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Questions >> CBSE XII >> Math

Math

Relations and Functions

Inverse Trigonometric Functions

Continuity and Differentiability

Application of Derivatives

Application of Integrals

Differential Equations

Three Dimensional Geometry

Linear Programming

Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1, x = 4$ and the $x- axis.$

asked Dec 8, 2016 by priyanka.c

1 answer

Define standing crop.

asked Dec 8, 2016 by meena.p

1 answer

Find the point on the curve $y = x^3 - 11 x + 5$ at which the target is $y = x -11.$

asked Dec 8, 2016 by priyanka.c

1 answer

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

asked Dec 8, 2016 by priyanka.c

1 answer

If $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$ , then evaluate $f o f(x)$

asked Dec 7, 2016 by priyanka.c

1 answer

The radius of a circle is increasing uniformly at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10cm long ?

asked Dec 7, 2016 by priyanka.c

1 answer

The total revenue in Rupees received from the sales of $x$ units of a product is given by $Rx = 3x^2 + 36x +5$ . Find the marginal revenue , when $x=15$ , where by marginal.

asked Dec 6, 2016 by priyanka.c

1 answer

If A and B are symmetric matrices, prove that AB - BA is a skew symmetric matrix

asked Dec 6, 2016 by priyanka.c

1 answer

Using cofactors of elements of second row, evaluate $\triangle = \begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}$

asked Dec 5, 2016 by priyanka.c

1 answer

Evaluate : $\tan^{-1} (1) + cos^{-1} ( \frac{-1}{2} )+ \sin^{-1} (\frac{-1}{2})$

asked Dec 5, 2016 by priyanka.c

2 answers

If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$ , Evaluate $A^TA^{-1}$

asked Dec 1, 2016 by priyanka.c

1 answer

Find the value of $\tan^{-1} (\frac{x}{y}) - \tan^{-1}(\frac{x-y}{x+y})$

asked Nov 30, 2016 by priyanka.c

1 answer

Define a binary operation $\ast$ on the set {0, 1, 2, 3, 4, 5} as $a*b=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.$ show that the zero is the identity for this operation and each element $a \neq 0$ of the set is invertible with $6-a$ being the inverse of $a$ .

asked Nov 30, 2016 by priyanka.c

1 answer

A coin is tossed 6 times. What Is the probability that tail appears an odd no of times ?

asked Nov 30, 2016 by priyanka.c

1 answer

If $\theta$ be the angle between two unit vectors. Evaluate $\sin \frac{\theta}{2}$

asked Nov 25, 2016 by priyanka.c

1 answer

Form the differential equation for the family of curves $y = a \sin(x+b)$ where $a \;and \; b$ are parameters

asked Nov 25, 2016 by priyanka.c

1 answer

Evaluate : $\begin{align}\int\limits_{-1}^1 log (\frac{2+x}{2-x}) dx \end{align}$

asked Nov 25, 2016 by priyanka.c

1 answer

Find the approximate value of $f'(3.02)$ where $f(x) = 3x^2+5x+3$

asked Nov 25, 2016 by priyanka.c

1 answer

The total cost C(x) in rupees associated with the production of x units of an item is given by $C(x) = 0.007 x^3 - 0.003 x^2 + 15x + 4000$ . Find the marginal cost when 10 units are produced.

asked Nov 23, 2016 by priyanka.c

1 answer

If $y = \sin (m \sin^{-1} x),$ evaluate $(1-x) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + m^2y = 0$

asked Nov 23, 2016 by priyanka.c

1 answer

Find the value of x if $\begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2& 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0$

asked Nov 23, 2016 by priyanka.c

1 answer

Let A = {1, 2}. Find the number of possible binary operations defined on A.

asked Nov 23, 2016 by priyanka.c

1 answer

A balloon which always remain spherical has a variable diameter $\frac{3}{2} (2x+ 3)$ : Determine the rate of change of volume w.r.t x

asked Nov 23, 2016 by priyanka.c

1 answer

Evalute : $\begin{vmatrix}152 & 24 & 40 \\ 3 & 7 & 1 \\ 19 & 3 & 5 \end{vmatrix}$

asked Nov 23, 2016 by priyanka.c

1 answer

Evaluate : $\sec^2 (\tan^{-1}(2)) + cosec^2(\cot^{-1}(3))$

asked Nov 23, 2016 by priyanka.c

1 answer

Event A and B are such that $P(A) = \frac{1}{2}, P(B) = \frac{7}{12}$ , P (not A or not B) = $\frac{1}{4}$ . State whether A and B are independent.

asked Nov 23, 2016 by priyanka.c

1 answer

If A, B, C are position vectors (2, 0, 0), (0, 1, 0) and (0, 0, 2) show that $\triangle ABC$ is isosceles .

asked Nov 23, 2016 by priyanka.c

1 answer

Find the value of $\lambda$ , so that the lines $\frac{1-x}{3} = \frac{7y - 14}{2 \lambda} = \frac{z-3}{2} \;and\; \frac{7-7 \lambda}{3 \lambda} = \frac{y-5}{1} = \frac{6-z}{5}$ are at right angle

asked Nov 22, 2016 by priyanka.c

1 answer

Find the value of 'a ' so that the function f(x) is defined by $f(x) = \begin{cases} \frac{\sin ^2 a x}{x^2} & x \neq 0 \\ 1 , & x =0 \end{cases}$ may be continuous at x = 0

asked Nov 22, 2016 by priyanka.c

1 answer

Use matrix method to examine if the following system of equation for consistency or inconsistency $4x - 2y = 3, \; \; 6x - 3y = 5$

asked Nov 22, 2016 by priyanka.c

1 answer

If $|\overrightarrow{a}| = 11, |\overrightarrow {b} | = 23 and |\overrightarrow {a} - \overrightarrow {b} |= 30$

asked Nov 22, 2016 by priyanka.c

1 answer

Solve the differential equation $\frac{dy}{dx} = log (x+1)$

asked Nov 22, 2016 by priyanka.c

1 answer

$\begin{align}\int_0^\frac{\pi}{2} \frac{\sin x}{1 + \cos^2 x } dx \end{align}$

asked Nov 22, 2016 by priyanka.c

1 answer

Without expanding evaluate: $\begin{vmatrix} \frac{1}{a} & a^2 & bc \\ \frac{1}{b} & b^2 & ca \\ \frac{1}{c} & c^2 & ab \end{vmatrix}$

asked Nov 22, 2016 by priyanka.c

1 answer

Evaluate : $\tan \frac{1}{2} (\cos^{-1} \frac{\sqrt 5}{3})$

asked Nov 22, 2016 by priyanka.c

1 answer

Verify Rolle's theorem for $f(x) = x^2 + 2$ in the interval [-2,2]

asked Nov 21, 2016 by priyanka.c

1 answer

differentiate $y = (\sin x)^x + \sin^{-1} \sqrt x$

asked Nov 21, 2016 by priyanka.c

1 answer

Using elementary row transformation, find the inverse of $A = \begin{bmatrix} 2 & -6 \\ 1 & -2\end{bmatrix}$

asked Nov 21, 2016 by priyanka.c

1 answer

If $P(A) = 0.25, P(B) = 0.4 \; and \; P (A \cup B) = 0.5 \; find \; P (A \cap B) \;and \; P (A \cap \bar{B})$

asked Nov 21, 2016 by priyanka.c

1 answer

Are the vectors $(\hat {i} + \hat{j} + \hat{k}), (2\hat{i} +3\hat{j} -\hat{k})$ and $(-\hat{i} -2\hat{j} +2 \hat{k})$ are linearly dependent ?

asked Nov 21, 2016 by priyanka.c

1 answer

A car stands from a point P at time t = 0 sec and stops at point Q. The distance x, in metres, covered by it, in t seconds in given by $x = t^2 (2 - \frac{t}{3})$ . Find the time taken by it to reach Q and also find the distance between P and Q.

asked Nov 21, 2016 by priyanka.c

1 answer

Find the point at which the target to the curve $y = \sqrt{4x-3} - 1$ has its slope $\frac{2}{3}$

asked Nov 21, 2016 by priyanka.c

1 answer

Solve the system of equation $2x + 5y = 1 \; \ \; \; and \; \; \; \; 3x + 2y = 7$

asked Nov 20, 2016 by priyanka.c

1 answer

Find X and Y, if $X + Y= \begin{bmatrix} 5 & 2 \\ 0 & 9 \end{bmatrix}$ and $X - Y = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$

asked Nov 20, 2016 by priyanka.c

1 answer

Evaluate $tan^{-1} (\frac{\cos x}{1-\sin x}), \;\; \; -\frac{\pi}{2} < x < \frac{\pi}{2}$

asked Nov 20, 2016 by priyanka.c

1 answer

On Q the set of all rational numbers, a binary operation $\ast$ is defined by $a \ast b=\frac{ab}{5}$ for all $a, b \in Q$ . Find the identity element $\ast$ in Q. Also prove that every non-zero element of Q is invertible.

asked Nov 20, 2016 by priyanka.c

1 answer

Find the shortest distance between the line $l_ 1$ and $l_2$ given by: $\overrightarrow {r} = \hat{i} +2\hat{j} -4\hat{k} + \lambda (2 \hat{i} + 3 \hat {j} + 6 \hat {k}) and \overrightarrow {r }= 3\hat{i} + 3\hat{j} -5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})$

asked Nov 20, 2016 by priyanka.c

1 answer

Evaluate : $\begin{align}\int_4^9 \frac{\sqrt x}{(30 - x^{\frac{3}{2}})^2} dx \end{align}$

asked Nov 20, 2016 by priyanka.c

1 answer

Find the value of k if f(x) is continuous at $x = \frac{\pi}{2}$ , when $f(x) =\begin{cases}\frac{k \cos x}{\pi - 2x }\;;\; x \neq \frac{\pi}{2} \\ 3 ,\; \; \; \; \; \; \; \; \; x = \frac{\pi}{2} \end{cases}$

asked Nov 20, 2016 by priyanka.c

1 answer

If $A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ , then find the value of $\theta$ satisfying the equation $A^T + A = I_2$

asked Nov 20, 2016 by priyanka.c

1 answer

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