## 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) = [x3 - 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 y2 = 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 = ex, 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) ay2 = $e^{x^{2}/y^{2}}$
b) ay = ex/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) cos4x2 + c
d) None of these

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

1. The part of circle x2 + y2 = 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