## 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. For the equation cos-1x + cos-12x + π = 0, the number of real solution is
a) 1
b) 2
c) 0
d) ∞

2. The solution of sin-1x - sin-12x = $\frac{\pm \pi}{3}$ is
a) $\pm\frac{1}{3}$
b) $\pm\frac{1}{4}$
c) $\pm \frac{\sqrt{3}}{2}$
d) $\pm\frac{1}{2}$

• 3. Matrices - Quiz

• 4. Determinants and Matrices - Quiz

1. If $\begin{bmatrix} sin^{2}\alpha &cos^{2}\alpha \\ cos^{2}\alpha& sin^{2}\alpha \end{bmatrix}$ = 0, α ε (0,π), then the values of α are
a) $\frac{\pi}{2}$ and $\frac{\pi}{12}$
b) $\frac{\pi}{2}$ and $\frac{\pi}{6}$
c) $\frac{\pi}{4}$ and $\frac{3\pi}{4}$
d) $\frac{\pi}{6}$ and $\frac{\pi}{3}$
e) $\frac{\pi}{2}$ and $\frac{\pi}{3}$

2. If matrix A = $\begin{bmatrix} 1 & 0 & -1\\ 3& 4 &5 \\ 0 & 6 & 7 \end{bmatrix}$ and its inverse is denoted by A-1 = $\begin{bmatrix} a_{11} & a_{12} &a_{13}\\ a_{21}& a_{22} &a_{23} \\ a_{31} &a_{32} & a_{33} \end{bmatrix}$, then the value of a23 =
a) $\frac{21}{20}$
b) $\frac{1}{5}$
c) $-\frac{1}{5}$
d) $\frac{2}{5}$

• 5. Continuity and Differentiability - Quiz

1. The function f(x) = [x]2 - [x2], (where [y] is the greatest integer less than or equal to y), is discontinuous at
a) All integers
b) All integers except 0 and 1
c) All integers except 0
d) All integers except 1

2. A = {1,2,3,4}, B = {1,2,3,4,5,6} are two sets and function f : A → B is defined by f(x) = x + 2, ∀ x ε A, then the function f is
a) Bijective
b) Onto
c) One-one
d) Many-one

• 6. Differentiation and Application of Derivatives - Quiz

1. f(x) = x5 - 5x4 + 5x3 + 1 has
a) Two maximum and two minimum value
b) Two maximum and one minimum value
c) One maximum and one minimum value
d) None of these

2. If y = $tan^{-1}\left (\frac{cosx}{1 + sinx} \right )$, then $\frac{dy}{dx}$ is equal to
a) $\frac{1}{2}$
b) 2
c) -2
d) $\frac{-1}{2}$
e) -1

• 7. Integrals - Quiz

• 8. Application of Integrals - Quiz

1. $int_{\pi/4}^{3\pi/4}\frac{dx}{1 + cosx}$ is equal to
a) 2
b) 2
c) $\frac{1}{2}$
d) $-\frac{1}{2}$

2. If [x] is the greatest integer function not greater than x, then $\int_{0}^{11}\left [x \right ]dx$ =
a) 55
b) 45
c) 66
d) 35

• 9. Differential Equations - Quiz

1. Solution of $\frac{dy}{dx}$ = $\frac{xlogx^{2} + x}{siny + ycosy}$ is
a) ysiny = x2logx + c
b) ysiny = x2 + c
c) ysiny = x2 + logx + c
d) ysiny = xlogx + c

2. A solution of the differential equation $\left (\frac{dy}{dx} \right )^{2} - x\frac{dy}{dx} + y$ = 0 is
a) y = 2
b) y = 2x
c) y = 2x - 4
d) y = 2x2 - 4

• 10. Vector Algebra - Quiz

1. If ABCDEF is regular hexagon, then $\overrightarrow{AD}$ + $\overrightarrow{EB}$ + $\overrightarrow{FC}$ =
a) 0
b) 2$\overrightarrow{AB}$
c) $3\overrightarrow{AB}$
d) $4\overrightarrow{AB}$

2. If a and b are two unit vectors such that a + 2b and 5a - 4b are perpendicular to each other, then the angle between a and b is
a) 450
b) 600
c) $cos^{-1}\left (\frac{1}{3} \right )$
d) $cos^{-1}\left (\frac{2}{7} \right )$

• 11. Three Dimensional Geometry - Quiz

1. In the space the equation by + cz + d = 0 represents a plane perpendicular to the plane
a) YOZ
b) Z = k
c) ZOX
d) XOY

2. The equation of the plane containing the lines
$\frac{x - 1}{2}$ = $\frac{y + 1}{-1}$= $\frac{z}{3}$ and $\frac{x}{2}$ = $\frac{y - 2}{-1}$ = $\frac{z + 1}{3}$ is
a) 8x - y + 5z - 8 = 0
b) 8x + y - 5z - 7 = 0
c) x - 8y + 3z + 6 = 0
d) 8x + y - 5z + 7 = 0
e) x + y + z - 6 = 0

• 12. Linear Programming - Quiz

1. For the following shaded area, the linear constraints except x ≥ 0 and y ≥ 0, are

a) 2x + y ≤ 2, x - y ≤ 1, x + 2y ≤ 8
b) 2x + y ≥ 2, x - y ≤ 1, x + 2y ≤ 8
c) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≤ 8
d) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≥ 8

2. 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

• 13. Probability - Quiz

1. Among 15 players, 8 are batsman and 7 are bowlers . Find the probability that a team is chosen of 6 batsman and 5 bowlers
a) $\frac{^{8}C_{6} \times ^{7}C_{5}}{^{15}C_{11}}$
b) $\frac{^{8}C_{6} + ^{7}C_{5}}{^{15}C_{11}}$
c) $\frac{15}{28}$
d) None of these

2. An unbiased coin is tossed. If the result is a head, a pait of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked andt he number on the card is noted. The probability that the noted number is either 7 or 8 is
a) 0.24
b) 0.244
c) 0.024
d) None of these

• 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. $\int \frac{x + sinx}{1 + cosx}dx$ is equal to
a) $-xtan\frac{x}{2}+ c$
b) $xtan\frac{x}{2}+ c$
c) xtanx + c
d) $\frac{1}{2}xtanx + c$

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

1. The intercepts on x-axis made by tangents to the curve, y = $\int_{0}^{x}|t| dt, x \epsilon R$, which are parallel to the line y = 2x, are equal to
a) ±1
b) ±2
c) ±3
d) ±4

2. Let a,b,c be non-zero real numbers such that $\int_{0}^{3}\left (3ax^{2} + 2bx + c \right )dx$ = $\int_{1}^{3}\left (3ax^{2} + 2bx + c \right )dx$, then
a) a + b + c = 3
b) a + b + c = 1
c) a + b + c = 0
d) a + b + c = 2