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 cos^{1}(cos12)  sin^{1}(sin 14) is
a) 2
b) 8π  26
c) 4π + 2
d) None of these
2. $sin\left (\frac{1}{2}cos^{1}\frac{4}{5} \right )$
a) $\frac{1}{\sqrt{10}}$
b) $\frac{1}{\sqrt{10}}$
c) $\frac{1}{10}$
d) $\frac{1}{10}$

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. Matrix A = $\begin{bmatrix} 1& 0&k \\ 2& 1& 3\\ k&0 & 1 \end{bmatrix}$ is invertible for
a) k = 1
b) k = 1
c) k = 0
d) All real k

5. Continuity and Differentiability  Quiz
1. The function f:R $\sim$ {0} → R, f(x) = $\frac{1}{x}  \frac{2}{e^{2x}  1}$ can be made continuous at x = 0 by defining f(0) as
a) 2
b) 1
c) 0
d) 1
2. Let f(x) = [x^{3}  3], [x] = G.I.F. then the no. of points in the interval (1,2) where function Is discontinuous is
a) 5
b) 4
c) 6
d) 3

6. Differentiation and Application of Derivatives  Quiz
1. If the normal to the curve y^{2} = 5x  1, at the point (1,2) is of the form ax  5y + b = 0, then a and b are
a) 4,14
b) 4,14
c) 4,14
d) 4, 14
2. Let y = $\left (\frac{3^{x}  1}{3^{x} + 1} \right )sinx + log_{e}\left (1 + x \right ),x > 1$. Then at x = 0, $\frac{dy}{dx}$ equals
a) 1
b) 0
c) 1
d) 2

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 area of figure bounded by y = e^{x}, y = e^{x} and the straight line x = 1 is
a) e + $\frac{1}{e}$
b) e  $\frac{1}{e}$
c) e + $\frac{1}{e}$  2
d) e + $\frac{1}{e}$ + 2

9. Differential Equations  Quiz
1. The solution of the differential equation $\frac{dy}{dx}$ = $\frac{xy}{x^{2} + y^{2}}$ is
a) ay^{2} = $e^{x^{2}/y^{2}}$
b) ay = e^{x/y}
c) y = $e^{x^{2}} + e^{y^{2}} + c$
d) y = $e^{x^{2}} + e^{y} + c$
2. Order of the differential equation of the family of all concentric circles centered at (h,k) is
a) 1
b) 2
c) 3
d) 4

10. Vector Algebra  Quiz
1. Let ABCD be a parallelogram such that $\overrightarrow{AB}$ = $\vec{q}.\overrightarrow{AD}$ = $\vec{p}$ and ∠BAD be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\vec{r}$ is given by
a) $\vec{r}$ = $3\vec{q}  \frac{3\left (\vec{p}.\vec{q} \right )}{\left (\vec{p}.\vec{p} \right )}\vec{p}$
b) $\vec{r}$ = $\vec{q}  \frac{\left (\vec{p}.\vec{q} \right )}{\left (\vec{p}.\vec{p} \right )}\vec{p}$
c) $\vec{r}$ = $\vec{q}  \frac{\left (\vec{p}.\vec{q} \right )}{\left (\vec{p}.\vec{p} \right )}\vec{p}$
d) $\vec{r}$ = $3\vec{q} + \frac{3\left (\vec{p}.\vec{q} \right )}{\left (\vec{p}.\vec{p} \right )}\vec{p}$
2. The vectors 2i + 3j  4k and ai + bj + ck are perpendicular, when
a) a = 2, b = 3, c = 4
b) a = 4, b = 4, c = 5
c) a = 4, c = 4, c = 5
d) None of these

11. Three Dimensional Geometry  Quiz
1. If the direction cosines of a line are $\left (\frac{1}{c}, \frac{1}{c}, \frac{1}{c} \right )$, then
a) c > 0
b) c = ±$\sqrt{3}$
c) 0 < c < 1
d) c > 2
2. A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron OABC is
a) $x^{2} + y^{2} + z^{2}$ = $16p^{2}$
b) $x^{2} + y^{2} + z^{2}$ = $16p^{1}$
c) $x^{2} + y^{2} + z^{2}$ = 16
d) None of these

12. Linear Programming  Quiz
1. A cold drink factory has two plants located at Bhopal and Gwalior. Each plant produces three diferent types of drinks A,B,C . The production capacity of the plants per day is as follows
Drinks Plant at Bhopal Plant at Gwalior A 6,000 Bottles 2,000 Bottles B 1,000 Bottles 2,500 Bottles C 3,000 Bottles 3,000 Bottles
A demand of 80,000 bottles of A, 22,000 bottles of B and 40,000 bottles of C in the month of June is forecasted. The operating costs per day of plants at Bhopal and Gwalior are Rs. 6,000 and Rs. 4000 respectively. The number of days for which each plant must be run in June so as to minimize the operating costs in meeting the demand are
a) 12,4
b) 4,12
c) 40,0
d) None of these
2. Shaded region is represented by
a) 4x  2y ≤ 3
b) 4x  2y ≤ 3
c) 4x  2y ≥ 3
d) 4x  2y ≥ 3

13. Probability  Quiz
1. If A and B are independent events of a random experiment such that P(A ∩ B) = $\frac{1}{6}$ and ($\bar{A}$ ∩ $\bar{B}$) = $\frac{1}{3}$, then P(A) is equal to (Here, $\bar{E}$ is the complement of the event E)
a) $\frac{1}{4}$
b) $\frac{1}{3}$
c) $\frac{1}{2}$
d) $\frac{2}{3}$
2. Um A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random from urn A, the probability that it is found to be red, is
a) 32/55
b) 21/55
c) 19/55
d) None of these

14. Statistics and Dynamics  Quiz

15. Indefinite Integration  Quiz
1. $\int \frac{e^{2x} + 1}{e^{2x}  1}dx$ equals
a) $log\left (e^{x}  e^{x} \right ) + c$
b) $log\left (e^{x} + e^{x} \right ) + c$
c) $log\left (e^{x}  e^{x} \right ) + c$
d) $log\left (1  e^{x} \right ) + c$
2. $\int 2x cos^{3}x^{2}sinx^{2}dx$ =
a) $\frac{1}{4}xos^{4}x^{2} + c$
b) $\frac{1}{4}xos^{4}x^{2} + c$
c) cos^{4}x^{2} + c
d) None of these

16. Definite Integration and Area under the curve  Quiz
1. The part of circle x^{2} + y^{2} = 9 in between y = 0 and y = 2 is revolved about y axis. The volume of generating solid will
a) $\frac{46}{3}\pi$
b) 12π
c) 16π
d) 28π
2. The value of $\int_{1/e}^{tanx}\frac{tdt}{1 + t^{2}} + \int_{1/e}^{cotx}\frac{dt}{t\left (1 + t^{2} \right )}$ =
a) 1
b) 1
c) 0
d) None of these