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. If sin^{1}x + sin^{1}y = $\frac{2\pi}{3}$, then cos^{1}x + cos^{1}y =
a) $\frac{2\pi}{3}$
b) $\frac{\pi}{3}$
c) $\frac{\pi}{6}$
d) π/2
2. $2tan^{1\left (\frac{1}{3} \right )} + tan^{1}\left (\frac{1}{7} \right )$ =
a) $tan^{1}\left (\frac{49}{29} \right )$
b) $\frac{\pi}{2}$
c) 0
d) π/4

3. Matrices  Quiz

4. Determinants and Matrices  Quiz
1. If the system of equations x+ay, az + y = 0 and ax + z = 0 has infinite solutions, then the value of a is
a) 1
b) 1
c) 0
d) No real values
2. If $\begin{vmatrix} a &b&0 \\ 0& a &b \\ b& 0 & a \end{vmatrix}$ = 0, then
a) a is one of the cube roots of unity
b) b is one of the cube roots of unity
c) $\left ( \frac{a}{b} \right )$ is one of the cube roots of unity
d) $\left ( \frac{a}{b} \right )$ is one of the cube roots of 1

5. Continuity and Differentiability  Quiz
1. If f is strictly increasing function, then $lim_{0 \rightarrow 0}\frac{f\left (x^{2} \right )  f\left (x \right )}{f\left (x \right )  f\left (0 \right )}$ is equal to
a) 0
b) 1
c) 1
d) 2
2. If f(x) = $\frac{x  1}{x + 1}$, then f(2x) is
a) $\frac{f\left (x \right ) + 1}{f\left (x \right ) + 3}$
b) $\frac{3f\left (x \right ) + 1}{f\left (x \right ) + 3}$
c) $\frac{f\left (x \right ) + 3}{f\left (x \right ) + 1}$
d) $\frac{f\left (x \right ) + 3}{3f\left (x \right ) + 1}$

6. Differentiation and Application of Derivatives  Quiz
1. The equation of the tangent to the curve x = 2cos^{3}θ and y = 3sin^{3}θ at the point θ = π/4 is
a) 2x + 3y = 3$\sqrt{2}$
b) 2x  3y = 3$\sqrt{2}$
c) 3x  2y = 3$\sqrt{2}$
d) 2x  2y = 3$\sqrt{2}$
2. If y = $sin^{1}\sqrt{x}$, then $\frac{dy}{dx}$ =
a) $\frac{2}{\sqrt{x}\sqrt{1  x}}$
b) $\frac{2}{\sqrt{x}\sqrt{1  x}}$
c) $\frac{1}{2\sqrt{x}\sqrt{1  x}}$
d) $\frac{1}{\sqrt{1  x}}$

7. Integrals  Quiz

8. Application of Integrals  Quiz
1. 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
2. The sin and cosine curves intersects infinitely many times giving bounded regions of equal areas. They area of one of such region is
a) $\sqrt{2}$
b) $2\sqrt{2}$
c) $3\sqrt{2}$
d) $4\sqrt{2}$

9. Differential Equations  Quiz
1. The differential equation satisfied by the family of curves y = $axcos\left (\frac{1}{x} + b \right )$, where a,b are parameters, is
a) x^{2}y_{2} + y = 0
b) x^{4}y_{2} + y = 0
c) xy_{2}  y = 0
d) x^{4}y_{2}  y = 0
2. Solution of the differential equation $\frac{dy}{dx} + \frac{y}{x}$ = sinx is
a) x(y + cosx) =+ sinx + c
b) x(y  cosx) = sinx + c
c) x(y . cosx) = sinx + c
d) x(y  cosx) = cosx + c
e) x(y + cosx) = cosx + c

10. Vector Algebra  Quiz
1. A and B are two points . The position vector of A is 6b  2a . A point P divides the line AB in the ratio 1:2. If ab is the position vector of P, then the position vector of B is given by
a) 7a  15b
b) 7a + 15b
c) 15a  7b
d) 15a + 7b
2. If the resultant of two vectors equals in magnitude to one of them and perpendicular to it in direction , the magnitude of the other vector is
a) Same as that of the first
b) $\sqrt{2}$ times that of the first
c) Twice that of the first
d) None of these

11. Three Dimensional Geometry  Quiz
1. The angle between the pair of lines with direction ratios (1,1,2) and ($\sqrt{3}$  1, $\sqrt{3}$  1,4) is
a) 30^{0}
b) 45^{0}
c) 60^{0}
d) 90^{0}
2. The radius of the circle in which the sphere x^{2} + y^{2} + z^{2} + 2x  2y  4z  19 = 0 is cut by the plane x + 2y + 2x + 7 = 0 is
a) 1
b) 2
c) 3
d) 4

12. Linear Programming  Quiz
1. Variables of the objective function of the linear programming problem are
a) Zero
b) Zero or positive
c) Negative
d) Zero or negative
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. A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$. If the signal received at station B is green, then the probability that the original signal was green is
a) $\frac{3}{5}$
b) $\frac{6}{7}$
c) $\frac{20}{23}$
d) $\frac{9}{20}$
2. If P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28 , P(ABC) = 0.09, P(A + B + C) ≥ 0.75 and P(BC) = x, then
a) 0.23 ≤ x ≤ 0.48
b) 0.32 ≤ x ≤ 0.84
c) 0.25 ≤ x ≤ 0.73
d) None of these

14. Statistics and Dynamics  Quiz

15. Indefinite Integration  Quiz
1. $\int e^{x}sin\left (e^{x} \right )dx$ =
a) cose^{x} + c
b) cose^{x} + c
c) cosece^{x} + c
d) None of these
2. $\int \frac{1}{1 + cosx + sinx}dx$ =
a) $log \left  1 + tan\frac{x}{2} \right  + c$
b) $\frac{1}{2} log \left  1 + tan\frac{x}{2} \right  + c$
c) $2log \left  1 + tan\frac{x}{2} \right  + c$
d) $\frac{1}{2} log \left  1  tan\frac{x}{2} \right  + c$

16. Definite Integration and Area under the curve  Quiz
1. $\int_{1}^{0}\frac{dx}{x^{2} + 2x + 2}$ =
a) 0
b) π/4
c) π/2
d) π/4
2. The value of the integral $\int_{0}^{1}x\left (1  x \right )^{5}dx$ is equal to
a) $\frac{1}{6}$
b) $\frac{1}{7}$
c) $\frac{6}{7}$
d) $\frac{5}{6}$
e) $\frac{1}{42}$