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) = x^{2} + 2bx + 2c^{2} and g(x) = x^{2}  2cx + b^{2} 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 xaxis 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. (x^{2} + y^{2})dy = xydx. If y(x_{0} = e, y(1) = 1, then value of x_{0} =
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) 0^{0}
b) π/3
c) π/6
d) π/2
2. The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x^{2} + y^{2} + 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 = x_{1} 1 2 3 4 P(X = x_{1}) 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 $\int \frac{e^{x}\left (1 + sinx \right )dx}{1 + cosx}$ = e^{x}f(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 x^{2} + y^{2} = 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