## 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. The value of $sin^{-1}\left (\frac{\sqrt{3}}{2} \right ) - sin^{-1}\left (\frac{1}{2} \right )$ is
a) 450
b) 900
c) 150
d) 300

2. The equation 2cos-1x + sin-1 = $\frac{11\pi}{6}$ has
a) No solution
b) Only one solution
c) Two solutions
d) Three solutions

• 3. Matrices - Quiz

• 4. Determinants and Matrices - Quiz

1. If A = [aij]2x2, where $a_{ij} = \left\{\begin{matrix} i +j, if \ i \ne j\\ i^{2} - 2j, if \ i = j \end{matrix}\right.$, then A01 is equal to
a) $\frac{1}{9}\begin{bmatrix} 4 &1 \\ -1& 2 \end{bmatrix}$
b) $\frac{1}{9}\begin{bmatrix} 0 &-3 \\ -3& -1 \end{bmatrix}$
c) $\frac{1}{9}\begin{bmatrix} 0 &3 \\ 3& 1 \end{bmatrix}$
d) None of these

2. The values of x,y,z in order of the system of equations 3x + y + 2z = 3, 2x - 3y - z = -3, x + 2y + z = 4, are
a) 2,1,5
b) 1,1,1
c) 1,-2,-1
d) 1,2,-1

• 5. Continuity and Differentiability - Quiz

1. If f(x) = x($\sqrt{x}$ - $\sqrt{x-1}$), then
a) f(x) is continuous but non-differentiable at x = 0
b) f(x) is differentiable at x = 0
c) f(x) is not differentiable at x = 0
d) None of these

2. $lim_{x \rightarrow 0} \frac{sin\left (\pi cos^{2}x \right )}{x^{2}}$ =
a) -π
b) π
c) π/2
d) 1

• 6. Differentiation and Application of Derivatives - Quiz

1. If y = sinx + ex, then $\frac{d^{2}y}{dy^{2}}$ =
a) (-sinx + ex)-1
b) $\frac{sinx - e^{x}}{\left (cosx + e^{x} \right )}^{2}$
c) $\frac{sinx - e^{x}}{\left (cosx + e^{x} \right )}^{3}$
d) $\frac{sinx + e^{x}}{\left (cosx + e^{x} \right )}^{3}$

2. If f(x) = $\frac{1}{4x^{2} + 2x + 1}$ , then its maximum value is
a) 4/3
b) 2/3
c) 1
d) 3/4

• 7. Integrals - Quiz

• 8. Application of Integrals - Quiz

1. The value of $\int_{0}^{0\pi + v}\left | sinx \right |dx$ is
a) 2n + 1 + cosv
b) 2n - 1 - cosv
c) 2n + 1
d) 2n + cosv

2. $\int_{0}^{\pi/2}\left (sinx - cosx \right )log\left (sinx + cosx \right )dx$ =
a) -1
b) 1
c) 0
d) None of these

• 9. Differential Equations - Quiz

1. The differential equation of the system of all circles of radius r in the xy-plane, is
a) $\left [1 + \left (\frac{dy}{dx} \right )^{3} \right ]^{2}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{2}$
b) $\left [1 + \left (\frac{dy}{dx} \right )^{3} \right ]^{2}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{3}$
c) $\left [1 + \left (\frac{dy}{dx} \right )^{2} \right ]^{3}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{2}$
d) $\left [1 + \left (\frac{dy}{dx} \right )^{2} \right ]^{3}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{3}$

2. If $\left ( \frac{dy}{dx} \right )$ = e -2y and y = 0 when x = 5, than value of x for y = 3 is
a) e5
b) e6 + 1
c) $\frac{e^{6} + 9}{2}$
d) loge6

• 10. Vector Algebra - Quiz

1. If a of magnitude 50 is collinear with the vector b = 6i - 8j - $\frac{15k}{2}$, and makes an acute angle with the positive direction of z-axis then the vector a is equal to
a) 24i - 32j + 30k
b) -24i + 32j + 30k
c) 16i - 16j - 15k
d) -12i + 16j - 30k

2. Let two non-collinear unit vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves so that at any time t the position vector $\overrightarrow{OP}$ (where O is the origin) is given by $\hat{a}cost + \hat{b}sint$. When P is farthest from origin O, let M be the length of $\overrightarrow{OP}$ and $\hat{u}$ be the unit vector along $\overrightarrow{OP}$. Then,
a) $\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$
b) $\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$
c) $\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$
d) $\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$

• 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. If the plane 3x + y + 2z + 6 = 0 is parallel to the line $\frac{3x - 1}{2b}$ = 3 - y = $\frac{z - 1}{a}$, then the value of 3a + 3b is
a) $\frac{1}{2}$
b) $\frac{3}{2}$
c) 3
d) 4
e) $\frac{5}{2}$

• 12. Linear Programming - Quiz

1. Shaded region is represented by

a) 4x - 2y ≤ 3
b) 4x - 2y ≤ -3
c) 4x - 2y ≥ 3
d) 4x - 2y ≥ -3

2. The maximum value of z = 5x - 3y subjected to the conditions 3x + 5y ≤ 5x + 2y ≤ 10, x, y ≥ 0 is
a) $\frac{235}{19}$
b) $\frac{325}{19}$
c) $\frac{529}{19}$
d) $\frac{532}{19}$

• 13. Probability - Quiz

1. A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is
a) $\frac{1}{3}$
b) $\frac{1}{2}$
c) $\frac{1}{4}$
d) None of these

2. Three numbers are chosen at random without replacement from {1,2,3,…,8}. The probability that their minimum is 3, given that their maximum is 6, is
a) $\frac{3}{8}$
b) $\frac{1}{5}$
c) $\frac{1}{4}$
d) $\frac{2}{5}$

• 14. Statistics and Dynamics - Quiz

• 15. Indefinite Integration - Quiz

1. Let I = $\int \frac{e^{x}}{e^{4x} + e^{2x} + 1}dx$,J = $\int \frac{e^{-x}}{e^{-4x} + e^{-2x} + 1}dx$. Then, for an arbitrary constant C, the value of J-I equals
a) $\frac{1}{2}log\left (\frac{e^{4x} - e^{2x} + 1 }{e^{4x} + e^{2x} + 1}\right ) + C$
b) $\frac{1}{2}log\left (\frac{e^{2x} + e^{x} + 1 }{e^{2x} - e^{x} + 1}\right ) + C$
c) $\frac{1}{2}log\left (\frac{e^{2x} - e^{x} + 1 }{e^{2x} + e^{x} + 1}\right ) + C$
d) $\frac{1}{2}log\left (\frac{e^{4x} + e^{2x} + 1 }{e^{4x} - e^{2x} + 1}\right ) + C$

2. $\int a^{x} dx$ =
a) $\frac{a^{x}}{log a} + c$
b) $a^{x}log a + c$
c) log a + c
d) ax + c

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

1. $\int_{0}^{1}sin\left (2tan^{-1}\sqrt{\frac{1 + x}{1 - x}} \right )dx$ =
a) π/6
b) π/4
c) π/2
d) π

2. $\int_{0}^{\infty}\frac{x ln x dx}{\left (1 + x^{2} \right )^{2}}$ is equal to
a) 0
b) 1
c) ∞
d) None of these