is not true?

• 3)

If A = $\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right]$ and AT = A−1 , then the value of x is

• 4)

If A = $\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right]$ be such that λA−1 =A, then λ is

• 5)

The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

#### 12th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Four - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The augmented matrix of a system of linear equations is $\left[\begin{array}{cccc} 1 & 2 & 7 & 3 \\ 0 & 1 & 4 & 6 \\ 0 & 0 & \lambda-7 & \mu+5 \end{array}\right]$. The system has infinitely many solutions if

• 2)

If |z1|=1, |z2| = 2|z3| = 3 and |9z1z+ 4z1z+ z2z3| = 12, then the value of |z1+z2+z3| is

• 3)

When the eccentricity of a ellipse becomes zero, then it becomes a

• 4)

The angle between the lines $\frac { x-2 }{ 3 } =\frac { y+1 }{ -2 }$, z=2 and $\frac { x-1 }{ 1 } =\frac { 2y+3 }{ 3 } =\frac { z+5 }{ 2 }$

• 5)

The number given by the Mean value theorem for the function $\cfrac { 1 }{ x }$,x∈[1,9] is

#### 12th Standard Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right]$ and AB = I , then B =

• 2)

If $\sqrt { a+ib }$ =x+iy, then possible value of $\sqrt { a-ib }$ is

• 3)

The complex number z which satisfies the condition $\left| \frac { 1+z }{ 1-z } \right|$ =1 lies on

• 4)

Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

• 5)

The value of tan $\left( { cos }^{ -1 }\cfrac { 3 }{ 5 } +{ tan }^{ -1 }\cfrac { 1 }{ 4 } \right)$ is ______

### TN Stateboard Education Study Materials

#### 12th Maths Chapter 3 Theory of Equations Theorem - by Satyadevi - Tiruchirappalli Sep 28, 2019 Sep 28, 2019

Theory of Equations Theorem

#### 12th Maths Chapter 1 Application Of Matrices And Determinants Theorem - by Satyadevi - Tiruchirappalli Sep 27, 2019 Sep 27, 2019

Application Of Matrices And Determinants Theorems

#### 12th Maths Two Dimensional Analytical Geometry-II Study Materials - by Satyadevi - Tiruchirappalli Sep 23, 2019 Sep 23, 2019

Two Dimensional Analytical Geometry-II

#### 12th Stateboard Maths 2019 - 2020 Academic Monthly Syllabus - by Satyadevi - Tiruchirappalli Aug 02, 2019 Aug 02, 2019

Maths 2019 - 2020 Academic Monthly Syllabus

#### Chapterwise classification - by MUTHU M Jul 28, 2019 Jul 28, 2019

2m,3m,5m classification

#### Question bank for the chapters 1 to 4 - by MUTHU M Jul 25, 2019 Jul 25, 2019

Question bank for the chapters 1 to 4

### TN Stateboard Updated Class 12th Maths Syllabus

#### Application of Matrices and Determinants

Introduction - Inverse of a Non-Singular Square Matrix - Elementary Transformations of a Matrix - Applications of Matrices: Solving System of Linear Equations - Applications of Matrices: Consistency of system of linear equations by rank method

#### Complex Numbers

Introduction to Complex Numbers - Complex Numbers - Basic Algebraic Properties of Complex Numbers - Conjugate of a Complex Number - Modulus of a Complex Number - Geometry and Locus of Complex Numbers - Polar and Euler form of a Complex Number - de Moivre’s Theorem and its Applications

#### Theory of Equations

Introduction - Basics of Polynomial Equations - Vieta’s Formulae and Formation of Polynomial Equations - Nature of Roots and Nature of Coefficients of Polynomial Equations - Applications to Geometrical Problems - Roots of Higher Degree Polynomial Equations - Polynomials with Additional Information - Polynomial Equations with no additional information - Descartes Rule

#### Inverse Trigonometric Functions

Introduction - Some Fundamental Concepts - Sine Function and Inverse Sine Function - The Cosine Function and Inverse Cosine Function - The Tangent Function and the Inverse Tangent Function - The Cosecant Function and the Inverse Cosecant Function - The Secant Function and Inverse Secant Function - The Cotangent Function and the Inverse Cotangent Function - Principal Value of Inverse Trigonometric Functions - Properties of Inverse Trigonometric Functions

#### Two Dimensional Analytical Geometry-II

Introduction - Circle - Conics - Conic Sections - Parametric form of Conics - Tangents and Normals to Conics - Real life Applications of Conics

#### Applications of Vector Algebra

Introduction - Geometric Introduction to Vectors - Scalar Product and Vector Product - Scalar triple product - Vector triple product - Jacobi’s Identity and Lagrange’s Identity - Different forms of Equation of a Straight line - Different forms of Equation of a plane - Image of a point in a plane - Meeting point of a line and a plane

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 12 Session 2019 - 2020

Latest Sample Question Papers & Study Material for class 12 session 2019 - 2020 for Subjects Chemistry, Physics, Biology, Computer Science, Business Maths, Economics, Commerce, Accountancy, History, Computer Applications, Computer Technology, English, உயிரியல், கணினி பயன்பாடுகள், கணினி அறிவியல், வணிகக் கணிதம், வணிகவியல், பொருளியல், கணிதவியல், வேதியியல், இயற்பியல், கணினி தொழில்நுட்பம், வரலாறு, கணக்குப்பதிவியல், தமிழ் in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

More than 1000+ TN Stateboard Syllabus Sample Question Papers & Study Material are based on actual Board question papers which help students to get an idea about the type of questions that will be asked in Class 12 Final Board Public examinations. All the Sample Papers are adhere to TN Stateboard guidelines and its marking scheme , Question Papers & Study Material are prepared and posted by our faculty experts , teachers , tuition teachers from various schools in Tamilnadu.

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