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^{1}x + cos^{1}2x + π = 0, the number of real solution is
a) 1
b) 2
c) 0
d) ∞
2. The solution of sin^{1}x  sin^{1}2x = $\frac{\pm \pi}{3}$ 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 a_{23} =
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}  [x^{2}], (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) Oneone
d) Manyone

6. Differentiation and Application of Derivatives  Quiz
1. f(x) = x^{5}  5x^{4} + 5x^{3} + 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 = x^{2}logx + c
b) ysiny = x^{2} + c
c) ysiny = x^{2} + 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 = 2x^{2}  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) 45^{0}
b) 60^{0}
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 = x_{1} + x_{2} such that 2x_{1} + x_{2} ≤ 1 , x_{1} ≤ 2, x_{1} + x_{2} ≤ 3 and x_{1}, x_{2} ≥ 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 xaxis 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 nonzero 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