## 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 $sin^{-1}\left (\frac{2a}{1 + a^{2}} \right ) + sin^{-1}\left (\frac{2b}{1 + b^{2}} \right )$ = $2tan^{-1}x$ , then x =
a) $\frac{a - b}{1 + ab}$
b) $\frac{b}{1 + ab}$
c) $\frac{b}{1 - ab}$
d) $\frac{a + b}{1 - ab}$

2. $\sum_{m=1}^{n}tan^{-1}\left (\frac{2m}{m^{4} + m^{2} + 2} \right )$ is equal to
a) $tan^{-1}\left (\frac{n^{2} + n }{n^{2} + n + 2}\right )$
b) $tan^{-1}\left (\frac{n^{2} - n }{n^{2} - n + 2}\right )$
c) $tan^{-1}\left (\frac{n^{2} + n + 2}{n^{2} + n }\right )$
d) None of these

• 3. Matrices - Quiz

• 4. Determinants and Matrices - Quiz

1. If x is a positive integer, then Δ = $\begin{vmatrix} x! & \left (x+1 \right )! &\left (x+2 \right )! \\ \left (x+1 \right )! & \left (x+2 \right )! & \left (x + 3 \right )!\\ \left (x + 2 \right )! & \left (x + 3 \right )! & \left (x + 4 \right )! \end{vmatrix}$ is equal to
a) 2(x!)(x + 1)!
b) 2(x!)(x + 1)!(x + 2)!
c) 2(x!)(x + 3)!
d) None of these

2. If P = $\begin{bmatrix} i & 0 &-i \\ 0& -i& i\\ -i& i& 0 \end{bmatrix}$ and Q = $\begin{pmatrix} -i &i \\ 0& 0\\ i &-i \end{pmatrix}$, then PQ is equal to
a) $\begin{pmatrix} -2 &2 \\ 1& -1\\ 1&-1 \end{pmatrix}$
b) $\begin{pmatrix} 2 &-2 \\ -1& 1\\ -1&1 \end{pmatrix}$
c) $\begin{pmatrix} 2 &-2 \\ -1 &1 \end{pmatrix}$
d) $\begin{pmatrix} 1 &0 &0 \\ 0 &1 &0 \\ 0& 0 & 1 \end{pmatrix}$

• 5. Continuity and Differentiability - Quiz

1. $lim_{x \rightarrow \infty}\left (1 - \frac{4}{x - 1} \right )^{3x - 1}$ =
a) e12
b) e-12
c) e4
d) e3

2. If f(x) = $\begin{vmatrix} sinx & cosx &tanx \\ x^{3} &x^{2} & x\\ 2x & 1 & 1 \end{vmatrix}$, then $lim_{x \rightarrow 0} \frac{f\left (x \right )}{x^{2}}$ is
a) 3
b) -1
c) 0
d) 1

• 6. Differentiation and Application of Derivatives - Quiz

1. The minimum value of f(x) = |3 - x| + 7 is
a) 0
b) 6
c) 7
d) 8
e) 10

2. If a ball is thrown vertically upward and the height s reached in time t is given by s = 22t - 11t2, then the total distance travelled by the ball is
a) 22 units
b) 44 units
c) 33 units
d) 11 units

• 7. Integrals - Quiz

• 8. Application of Integrals - Quiz

1. $\int_{-\pi}^{\pi} \left (cospx - sinqx \right )^{2}dx$ is equal to (where p and q are integers)
a) -π
b) 0
c) &pi
d) 2π

2. The area of the region between the curves y = $\sqrt{\frac{1 + sinx}{cosx}}$ and y = $\sqrt{\frac{1 - sinx}{cosx}}$ bounded by the lines x = 0 and x = $\frac{\pi}{4}$ is
a) $\int_{0}^{\sqrt{2}-1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
b) $\int_{0}^{\sqrt{2}-1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
c) $\int_{0}^{\sqrt{2}+1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
d) $\int_{0}^{\sqrt{2}+1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$

• 9. Differential Equations - Quiz

1. The degree of the differential equation y(x) = $1 + \frac{dy}{dx} + \frac{1}{1.2}\left (\frac{dy}{dx} \right )^{2} + \frac{1}{1.2.3}\left (\frac{dy}{dx} \right )^{3} + ...$ is
a) 2
b) 3
c) 1
d) None of these

2. The differential equation of all conics whose centre lie at the origin is of order
a) 2
b) 3
c) 4
d) None of these

• 10. Vector Algebra - Quiz

1. The vectors $\overrightarrow{AB}$ = 3i + 5j + 4k and $\overrightarrow{AC}$ = 5i - 5j + 2k are the sides of a triangle ABC. The length of the median through A is
a) $\sqrt{13}$ unit
b) 2$\sqrt{5}$ unit
c) 5 unit
d) 10 unit

2. If a, ,b and c are unit vectors such that a + b - c = 0, then the angle between a and b is
a) π/6
b) π/3
c) π/2
d) 2π/3

• 11. Three Dimensional Geometry - Quiz

1. Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2 . If L makes an angle α with the positive x-axis , then cosα equals
a) $\frac{1}{\sqrt{3}}$
b) $\frac{1}{2}$
c) 1
d) $\frac{1}{\sqrt{2}}$

2. The co-ordinates of the foot of perpendicular drawn from point P(1,0,3) to the join of points A(4,7,1) and B(3,5,3) is
a) (5,7,1)
b) $\left (\frac{5}{7}, \frac{7}{3}, \frac{17}{3} \right )$
c) $\left (\frac{2}{7}, \frac{5}{3}, \frac{7}{3} \right )$
d) $\left (\frac{5}{7}, \frac{2}{3}, \frac{7}{3} \right )$

• 12. Linear Programming - Quiz

1. The L.P. problem MaxZ = x1 + x2 such that -2x1 + x2 ≤ 1 , x1 ≤ 2, x1 + x2 ≤ 3 and x1, x2 ≥ 0 has
a) One solution
b) Three solution
c) An infinite no. of solution
d) None of these

2. The minimum value of z = 2x1 + 3x2 subject to the constraints 2x1 + 7x2 ≥ 22, x1 + x2 ≥ 6, 5x1 + x2 ≥ 100
a) 14
b) 20
c) 10
d) 16

• 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. A coin is tossed 3 times. The probability of obtaining at least two heads is
or
Three coins are tossed all together. The probablity of getting at least two heads is
a) $\frac{1}{8}$
b) $\frac{3}{8}$
c) $\frac{1}{2}$
d) $\frac{2}{3}$

• 14. Statistics and Dynamics - Quiz

• 15. Indefinite Integration - Quiz

1. If $\int \frac{1}{x + x^{5}}dx$ = f(x) + c, then the value of $\int \frac{x^{4}}{x + x^{5}}dx$ is
a) logx - f(x) + c
b) f(x) + logx + c
c) f(x) - logx + c
d) None of these

2. $\int \frac{x^{3} - x - 2}{\left (1 - x^{2} \right )}dx$ =
a) $log\left (\frac{x + 1}{x - 1} \right ) - \frac{x^{2}}{2} + c$
b) $log\left (\frac{x - 1}{x + 1} \right ) + \frac{x^{2}}{2} + c$
c) $log\left (\frac{x + 1}{x - 1} \right ) + \frac{x^{2}}{2} + c$
d) $log\left (\frac{x - 1}{x + 1} \right ) - \frac{x^{2}}{2} + c$

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

1. If Im = $\int_{1}^{x}\left (logx \right )^{m}dx$ datisfies the relation Im = k - lIm-1, then
a) k = e
b) l = m
c) k = $\frac{1}{e}$
d) None of these

2. The area (in sq. unit) of the region bounded by the curves 2x = y2 - 1 and x = 0 is
a) $\frac{1}{3}$
b) $\frac{2}{3}$
c) 1
d) 2