## Class/Course - Class XII

### Subject - Math

#### Total Number of Question/s - 3349

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• 1. Relations and Functions - Quiz

• 2. Inverse Trigonometric Functions - Quiz

1. $cos^{-1}\left (\frac{3 + 5cosx}{5 + 3cosx} \right )$ is equal to
a) $tan^{-1}\left (\frac{1}{2}tan\frac{x}{2} \right )$
b) $2tan^{-1}\left (2tan\frac{x}{2} \right )$
c) $\frac{1}{2}tan^{-1}\left (2tan\frac{x}{2} \right )$
d) $2tan^{-1}\left (\frac{1}{2}tan\frac{x}{2} \right )$
e) $tan^{-1}\left (tan\frac{x}{2} \right )$

2. If $2cos^{-1}\sqrt{\frac{1 + x}{2}}$ = $\frac{\pi}{2}$, then x =
a) 1
b) 0
c) -1/2
d) 1/2

• 3. Matrices - Quiz

• 4. Determinants and Matrices - Quiz

1. Solution of the equation $\begin{vmatrix} 1 &1 &x \\ p+1& p+1 &p+x \\ 3& x+1& x+2 \end{vmatrix}$ = 0 are
a) x = 1,2
b) x = 2,3
c) x = 1,p,2
d) x = 1,2,-p

2. The value of x obtained from the equation $\begin{vmatrix} x+\alpha &\beta &\gamma \\ \gamma& x+\beta & \alpha\\ \alpha &\beta & x+\gamma \end{vmatrix}$ = 0 will be
a) 0 and -($\alpha+ \beta+ \gamma$)
b) 0 and ($\alpha+ \beta+ \gamma$)
c) 1 and ($\alpha- \beta- \gamma$)
d) 0 and ($\alpha$2 + $\beta$2 + $\gamma$ 2)

• 5. Continuity and Differentiability - Quiz

1. If f(x) = $\left\{\begin{matrix} \frac{\sqrt{1 + kx} - \sqrt {1 - kx}}{x} &, for - 1 \le x < 0 \\ 2x^{2} + 3x - 2 &,for \ 0 \le x \le 1 \end{matrix}\right.$ is continuous at x = 0, then k =
a) -4
b) -3
c) -1
d) 1

2. f(x) = ||x| - 1| is not differentiable at
a) 0
b) ± 1,0
c) 1
d) ± 1

• 6. Differentiation and Application of Derivatives - Quiz

1. A spherical balloon is filled with 4500 π cubic meters of helium gas . If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is
a) $\frac{9}{7}$
b) $\frac{7}{9}$
c) $\frac{2}{9}$
d) $\frac{9}{2}$

2. If f(x) = x2 + 2bx + 2c2 and g(x) = -x2 - 2cx + b2 such that min f(x) > max g(x), then the relation between b and c is
a) No real value of b and c
b) 0 < c < b$\sqrt{2}$
c) |c| < |b|$\sqrt{2}$
d) |c| > |b|$\sqrt{2}$

• 7. Integrals - Quiz

• 8. Application of Integrals - Quiz

1. $\int_{0}^{\pi/2}sin2x log tanx dx$ is equal to
a) π
b) π/2
c) 0
d) 2π

2. The function L(x) = $\int_{1}^{x}\frac{dt}{t}$ satisfies the equation
a) L(x+y) = L(x) + L (y)
b) $L\left (\frac{x}{y} \right )$ = $L\left (x \right ) + L\left (y \right )$
c) L(xy) = L(x) + L(y)
d) None of these

• 9. Differential Equations - Quiz

1. The differential equation representing the family of parabolas having at orgin and axis along positive direction of x-axis is
a) $y^{2} - 2xy\frac{dy}{dx}$ = 0
b) $y^{2} + 2xy\frac{dy}{dx}$ = 0
c) $y^{2} - 2xy\frac{d^{2}y}{dx^{2}}$ = 0
d) $y^{2} + 2xy\frac{d^{2}y}{dx^{2}}$ = 0

2. (x2 + y2)dy = xydx. If y(x0 = e, y(1) = 1, then value of x0 =
a) $\sqrt{3}e$
b) $\sqrt{e^{2} - \frac{1}{2}}$
c) $\sqrt{\frac{e^{2} - 1}{2}}$
d) $\sqrt{\frac{e^{2} + 1}{2}}$

• 10. Vector Algebra - Quiz

1. If the vectors $\hat{a}$ = $\hat{i} - \hat{j} + 2\hat{k}$, $\vec{b}$ = $2\hat{i} + 4\hat{j} + \hat{k}$ and $\vec{c}$ = $\lambda \hat{i} + \hat{j} + \mu\hat{k}$ are mutually orthogonal , then (λ, μ)
a) (-3,2)
b) (2,-3)
c) (-2,3)
d) (3,-2)

2. The vectors 2i + 3j - 4k and ai + bj + ck are perpendicular, when
a) a = 2, b = 3, c = -4
b) a = 4, b = 4, c = 5
c) a = 4, c = 4, c = -5
d) None of these

• 11. Three Dimensional Geometry - Quiz

1. The angle between the lines x = 1, y = 2 and y = -1 , z = 0 is
a) 00
b) π/3
c) π/6
d) π/2

2. The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + 4x - 2y - 6z = 155 is
a) 26
b) $11\frac{4}{13}$
c) 13
d) 39

• 12. Linear Programming - Quiz

1. In LPP, ΔJ for all basic variables is equal to
a) 1
b) -1
c) 0
d) None of these

2. The objective function P(x,y) = 2x + 3y is maximized subject to the constraints x + y ≤ 30, x - y ≥ 0, 3 ≤ y ≤ 12, 0 ≥ x ≤ 20. The function attains the maximum value at the point
a) (12,18)
b) (18,12)
c) (15,15)
d) None of these

• 13. Probability - Quiz

1. An objective type least paper has 5 questions. Out of these 5 questions, 3 questions have four options each (A, B, C, D) with one option being the correct answer. The other 2 questions have two options each , namely True and False. A candidate randomly ticks the options. Then the probability that he/she will ticks the correct option in at least four questions, is
a) 5/32
b) 3/128
c) 3/256
d) 3/64

2. A random variable X has the following probability distribution
 X = x1 1 2 3 4 P(X = x1) 0.1 0.2 0.3 0.4

The mean and the standard deviation are respectively
a) 3 and 2
b) 3 and 1
c) 3 and $\sqrt{3}$
d) 2 and 1
e) 3 and $\sqrt{2}$

• 14. Statistics and Dynamics - Quiz

• 15. Indefinite Integration - Quiz

1. If $\int \frac{e^{x}\left (1 + sinx \right )dx}{1 + cosx}$ = exf(x) + c, then f(x) =
a) $sin\frac{x}{2}$
b) $cos\frac{x}{2}$
c) $tan\frac{x}{2}$
d) $log\frac{x}{2}$

2. The integral $\int \frac{sec^{2}x}{\left (secx + tanx \right )^{9/2}}dx$ equals (for some arbitrary constant K)
a) $\frac{-1}{\left (secx + tanx \right )^{11/2}}\left \{ \frac{1}{11} - \frac{1}{7}\left (secx + tanx \right )^{2} \right \} + K$
b) $\frac{1}{\left (secx + tanx \right )^{11/2}}\left \{ \frac{1}{11} - \frac{1}{7}\left (secx + tanx \right )^{2} \right \} + K$
c) $\frac{-1}{\left (secx + tanx \right )^{11/2}}\left \{ \frac{1}{11} + \frac{1}{7}\left (secx + tanx \right )^{2} \right \} + K$
d) $\frac{1}{\left (secx + tanx \right )^{11/2}}\left \{ \frac{1}{11} + \frac{1}{7}\left (secx + tanx \right )^{2} \right \} + K$

• 16. Definite Integration and Area under the curve - Quiz

1. The part of circle x2 + y2 = 9 in between y = 0 and y = 2 is revolved about y -axis. The volume of generating solid will
a) $\frac{46}{3}\pi$
b) 12π
c) 16π
d) 28π

2. $\int_{\pi}^{10\pi}\left | sinx \right |$ is
a) 20
b) 8
c) 10
d) 18