### 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 Maths - Discrete Mathematics Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A binary operation on a set S is a function from

• 2)

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

• 3)

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

• 4)

Which of the following is a tautology?

• 5)

The identity element in the group {R - {1},x} where a * b = a + b - ab is

#### 12th Maths - Probability Distributions Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
The expected amount to win at this game in Rs is

• 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 roUed 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)

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)

If P{X = 0} = 1- P{X = I}. IfE[X) = 3Var(X), then P{X = 0}.

• 5)

Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, P(X = I) = k P(X = i-I) i = 1, 2 and P(X = 0) =$\cfrac { 1 }{ 7 }$ then the value of k is

#### 12th Maths - Ordinary Differential Equations Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

The solution of (x2-ay)dx=(ax-y2)dy is

• 5)

The transformation y=vx reduces $\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x }$

#### 12th Maths - Applications of Integration Model Question Paper - 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 $\int _{ 0 }^{ \infty }{ { e }^{ -3x }{ x }^{ 2 }dx } \\$ is

• 3)

The value of $\int _{ 0 }^{ \frac { 2 }{ 3 } }{ \frac { dx }{ \sqrt { 4-9{ x }^{ 2 } } } }$ is

• 4)

If $\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ a }{ f(x) }$ then

• 5)

The ratio of the volumes generated by revolving the ellipse $\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 }$ = 1 about major and minor axes is

#### 12th Maths - Differentials and Partial Derivatives Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

If u = xy + yx then ux + uy at x = y = 1 is

#### 12th Maths - Application of Differential Calculus Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

• 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)

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

• 5)

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

#### 12th Maths - Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

If $\vec { a }$ 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 $\vec { a } ,\vec { b } ,\vec { c }$ 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

• 4)

The number of vectors of unit length perpendicular to the vectors $\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right)$ and $\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right)$is

• 5)

If $\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right)$, then

#### 12th Maths - Two Dimensional Analytical Geometry II Model Question Paper - 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 centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

• 3)

If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
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)

If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

#### 12th Maths - Inverse Trigonometric Functions Model Question Paper - 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 cot−1x=$\frac{2\pi}{5}$ for some x$\in$R, the value of tan-1 x is

• 3)

If the function f(x)sin-1(x2-3), then x belongs to

• 4)

The value of ${ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right)$ 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 Maths - Theory of Equations Model Question Paper - 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)

A polynomial equation in x of degree n always has

• 3)

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

• 4)

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

• 5)

If (2+√3)x2-2x+1+(2-√3)x2-2x-1=$\frac { 2 }{ 2-\sqrt { 3 } }$ then x=

#### 12th Maths - Complex Numbers Important Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

The principal argument of the complex number $\cfrac { \left( 1+i\sqrt { 3 } \right) ^{ 2 } }{ 4i\left( 1-i\sqrt { 3 } \right) }$ is

• 4)

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

• 5)

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

#### 12th Maths - Application of Matrices and Determinants Important Questions - 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)

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)

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

• 4)

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

• 5)

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

#### 12th Maths Half Yearly Model Question Paper 2019 - 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)

The principal argument of $\cfrac { 3 }{ -1+i }$

• 4)

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

• 5)

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

#### 12th Maths - Applications of Vector Algebra One Mark Questions with Answer - 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 a vector $\vec { \alpha }$ lies in the plane of $\vec { \beta }$ and $\vec { \gamma }$ , then

• 3)

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

• 4)

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

• 5)

If $[\vec { a } ,\vec { b } ,\vec { c } ]=1$$\frac { \vec { a } .(\vec { b } \times \vec { c } ) }{ (\vec { c } \times \vec { a } ).\vec { b } ) } +\frac { \vec { b } .(\vec { c } \times \vec { a } ) }{ (\vec { a } \times \vec { b } ).\vec { c } } +\frac { \vec { c } .(\vec { a } \times \vec { b } ) }{ (\vec { c } \times \vec { b } ).\vec { a } }$ is

#### 12th Maths - Two Dimensional Analytical Geometry II One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

• 2)

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

• 3)

If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

• 4)

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

• 5)

The length of the latus rectum of the ellipse $\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 }$ = 1 is

#### 12th Maths - Inverse Trigonometric Functions One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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 =

• 2)

If ${ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 }$ then

• 3)

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

• 4)

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

• 5)

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

#### 12th Maths - Theory of Equations One Mark Questions with Answer - 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)

A polynomial equation in x of degree n always has

• 4)

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

• 5)

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

#### 12th Maths - Complex Numbers One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of (1+i) (1+i2) (1+i3) (1+i4) is

• 2)

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

• 3)

If, i2 = -1, then i1 + i2 + i3 + ....+ up to 1000 terms is equal to

• 4)

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

• 5)

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

#### 12th Maths - Application of Matrices and Determinants One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ $\in$ R) is consistent with unique solution if

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### 12th Maths - Discrete Mathematics Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Write the statements in words corresponding to ¬p, p ∧ q , p ∨ q and q ∨ ¬p, where p is ‘It is cold’ and q is ‘It is raining.’

• 2)

How many rows are needed for following statement formulae?
p ∨ ¬ t ( p ∨ ¬s)

• 3)

How many rows are needed for following statement formulae?
(( p ∧ q) ∨ (¬r ∨¬s)) ∧ (¬ t ∧ v))

• 4)

Construct the truth table for $(p\overset { \_ \_ }{ \vee } q)\wedge (p\overset { \_ \_ }{ \vee } \neg q)$

• 5)

Verify
(i) closure property,
(ii) commutative property,
(iii) associative property,
(iv) existence of identity, and
(v) existence of inverse for the operation +5 on Z5 using table corresponding to addition modulo 5.

#### 12th Maths - Probability Distributions Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Two fair coins are tossed simultaneously (equivalent to a fair coin is tossed twice). Find the probability mass function for number of heads occurred.

• 2)

A pair of fair dice is rolled once. Find the probability mass function to get the number of fours.

• 3)

If the probability mass function f (x) of a random variable X isx

 x 1 2 3 4 f (x) $\cfrac { 1 }{ 12 }$ $\cfrac { 5 }{ 12 }$ $\cfrac { 5 }{ 12 }$ $\cfrac { 1 }{ 12 }$

find (i) its cumulative distribution function, hence find
(ii) P(X ≤ 3) and,
(iii) P(X ≥ 2)

• 4)

A six sided die is marked ‘1’ on one face, ‘2’ on two of its faces, and ‘3’ on remaining three faces. The die is rolled twice. If X denotes the total score in two throws.
(i) Find the probability mass function.
(ii) Find the cumulative distribution function.
(iii) Find P(3 ≤ X< 6) (iv) Find P(X ≥ 4) .

• 5)

Find the probability mass function f (x) of the discrete random variable X whose cumulative distribution function F(x) is given by

Also find (i) P(X < 0) and (ii)$P(X\ge -1$

#### 12th Maths - Ordinary Differential Equations Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Form the differential equation by eliminating the arbitrary constants A and B from y = Acos x + B sin x.

• 2)

Find the differential equation of the family of circles passing through the points (a,0) and (−a,0).

• 3)

Find the differential equation of the family of all ellipses having foci on the x -axis and centre at the origin.

• 4)

Find the particular solution of (1+ x3 )dy − x2 ydx = satisfying the condition y(1) = 2.

• 5)

Solve y ' = sin2 (x − y + )1.

#### 12th Maths - Applications of Integration Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Evaluate$\int _{ 0 }^{ 1 }{ x^3dx }$, as the limit of a sum.

• 2)

Evaluate$\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }-3) }$ dx, as the limit of a sum

• 3)

Evaluate $\int _{ 0 }^{ x }{ { x }^{ 2 } }$cos nxdx, where n is a positive integer.

• 4)

Evaluate: $\\ \\ \int _{ -1 }^{ 1 }{ { e }^{ -\lambda x }(1-{ x }^{ 2 }) } dx$

• 5)

Evaluate $\int ^\frac {\pi}{2}_{0}$( sin2 x + cos4 x ) dx

#### 12th Maths - Application of Differential Calculus Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

For what value of x the tangent of the curve y = x3 − x2 + x − 2 is parallel to the line y = x.

• 2)

Find the equation of the tangent and normal to the Lissajous curve given by x = 2cos3t and y = 3sin 2t, t ∈ R

• 3)

Expand log(1+ x) as a Maclaurin’s series upto 4 non-zero terms for –1 < x ≤ 1.

• 4)

Expand tan x in ascending powers of x upto 5th power for $(-\frac{\pi}{2} <x<\frac{\pi}{2} )$

• 5)

Find the intervals of monotonicity and hence find the local extrema for the function f (x) = x2 − 4x + 4

#### 12th Maths - Differentials and Partial Derivatives Five Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let f , g : (a,b)→R be differentiable functions. Show that d(fg) = fdg + gdf

• 2)

Let g(x) = x2 + sin x. Calculate the differential dg.

• 3)

If the radius of a sphere, with radius 10 cm, has to decrease by 0 1. cm, approximately how much will its volume decrease?

• 4)

Let f (x, y) = 0 if xy ≠ 0 and f (x, y) =1 if xy = 0.
(i) Calculate: $\frac { \partial f }{ \partial x } (0,0),\frac { \partial f }{ \partial y } (0,0).$
(ii) Show that f is not continuous at (0,0)

• 5)

Let F(x, y) = x3 y + y2x + 7 for all (x, y)∈ R2. Calculate $\frac { \partial F }{ \partial x }$(-1,3) and $\frac { \partial F }{ \partial y }$(-2,1).

#### 12th Maths - Discrete Mathematics Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Verify the
(i) closure property,
(ii) commutative property,
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the arithmetic operation - on Z.

• 2)

Verify the
(i) closure property,
(ii) commutative property,
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the arithmetic operation + on
Ze = the set of all even integers

• 3)

Verify the
(i) closure property,
(ii) commutative property,
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the arithmetic operation + on
Zo = the set of all even integers

• 4)

Verify
(i) closure property
(ii) commutative property, and
(iii) associative property of the following operation on the given set.
(a*b) = ab;∀a,b∈N (exponentiation property)

• 5)

Determine whether ∗ is a binary operation on the sets given below.
a*b=b=a.|b| on R

#### 12th Maths - Probability Distributions Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Suppose two coins are tossed once. If X denotes the number of tails,
(i) write down the sample space
(ii) find the inverse image of 1
(iii) the values of the random variable and number of elements in its inverse images

• 2)

Suppose a pair of unbiased dice is rolled once. If X denotes the total score of two dice, write down
(i) the sample space
(ii) the values taken by the random variable X,
(iii) the inverse image of 10, and
(iv) the number of elements in inverse image of X.

• 3)

An urn contains 2 white balls and 3 red balls. A sample of 3 balls are chosen at random from the urn. If X denotes the number of red balls chosen, find the values taken by the random variable X and its number of inverse images

• 4)

Two balls are chosen randomly from an urn containing 6 white and 4 black balls. Suppose that we win Rs.30 for each black ball selected and we lose Rs.20 for each white ball selected. If X denotes the winning amount, then find the values of X and number of points in its inverse images.

• 5)

Find the constant C such that the function $f(x)=\begin{cases} \begin{matrix} { Cx }^{ 2 } & 1 is a density function, and compute (i) P(1.5 < X < 3.5) (ii) P(X ≤2) (iii) P(3 < X ) . #### 12th Maths - Ordinary Differential Equations Three Marks Questions Paper - by Satyadevi - Tiruchirappalli - View & Read • 1) Determine the order and degree (if exists) of the following differential equations: \(\frac { dy }{ dx } =x+y+5$

• 2)

Determine the order and degree (if exists) of the following differential equations:
${ \left( \frac { { d }^{ 4 }y }{ { dx }^{ 4 } } \right) }^{ 3 }+4{ \left( \frac { dy }{ dx } \right) }^{ 7 }+6y=5cos3x$

• 3)

Determine the order and degree (if exists) of the following differential equations:
$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +3{ \left( \frac { dy }{ dx } \right) }^{ 2 }={ x }^{ 2 }log\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right)$

• 4)

Determine the order and degree (if exists) of the following differential equations:
$3\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ={ \left[ 4+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 3 }{ 2 } }$

• 5)

Determine the order and degree (if exists) of the following differential equations:
dy + (xy − cos x)dx = 0

#### 12th Maths - Applications of Integration Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Estimate the value of $\int _{ 0 }^{ 0.5 }{ { x }^{ 2 } } dx$using the Riemann sums corresponding to 5 subintervals of equal width and applying (i) left-end rule (ii) right-end rule (iii) the mid-point rule.

• 2)

Evaluate: $\int _{ 0 }^{ 3 }{ (3{ x }^{ 2 }-4x+5) } dx$

• 3)

Evaluate :$\int _{ 0 }^{ 1 }{ \frac { 2x+7 }{ { 5x }^{ 2 }+9 } } dx$

• 4)

Evaluate :$\int _{ 0 }^{ 9 }{ \frac { 1 }{ x+\sqrt { x } } dx }$

• 5)

Show that $\int ^\frac{\pi}{2}_0$ $\frac {dx}{4+5 sin x}$ = $\frac {1}{3}$ log2

#### 12th Maths - Differentials and Partial Derivatives Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the linear approximation for f(x) = $\sqrt { 1+x } ,x\ge -1$ at x0 = 3. Use the linear approximation to estimate f(3.2)

• 2)

Use linear approximation to find an approximate value of $\sqrt { 9.2 }$ without using a calculator.

• 3)

Let us assume that the shape of a soap bubble is a sphere. Use linear approximation to approximate the increase in the surface area of a soap bubble as its radius increases from 5 cm to 5.2 cm. Also, calculate the percentage error.

• 4)

A right circular cylinder has radius r =10 cm. and height h = 20 cm. Suppose that the radius of the cylinder is increased from 10 cm to 10. 1 cm and the height does not change. Estimate the change in the volume of the cylinder. Also, calculate the relative error and percentage error.

• 5)

Let f (x,y) = $\frac { 3x-5y+8 }{ { x }^{ 2 }+{ y }^{ 2 }+1 }$ for all (x, y) ∈RShow that f is continuous on R2

#### 12th Maths - Application of Differential Calculus Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

For the function f(x) = x2 ∈ [0, 2] compute the average rate of changes in the subintervals [0,0.5], [0.5,1], [1,1.5], [1.5,2] and the instantaneous rate of changes at the points x = 0.5,1,1.5, 2

• 2)

The temperature in celsius in a long rod of length 10 m, insulated at both ends, is a function of
length x given by T = x(10 − x). Prove that the rate of change of temperature at the midpoint of the
rod is zero.

• 3)

A particle moves along a horizontal line such that its position at any time t ≥ 0 is given by s(t) = t3 − t2 + t + 6 9 1, where s is measured in metres and t in seconds?
(1) At what time the particle is at rest?
(2) At what time the particle changes direction?
(3) Find the total distance travelled by the particle in the first 2 seconds.

• 4)

The price of a product is related to the number of units available (supply) by the equation Px + 3P −16x = 234, where P is the price of the product per unit in Rupees(Rs) and x is the number of units. Find the rate at which the price is changing with respect to time when 90 units are available and the supply is increasing at a rate of 15 units/week.

• 5)

Compute the value of 'c' satisfied by the Rolle’s theorem for the function f (x) = x2 (1 - x)2, x ∈ [0.1]

#### 12th Maths - Discrete Mathematics Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
a*b = a + 3ab − 5b2;∀a,b∈Z

• 2)

Examine the binary operation (closure property) of the following operations on the respective sets (if it is not, make it binary)
$a*b=\left( \frac { a-1 }{ b-1 } \right) ,\forall a,b\in Q$

• 3)

Verify the
(i) closure property,
(ii) commutative property,
(iii) associative property
(iv) existence of identity and
(v) existence of inverse for the arithmetic operation + on Z.

• 4)

Let A =$\begin{bmatrix} 0 & 1 \\ 1 & 1 \end{bmatrix},B=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$be any two boolean matrices of the same type. Find AvB and A^B.

• 5)

Let p: Jupiter is a planet and q: India is an island be any two simple statements. Give
verbal sentence describing each of the following statements.
(i) ¬p
(ii) p ∧ ¬q
(iii) ¬p ∨ q
(iv) p➝ ¬q
(v) p↔q

#### 12th Maths - Probability Distributions Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values ofthe random variable X and number of points in its inverse images.

• 2)

Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred

• 3)

A six sided die is marked '1' on one face, '3' on two of its faces, and '5' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find
(i) the probability mass function
(ii) the cumulative distribution function
(iii) P(4 ≤ X < 10)
(iv) P(X ≥ 6)

• 4)

Find the probability mass function and cumulative distribution function of number of girl child in families with 4 children, assuming equal probabilities for boys and girls.

• 5)

The probability density function of X is given by $f(x)=\begin{cases} \begin{matrix} kxe^{ -2x } & forx>0 \end{matrix} \\ \begin{matrix} 0 & for\quad x\le 0 \end{matrix} \end{cases}$ Find the value opf .

#### 12th Maths - Ordinary Differential Equations Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

For each of the following differential equations, determine its order, degree (if exists)
${ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0$

• 2)

For each of the following differential equations, determine its order, degree (if exists)
$\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +\int { ydx } ={ x }^{ 3 }$

• 3)

Find the differential equation of the family of all nonhorizontal lines in a plane.

• 4)

Form the differential equation of all straight lines touching the circle x2 + y2 = r2.

• 5)

Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin.

#### 12th Maths - Applications of Integration Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Evaluate the following integrals as the limits of sums.
$\int _{ 0 }^{ 1 }{ (5x+4)dx }$

• 2)

Evaluate the following integrals as the limits of sums.
$\int _{ 1 }^{ 2 }{ 4x^2-1)dx }$

• 3)

Evaluate the following definite integrals:
$\int _{ 3 }^{ 4 }{ \frac { dx }{ { x }^{ 2 }-4 } }$

• 4)

Evaluate the following definite integrals:
$\int _{ -1 }^{ 1 }{ \frac { dx }{ { x }^{ 2 }+2x+5 } }$

• 5)

Evaluate the following integrals using properties of integration:
$\int _{ 0 }^{ 2\pi }{ xlog\left( \frac { 3+cos\quad x }{ 3-cos\quad x } \right) } dx$

#### 12th Maths - Differentials and Partial Derivatives Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find a linear approximation for the following functions at the indicated points.
g(x) = $g(x)=\sqrt { { x }^{ 2 }+9 } ,{ x }_{ 0 }=-4$

• 2)

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm.find the following in calculating the area of the circular plate:
Absolute error

• 3)

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm.find the following in calculating the area of the circular plate:
Relative error

• 4)

Find differential dy for each of the following function
$y=\frac { { \left( 1-2x \right) }^{ 3 } }{ 3-4x }$

• 5)

Find differential dy for each of the following function
y = (3 + sin(2x)) 2/3

#### 12th Maths - Application of Differential Calculus Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A particle moves along a line according to the law s(t) = 2t3 − 9t2 +12t − 4, where t ≥ 0.
Find the total distance travelled by the particle in the first 4 seconds.

• 2)

A particle moves along a line according to the law s(t) = 2t3 − 9t2 +12t − 4, where t ≥ 0.
Find the particle’s acceleration each time the velocity is zero.

• 3)

A police jeep, approaching an orthogonal intersection from the northern direction, is chasing a speeding car that has turned and moving straight east. When the jeep is 0.6 km north of the intersection and the car is 0.8 km to the east. The police determine with a radar that the distance between them and the car is increasing at 20 km/hr. If the jeep is moving at 60 km/hr at the instant of measurement, what is the speed of the car?

• 4)

Find the slope of the tangent to the curves at the respective given points.
y = x4 + 2x2 − x at x =1

• 5)

Find the equations of the tangents to the curve y =1+ x3 for which the tangent is orthogonal with the line x +12y =12

#### 12th Maths - Discrete Mathematics One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A binary operation on a set S is a function from

• 2)

Subtraction is not a binary operation in

• 3)

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

• 4)

In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?

• 5)

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

#### 12th Maths - Probability Distributions One Mark Questions with Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let X be random variable with probability density function
$f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x\ge l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}$
Which of the following statement is correct

• 2)

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
$f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x>l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}$

• 3)

Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
The expected amount to win at this game in Rs is

• 4)

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 roUed 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

• 5)

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

#### 12th Maths - Ordinary Differential Equations One Mark Questions with Answer - 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 representing the family of curves y = Acos(x + B), where A and B are parameters, is

• 3)

The order and degree of the differential equation $\sqrt { sin\quad x } (dx+dy)=\sqrt { cos\quad x } (dx-dy)$

• 4)

The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

• 5)

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

#### 12th Maths - Applications of Integration One Mark Questions with Answer - 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 $\int _{ -\frac { \pi }{ 4 } }^{ \frac { \pi }{ 4 } }{ \left( \frac { { 2x }^{ 7 }-{ 3x }^{ 5 }+{ 7x }^{ 3 }-x+1 }{ { cos }^{ 2 }x } \right) dx }$ is

• 3)

If $f(x)=\int _{ 0 }^{ x }{ t\ cos\ t\ dt,\ then\ \frac { dx }{ dx } }$

• 4)

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

• 5)

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

#### 12th Maths - Differentials and Partial Derivatives One Mark Questions with Answer - 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)

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

• 3)

If u (x, y) = ex2+y2, then $\frac { \partial u }{ \partial x }$ is equal to

• 4)

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

• 5)

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

#### 12th Maths - Application of Differential Calculus One Mark Questions with Answer - 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)

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.

• 3)

The position of a particle moving along a horizontal line of any time t is given by set) = 3t2 -2t- 8. The time at which the particle is at rest is

• 4)

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

• 5)

Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

#### 12th Standard Maths - Discrete Mathematics Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A binary operation on a set S is a function from

• 2)

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

• 3)

Which one of the following statements has truth value F?

• 4)

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

• 5)

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

#### 12th Standard Maths - Probability Distributions Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Let X be random variable with probability density function
$f(x)=\begin{cases} \begin{matrix} \frac { 2 }{ { x }^{ 3 } } & 0<x\ge l \end{matrix} \\ \begin{matrix} 0 & 1\le x<2l \end{matrix} \end{cases}$
Which of the following statement is correct

• 2)

Consider a game where the player tosses a sixsided fair die. H the face that comes up is 6, the player wins Rs.36, otherwise he loses Rs. k2 , where k is the face that comes up k = {I, 2,3,4, 5}.
The expected amount to win at this game in Rs is

• 3)

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 roUed 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

• 4)

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

• 5)

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

#### 12th Standard Maths - Ordinary Differential Equations Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

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

• 5)

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

#### 12th Standard Maths - Applications of Integration Model Question Paper - 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 $\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx }$

• 3)

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

• 4)

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

• 5)

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

#### 12th Standard Maths - Differentials and Partial Derivatives Model Question Paper - 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 f (x, y) = exy then $\frac { { \partial }^{ 2 }f }{ \partial x\partial y }$ is equal to

• 3)

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

• 4)

If g(x, y) = 3x2 - 5y + 2y, x(t) = et and y(t) = cos t, then $\frac{dg}{dt}$ is equal to

• 5)

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

#### 12th Standard Maths - Application of Differential Calculus Model Question Paper - 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)

Find the point on the curve 6y = .x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

• 3)

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 ?

• 4)

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

• 5)

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

#### 12th Maths - Term II Model Question Paper - by Meera - Namakkal - View & Read

• 1)

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

• 2)

The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

• 3)

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

• 4)

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

• 5)

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

#### 12th Standard Maths - Applications of Vector Algebra Model Question Paper - by Meera - Namakkal - View & Read

• 1)

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

• 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 } =\hat { i } +\hat { j } +\hat { k }$$\vec { b } =\hat { i } +\hat { j }$$\vec { c } =\hat { i }$ and $(\vec { a } \times \vec { b } )\times\vec { c }$ = $\lambda \vec { a } +\mu \vec { b }$ then the value of $\lambda +\mu$ is

• 4)

Consider the vectors $\vec { a } ,\vec { b } ,\vec { c } ,\vec { c }$ 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 $\vec { a } =2\hat { i } +3\hat { j } -\hat { k } ,\vec { b } =\hat { i } +2\hat { j } +5\hat { k } ,\vec { c } =3\hat { i } +5\hat { j } -\hat { k }$ then a vector perpendicular to $\vec { a }$ and lies in the plane containing $\vec { b }$ and $\vec { c }$ is

#### 12th Standard Maths - Two Dimensional Analytical Geometry-II Model Question Paper - by Meera - Namakkal - 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)

The radius of the circle passing through the point(6,2) two of whose diameter arex+y=6
and x+2y=4 is

• 5)

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

#### 12th Standard Maths - Inverse Trigonometric Functions Model Question Paper - by Meera - Namakkal - View & Read

• 1)

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

• 2)

sin−1(cos x)$=\frac{\pi}{2}-x$ is valid for

• 3)

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

sin(tan-1x), |x|<1 ia equal to

#### 12th Standard Maths - Theory of Equations Model Question Paper - by Meera - Namakkal - View & Read

• 1)

A zero of x3 + 64 is

• 2)

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

• 3)

The number of positive zeros of the polynomial $\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }$(-1)rxr is

• 4)

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

• 5)

If x2 - hx - 21 = 0 and x2 - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

#### 12th Maths - Applications of Vector Algebra Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Dot product of a vector with vector $\overset { \wedge }{ 3i } -5\overset { \wedge }{ k }$$2\overset { \wedge }{ i } +7\overset { \wedge }{ j }$ and $\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k }$ are respectively -1, 6 and 5. Find the vector.

• 2)

Find the Cartesian form of the equation of the plane $\overset { \rightarrow }{ r } =\left( s-2t \right) \overset { \wedge }{ i } +\left( 3-t \right) \overset { \wedge }{ j } +\left( 2s+t \right) \overset { \wedge }{ k }$

• 3)

Find the equation of the plane through the intersection of the planes lx-3y+ z-4 -0 and x - y + Z + 1 - 0 and perpendicular to the plane x + 2y - 3z + 6 = 0

• 4)

Find the angle between the line $\frac { x-2 }{ 3 } =\frac { y-1 }{ -1 } =\frac { z-3 }{ 2 }$ and the plane 3x + 4y + z + 5 = 0

• 5)

If $\overset { \rightarrow }{ a } =\overset { \wedge }{ i } -\overset { \wedge }{ j } ,\overset { \rightarrow }{ b } =\overset { \wedge }{ j } -\overset { \wedge }{ k } ,\overset { \rightarrow }{ c } =\overset { \wedge }{ k } -\overset { \wedge }{ i }$ then find $\left[ \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ b } -\overset { \rightarrow }{ c } ,\overset { \rightarrow }{ c } -\overset { \rightarrow }{ a } \right]$

#### 12th Maths - Two Dimensional Analytical Geometry-II Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the circumference and area of the circle x2 +y2 - 2x + 5y + 7 = 0

• 2)

Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x2 +y2 - 64 = 0.

• 3)

Find the condition for the line lx + my + n = 0 is Rtangent to the circle x2 + y2 = a2

• 4)

Find the area of th triangle found by the Unel Joining the vertex of the parabola x2 = -36y to the ends of the latus rectum.

• 5)

Find the equatlon of the ellipse whose e = $\frac34$, foci ony-axl ,centre at origin and passing through (6,4).

#### 12th Maths - Inverse Trigonometric Functions Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Prove that ${ cos }^{ -1 }\left( \cfrac { 4 }{ 5 } \right) +{ tan }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) ={ tan }^{ -1 }\left( \cfrac { 27 }{ 11 } \right)$

• 2)

Evaluate $cos\left[ { sin }^{ -1 }\cfrac { 3 }{ 5 } +{ sin }^{ -1 }\cfrac { 5 }{ 13 } \right]$

• 3)

Prove that ${ tan }^{ -1 }\left( \cfrac { m }{ n } \right) -{ tan }^{ -1 }\left( \cfrac { m-n }{ m+n } \right) =\cfrac { \pi }{ 4 }$

• 4)

Solve: ${ tan }^{ -1 }\left( \cfrac { x-1 }{ x-2 } \right) +{ tan }^{ -1 }\left( \cfrac { x+1 }{ x+2 } \right) =\cfrac { \pi }{ 4 }$

• 5)

Solve ${ tan }^{ -1 }\left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) +{ cot }^{ -1 }\left( \cfrac { 1-{ x }^{ 2 } }{ 2x } \right) =\cfrac { \pi }{ 3 } ,x>0$

#### 12th Maths - Theory of Equations Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If α, β, and γ are the roots of the polynomial equation ax3+bx2+cx+d=0 , find the value of $\Sigma \frac { \alpha }{ \beta \gamma }$ in terms of the coefficients.

• 2)

If p and q are the roots of the equation lx2+nx+n = 0, show that $\sqrt { \frac { p }{ q } } +\sqrt { \frac { q }{ p } } +\sqrt { \frac { n }{ l } }$=0.

• 3)

If the equations x2+px+q= 0 and x2+p'x+q'= 0 have a common root, show that it must  be equal to $\frac { pq'-p'q }{ q-q' }$ or $\frac { q-q' }{ p'-p }$.

• 4)

Solve the equation 9x-36x2+44x-16=0 if the roots form an arithmetic progression.

• 5)

Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

#### 12th Maths - Complex Numbers Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Explain the falacy:

• 2)

Find the circle roots of -27.

• 3)

Find the principal value of -2i.

• 4)

Show that $\left| \frac { z-3 }{ z+3 } \right|$ = 2 represent a circle.

• 5)

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

#### 12th Maths - Application of Matrices and Determinants Three Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\frac { 1 }{ 9 } \left[ \begin{matrix} -8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & -8 & 4 \end{matrix} \right]$, prove that A−1 = AT.

• 2)

If A = $\left[ \begin{matrix} 8 & -4 \\ -5 & 3 \end{matrix} \right]$, verify that A(adj A) = |A|I2.

• 3)

If A = $\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right]$ and B = $\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right]$, verify that (AB)-1 = B-1A-1

• 4)

Decrypt the received encoded message $\left[ \begin{matrix} 2 & -3 \end{matrix} \right] \left[ \begin{matrix} 20 & 4 \end{matrix} \right]$ with the encryption matrix $\left[ \begin{matrix} -1 & -1 \\ 2 & 1 \end{matrix} \right]$
and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 - 26 to the letters A - Z respectively, and the number 0 to a blank space.

• 5)

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

#### 12th Standard Maths - Complex Numbers Model Question Paper - by Meera - Namakkal - View & Read

• 1)

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

• 2)

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

• 3)

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

If $\omega =cis\cfrac { 2\pi }{ 3 }$, then the number of distinct roots of $\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right|$

#### 12th Maths- Application of Matrices and Determinants Model Question Paper - by Meera - Namakkal - View & Read

• 1)

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

• 2)

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)| =

• 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 ρ(A) = ρ([A | B]), then the system AX = B of linear equations is

• 5)

If A = $\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right]$, then adj(adj A) is

#### 12th Maths - Term 1 Model Question Paper - by Meera - Namakkal - 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)

The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

• 4)

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

• 5)

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

#### 12th Maths - Term 1 Five Mark Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right]$, show that A2 - 3A - 7I2 = O2. Hence find A−1.

• 2)

If ax2 + bx + c is divided by x + 3, x − 5, and x − 1, the remainders are 21,61 and 9 respectively. Find a,b and c. (Use Gaussian elimination method.)

• 3)

Solve the system: x + y − 2z = 0, 2x − 3y + z = 0, 3x − 7y + 10z = 0, 6x − 9y + 10z = 0.

• 4)

Solve the following systems of linear equations by Cramer’s rule:
3x + 3y − z = 11, 2x − y + 2z = 9, 4x + 3y + 2z = 25.

• 5)

Solve the equation z3+27=0 .

#### 12th Maths - Applications of Vector Algebra Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the parametric form of vector equation and Cartesian equations of the straight line passing through the point (−2,3, 4) and parallel to the straight line $\frac { x-1 }{ -4 } =\frac { y-3 }{ 5 } =\frac { z-8 }{ 6 }$

• 2)

Find the vector and Cartesian equations of the plane passing through the point with position vector $4\hat { i } +2\hat { j } -3\hat { k }$ and normal to vector $2\hat { i } -\hat { j } +\hat { k }$

• 3)

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant. Show that the plane passes through a fixed point

• 4)

Find the vector and Cartesian equations of the plane passing through the point with position vector $2\hat { i } +6\hat { j } +3\hat { k }$ and normal to the vector $\hat { i } +3\hat { j } +5\hat { k }$

• 5)

A plane passes through the point (−1,1, 2) and the normal to the plane of magnitude $3\sqrt { 3 }$ makes equal acute angles with the coordinate axes. Find the equation of the plane.

#### 12th Maths - Two Dimensional Analytical Geometry II Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

Find the general equation of a circle with centre(-3,-4) and radius 3 units.

• 2)

Find the general equation of the circle whose diameter is the line segment joining the points (−4,−2)and (1,1).

• 3)

Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

• 4)

Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

• 5)

Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

#### 12th Maths - Inverse Trigonometric Functions Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

State the reason for cos-1$[cos(-\frac{\pi}{6})]\neq \frac{\pi}{6}.$

• 2)

Is cos-1(-x)=$\pi$-cos−1(x) true? Justify your answer.

• 3)

Find the principal value of cos-1$(\frac{1}{2})$.

• 4)

Find the value of sec−1$\left( -\frac { 2\sqrt { 3 } }{ 3 } \right)$

• 5)

If cot-1$\frac{1}{7}=\theta$, find the value of cos$\theta$.

#### 12th Maths - Theory of Equations Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

• 2)

Find the monic polynomial equation of minimum degree with real coefficients having 2-$\sqrt{3}$i as a root.

• 3)

Find a polynomial equation of minimum degree with rational coefficients, having 2+$\sqrt{3}$i as a root.

• 4)

Find a polynomial equation of minimum degree with rational coefficients, having 2i+3 as a root.

• 5)

Show that the polynomial 9x9+2x5-x4-7x2+2 has at least six imaginary roots.

#### 12th Maths - Complex Numbers Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If z=x+iy, find the following in rectangular form.
$Re\left( \cfrac { 1 }{ z } \right)$

• 2)

Represent the complex number −1−i

• 3)

Write the following in the rectangular form:
$\cfrac { 10-5i }{ 6+2i }$

• 4)

Find the square roots of −6+8i

• 5)

Obtain the Cartesian form of the locus of z=x+iy in
$\overline { z } =2^{ -1 }$

#### 12th Maths Unit 1 Application of Matrices and Determinants Two Marks Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right]$ is non-singular, find A−1.

• 2)

If adj A = $\left[ \begin{matrix} -1 & 2 & 2 \\ 1 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right]$, find A−1.

• 3)

Find the rank of the following matrices which are in row-echelon form :
$\left[ \begin{matrix} 2 & 0 & -7 \\ 0 & 3 & 1 \\ 0 & 0 & 1 \end{matrix} \right]$

• 4)

Find the rank of the following matrices by minor method:
$\left[ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 8 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 2 \\ 1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ 0 \end{matrix} \end{matrix}\begin{matrix} 1 \\ \begin{matrix} 3 \\ 2 \end{matrix} \end{matrix} \right]$

• 5)

Find the rank of the following matrices which are in row-echelon form :
$\left[ \begin{matrix} 6 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} 0 \\ \begin{matrix} 2 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix}\begin{matrix} -9 \\ \begin{matrix} 0 \\ \begin{matrix} 0 \\ 0 \end{matrix} \end{matrix} \end{matrix} \right]$

#### 12th Maths Quarterly Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

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

• 5)

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

#### unit test - by Maths TAMILMedium - New syllabus 2019 - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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)| =

• 5)

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

#### 12th Standard Maths Unit 6 Applications of Vector Algebra Book Back Questions - 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 $\vec { a } ,\vec { b } ,\vec { c }$ 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

• 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 $\vec { a } ,\vec { b }$ $\neq$ 0 and  $\vec { a } .\vec { b }$ $\neq$ 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 Maths - Two Dimensional Analytical Geometry-II Book Back Questions - 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)

If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
is

• 4)

The ellipse E1$\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1$ is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

• 5)

Tangents are drawn to the hyperbola  $\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1$ 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

#### 12th Standard Maths - Theory of Equations Book Back Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If α,β and γ are the roots of x3+px2+qx+r, then $\Sigma \frac { 1 }{ \alpha }$ 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 x3+2x+3 has

• 5)

The number of positive zeros of the polynomial $\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }$(-1)rxr is

#### 12th Standard Maths - Inverse Trigonometric Functions Book Back Questions - 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)

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

• 4)

${ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right)$is equal to

• 5)

If the function f(x)sin-1(x2-3), then x belongs to

#### 12th Standard Maths Unit 2 Complex Numbers Book Back Questions - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

If |z1|=1,|z2|=2|z3|=3 and |9z1z2+4z1z3+z2z3|=12, then the value of |z1+z2+z3| is

• 5)

The principal argument of $\cfrac { 3 }{ -1+i }$

#### 12th Standard Maths Unit 1 Application of Matrices and Determinants Book Back 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 is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 3)

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

• 4)

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

• 5)

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)| =

#### 12th Standard Maths Unit 3 Theory of Equations One Mark Question and Answer - 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)

A polynomial equation in x of degree n always has

• 4)

If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

• 5)

The quadratic equation whose roots are ∝ and β is

#### 12th Standard Maths Unit 2 Complex Numbers One Mark Question and Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

in+in+1+in+2+in+3 is

• 2)

The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

• 3)

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

• 4)

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

• 5)

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

#### 12th Standard Maths - Application of Matrices and Determinants One Mark Question and Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### 12th Standard Physics Unit 6 Applications of Vector Algebra One Mark Question and Answer - 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 $\vec { a } =\hat { i } +\hat { j } +\hat { k }$$\vec { b } =\hat { i } +\hat { j }$$\vec { c } =\hat { i }$ and $(\vec { a } \times \vec { b } )\times\vec { c }$ = $\lambda \vec { a } +\mu \vec { b }$ then the value of $\lambda +\mu$ is

• 4)

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

• 5)

The number of vectors of unit length perpendicular to the vectors $\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right)$ and $\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right)$is

#### 12th Physics Chapter 5 Two Dimensional Analytical Geometry-II One Mark Question and Answer - 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 centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

• 4)

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

• 5)

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

#### 12th Standard Physics Chapter 4 Inverse Trigonometric Functions One Mark Question and Answer - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

${ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 }$is equal to

• 3)

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

• 4)

If ${ sin }^{ -1 }x-cos^{ -1 }x=\cfrac { \pi }{ 6 }$ then

• 5)

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

#### 12th Physics Unit 2 Theory of Equations One Mark Question with Answer Key - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If α,β and γ are the roots of x3+px2+qx+r, then $\Sigma \frac { 1 }{ \alpha }$ 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 $\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }$(-1)rxr is

• 5)

If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

#### 12th Maths Chapter 2 Complex Numbers One Mark Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### Unit test 12th Standard Maths New syllabus - by Maths TAMILMedium - New syllabus 2019 - View & Read

• 1)

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

• 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)

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

• 4)

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 =

• 5)

If ATA−1 is symmetric, then A2 =

#### 12th Maths Chapter 1 Application of Matrices and Determinants 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 is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

• 3)

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)| =

• 4)

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

• 5)

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

#### 12th Maths Quarterly Exam Model Two Marks Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If A = $\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right]$ is non-singular, find A−1.

• 2)

Reduce the matrix $\left[ \begin{matrix} 3 & -1 & 2 \\ -6 & 2 & 4 \\ -3 & 1 & 2 \end{matrix} \right]$ to a row-echelon form.

• 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)

Simplify $\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }$

• 5)

Represent the complex number −1−i

#### 12th Maths Unit 6 Applications of Vector Algebra Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

If $\vec { a }$ 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 $\vec { a } ,\vec { b } ,\vec { c }$ 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

• 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)

Distance from the origin to the plane 3x - 6y + 2z 7 = 0 is

#### 12th Standard Maths Quarterly Exam Model One Mark Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### Plus 2 Maths Chapter 5 Two Dimensional Analytical Geometry - II Model Questions - 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 centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

• 3)

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

• 4)

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

• 5)

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

#### 12th Standard Maths First Mid Term Model Question Paper - 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)

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

• 3)

The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ $\in$ R) is consistent with unique solution if

• 4)

The value of (1+i)4 + (1-i)4 is

• 5)

The value of $\frac { (cos{ 45 }^{ 0 }+isin{ 45 }^{ 0 })^{ 2 }(cos{ 30 }^{ 0 }-isin{ 30 }^{ 0 }) }{ cos{ 30 }^{ 0 }+isin{ 30 }^{ 0 } }$ is

#### 11th Standard Mathematics Chapter 4 Inverse Trigonometric Functions Important Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 3)

${ sin }^{ -1 }\frac { 3 }{ 5 } -{ cos }^{ -1 }\frac { 12 }{ 13 } +{ sec }^{ -1 }\frac { 5 }{ 3 } { -cosec }^{ 1- }\frac { 13 }{ 2 }$is equal to

• 4)

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

• 5)

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

#### 12th Standard Maths Chapter 3 Theory of Equations Important Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

A zero of x3 + 64 is

• 2)

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

• 3)

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

• 4)

The polynomial x3+2x+3 has

• 5)

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

#### 12th Maths Unit 2 Important Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

• 2)

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

• 3)

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

• 4)

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

• 5)

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

Hello Students, if you like our sample question papers & study materials , please share these with your friends and classmates.