## 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-1x + sin-1y = $\frac{2\pi}{3}$, then cos-1x + cos-1y =
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 = 2cos3θ and y = 3sin3θ 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) x2y2 + y = 0
b) x4y2 + y = 0
c) xy2 - y = 0
d) x4y2 - 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 a-b 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) 300
b) 450
c) 600
d) 900

2. The radius of the circle in which the sphere x2 + y2 + z2 + 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) -cosex + c
b) cosex + c
c) -cosecex + 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) $\frac{1}{42}$