### 12th Standard EM 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 - Two Marks Study Materials - by 8682895000 - 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)

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

• 4)

Determine whether ∗ is a binary operation on the sets given below.
(A*v)=a√b is binary on R

• 5)

Let A={a+$\sqrt5$b:a,b∈Z}. Check whether the usual multiplication is a binary operation on A.

#### 12th Maths - Probability Distributions - Two Marks Study Materials - by 8682895000 - 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)

An urn contains 5 mangoes and 4 apples Three fruits are taken at randaom If the number of apples taken is a random variable, then find the values of the random variable and number of points in its inverse images.

• 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)

The cumulative distribution function of a discrete random variable is given by

Find
(i) the probability mass function
(ii) P(X < 1 ) and
(iii) P(X ~ 2

• 5)

A random variable X has the following probability mass function.

 x 1 2 3 4 5 f(x) k2 2k2 3k2 2k 3k

#### 12th Maths - Ordinary Differential Equations - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

A differential equation, determine its order, degree (if exists)
$\frac { dy }{ dx } +xy=cotx$

• 2)

A differential equation, determine its order, degree (if exists)
${ \left( \frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \right) }^{ \frac { 2 }{ 3 } }-3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +4=0$

• 3)

A differential equation, determine its order, degree (if exists)
${ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0$

• 4)

A differential equation, determine its order, degree (if exists)
${ \left( \frac { dy }{ dx } \right) }^{ 3 }=\sqrt { 1+\left( \frac { dy }{ dx } \right) }$

• 5)

Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be-8x, where A and B are arbitrary constants.

#### 12th Maths - Applications of Integration - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

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

• 2)

Evaluate the following:
$\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ e }^{ -2x }dx }$

• 3)

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

• 4)

Evaluate the following
$\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }x{ cos }^{ 4 }xdx }$

• 5)

Evaluate the following
$\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ (1-x) }^{ 3 }dx }$

#### 12th Maths - Differentials and Partial Derivatives - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

Use the linear approximation to find approximate values of
${ (123) }^{ \frac { 2 }{ 3 } }$

• 2)

Find a linear approximation for the following functions at the indicated points.
${ h }({ x })=\frac { x }{ 1+x } =\frac { 1 }{ 2 }$

• 3)

A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9-8 cm. Find approximations for the following:
change in the volume

• 4)

Find ∆f and df for the function f for the indicated values of x, ∆x and compare
f(x) = x2 + 2x + 3; x = -0.5, ∆x = dx = 0.1

• 5)

Let g(x, y) = $\frac { { x }^{ 2 }y }{ { x }^{ 4 }+{ y }^{ 2 } }$ for (x, y) ≠ (0, 0) and f(0, 0) = 0
Show that $\begin{matrix} lim \\ (x,y)\rightarrow (1,2) \end{matrix}$ g(x, y) = 0 along every line y = mx, m ∈ R

#### 12th Maths - Application of Differential Calculus - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

A person learnt 100 words for an English test. The number of words the person remembers in t days after learning is given by W(t) =100×(1− 0.1t)2, 0 ≤ t ≤ 10. What is the rate at which the person forgets the words 2 days after learning?

• 2)

A point moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres
Find the instantaneous velocities at t = 3 and t = 6 seconds.

• 3)

A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s =16t2 in t seconds
What is the instantaneous velocity of the camera when it hits the ground?

• 4)

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

• 5)

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.
$f(x)=|\frac{1}{x}|, x\in [-1,1]$

#### 12th Maths - Applications of Vector Algebra - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

Show that the vectors $\hat { i } +\hat { 2j } -\hat { 3k }$,$\hat { i } +\hat { 2j } -\hat { 3k }$ and $\hat { 3i } +\hat { j } -\hat { k }$

• 2)

Determine whether the three vectors $2\hat { i } +3\hat { j } +\hat { k }$$\hat { i } -2\hat { j } +2\hat { k }$ and $\hat { 3i } +\hat { j } +2\hat { k }$ are coplanar.

• 3)

Find the non-parametric form of vector equation and Cartesian equations of the straight line passing through the point with position vector  $4\hat { i } +3\hat { j } -7\hat { k }$ and parallel to the vector $2\hat { i } -6\hat { j } +7\hat { k }$.

• 4)

Find the angle between the line $\vec { r } =(2\hat { i } -\hat { j } +\hat { k } )+t(\hat { i } +2\hat { j } -2\hat { k } )$ and the plane $\vec { r } =(6\hat { i } +3\hat { j } +2\hat { k } )=8$

• 5)

Find the angle between the following lines.
2x = 3y =  −z and 6x = − y = −4z.

#### 12th Maths - Two Dimensional Analytical Geometry II - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

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

• 2)

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

• 3)

11x2−25y2−44x+50y−256 = 0

• 4)

Find centre and radius of the following circles.
x2+y2+6x−4y+4=0

• 5)

Find centre and radius of the following circles.
2x2+2y2−6x+4y+2=0

#### 12th Maths - Inverse Trigonometric Functions - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

Find the principal value of sin-1(2), if it exists.

• 2)

Find the period and amplitude of
y=sin 7x

• 3)

Find the value of
$2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right)$

• 4)

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

• 5)

Prove that $\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}$.

#### 12th Maths - Theory of Equations - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

Construct a cubic equation with roots 1,2, and 3

• 2)

If α, β, γ  and $\delta$ are the roots of the polynomial equation 2x4+5x3−7x2+8=0 , find a quadratic equation with integer coefficients whose roots are α + β + γ + $\delta$ and αβ૪$\delta$.

• 3)

Show that the equation 2x2−6x+7=0 cannot be satisfied by any real values of x.

• 4)

Show that, if p,q,r are rational, the roots of the equation x2−2px+p2−q2+2qr−r2=0 are rational.

• 5)

Obtain the condition that the roots of x3+px2+qx+r=0 are in A.P.

#### 12th Maths - Complex Numbers - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

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

• 2)

If z1=3-2i and z2=6+4i, find $\cfrac { { z }_{ 1 } }{ z_{ 2 } }$

• 3)

Find the modulus of the following complex numbers
$\cfrac { 2i }{ 3+4i }$

• 4)

Find the square roots of 4+3i

• 5)

Show that the following equations represent a circle, and, find its centre and radius|
$\left| z-2-i \right| =3$

#### 12th Maths - Application of Matrices and Determinants - Two Marks Study Materials - by 8682895000 - View & Read

• 1)

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

• 2)

If A is a non-singular matrix of odd order, prove that |adj A| is positive

• 3)

If A is symmetric, prove that then adj Ais also symmetric.

• 4)

If adj(A) = $\left[ \begin{matrix} 0 & -2 & 0 \\ 6 & 2 & -6 \\ -3 & 0 & 6 \end{matrix} \right]$, find A−1.

• 5)

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

#### 12th Maths - Full Portion Five Marks Question Paper - by 8682895000 - View & Read

• 1)

If A = $\left[ \begin{matrix} 4 & 3 \\ 2 & 5 \end{matrix} \right]$, find x and y such that A2 + xA + yI2 = O2. Hence, find A-1.

• 2)

In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball left to go in the last over. The last ball was bowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equation of the path is y = ax2 + bx + c with respect to a xy-coordinate system in the vertical plane and the ball traversed through the points (10, 8), (20, 16) (30, 18) can you conclude that Chennai Super Kings won the match?
Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with the farthest boundary line is (70, 0).)

• 3)

Determine the values of λ for which the following system of equations (3λ − 8)x + 3y + 3z = 0, 3x + (3λ − 8)y + 3z = 0, 3x + 3y + (3λ − 8)z = 0. has a non-trivial solution.

• 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)

For what value of λ, the system of equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 is consistent.

#### 12th Maths - Full Portion Three Marks Questions - by 8682895000 - View & Read

• 1)

If adj(A) = $\left[ \begin{matrix} 2 & -4 & 2 \\ -3 & 12 & -7 \\ -2 & 0 & 2 \end{matrix} \right]$, find A.

• 2)

4 men and 4 women can finish a piece of work jointly in 3 days while 2 men and 5 women can finish the same work jointly in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using matrix inversion method.

• 3)

Find,the rank of the matrix math $\left[ \begin{matrix} 4 \\ -2 \\ 1 \end{matrix}\begin{matrix} 4 \\ 3 \\ 4 \end{matrix}\begin{matrix} 0 \\ -1 \\ 8 \end{matrix}\begin{matrix} 3 \\ 5 \\ 7 \end{matrix} \right]$.

• 4)

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.

• 5)

If (x1+iy1)(x2+iy2)(x3+iy3)...(xn+iyn) =a+ib, show that
i) (x12+y12)(x22+y22)(x32+y32)...(xn2+yn2)=a2+b2
ii) $\sum _{ r=1 }^{ n }{ tan^{ -1 } } \left( \cfrac { { y }_{ r } }{ { x }_{ r } } \right) ={ tan }^{ -1 }\left( \cfrac { b }{ a } \right) +2k\pi ,k\epsilon Z$

#### 12th Maths - Full Portion Two Marks Question Paper - by 8682895000 - View & Read

• 1)

If A is a non-singular matrix of odd order, prove that |adj A| is positive

• 2)

Find the rank of the matrix $\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{matrix} \right]$ by reducing it to a row-echelon form.

• 3)

Solve the following system of homogenous equations.
2x + 3y − z = 0, x − y − 2z = 0, 3x + y + 3z = 0

• 4)

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

• 5)

Find z−1, if z=(2+3i)(1− i).

#### REVISION TEST - by 9894814613 - 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 is a non-singular matrix such that A-1 = $\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right]$, then (AT)−1 =

• 3)

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

• 4)

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

• 5)

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

#### 12th Maths -Public Exam Model Question Paper 2019 - 2020 - 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 = [2 0 1] then the rank of AAT is ______

• 3)

If x=cosθ + i sinθ, then xn+$\frac { 1 }{ { x }^{ n } }$ is ______

• 4)

A polynomial equation in x of degree n always has

• 5)

If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

#### 12th Maths - Applications of Integration Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 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)

The value of $\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } }$ dx is

• 5)

The area enclosed by the curve y = $\frac { { x }^{ 2 } }{ 2 }$ , the x - axis and the lines x = 1, x = 3 is

#### 12th Maths - Differentials and Partial Derivatives Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 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)

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

• 4)

If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

• 5)

If f(x,y) = 2x2 - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is

#### 12th Standard Maths - Applications of Vector Algebra Model Question Paper 1 - by 8682895000 - 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 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

• 3)

The coordinates of the point where the line $\vec { r } =(6\hat { i } -\hat { j } -3\hat { k } )+t(\hat { i } +4\hat { j } )$ meets the plane $\vec { r } =(\hat { i } +\hat { j } -\hat { k } )$ = 3 are

• 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

#### Plus 2 Maths - Two Dimensional Analytical Geometry-II Model Question Paper 1 - by 8682895000 - 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 equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

• 3)

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

• 4)

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

• 5)

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

#### 12th Stateboard Maths - Probability Distributions Model Question Paper 1 - by 8682895000 - 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 random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

• 3)

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

• 4)

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 followingcannot be the value of a and b?

• 5)

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

#### 12th Maths Chapter 12 Discrete Mathematics Model Question Paper 1 - by 8682895000 - View & Read

• 1)

Subtraction is not a binary operation in

• 2)

Which one of the following statements has truth value F?

• 3)

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

• 4)

The Identity element of $\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\}$ |x$\in$R, x≠0} under matrix multiplication is

• 5)

Which of the following is a contradiction?

#### 12th Maths - Ordinary Differential Equations Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

The solution of sec2x tan y dx+sec2y tan x dy=0 is

• 5)

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

#### 12th Maths - Application of Differential Calculus Model Question Paper 1 - by 8682895000 - 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 number given by the Mean value theorem for the function $\cfrac { 1 }{ x }$,x∈[1,9] is

• 4)

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

• 5)

The value of $\underset { x\rightarrow \infty }{ lim } { e }^{ -x }$ is

#### 12th Maths - Inverse Trigonometric Functions Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

If ${ cos }^{ -1 }x>x>{ sin }^{ -1 }x$ then

#### 12th Maths - Theory of Equations Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

If ∝, β, ૪ are the roots of the equation x3-3x+11=0, then ∝+β+૪ is __________.

#### 12th Maths - Complex Numbers Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### 12th Maths - Application of Matrices and Determinants Model Question Paper 1 - by 8682895000 - View & Read

• 1)

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

• 2)

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

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

• 5)

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

#### 12th Maths - Two Dimensional Analytical Geometry-II Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

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

• 4)

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

• 5)

The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

#### 12th Maths - Inverse Trigonometric Functions Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

If $\\ \\ \\ { cot }^{ -1 }\left( \sqrt { sin\alpha } \right) +{ tan }^{ -1 }\left( \sqrt { sin\alpha } \right) =u$, then cos2u is equal to

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### 12th Maths - Theory of Equations Model Question Paper - by Satyadevi - Tiruchirappalli - View & Read

• 1)

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

• 2)

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

• 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 the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

#### 12th Maths - Complex Numbers Model Question Paper - 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)

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

• 4)

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

• 5)

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

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

• 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)

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

• 5)

The rank of any 3 x 4 matrix is
(1) May be 1
(2) May be 2
(3) May be 3
(4) Maybe 4

#### 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)

A differential equation, 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)

A differential equation, 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.

### 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.

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