Total Number of Question/s - 3349

Just Exam provide question bank for Class XII standard. Currently number of question's are 3349. We provide this data in all format (word, excel, pdf, sql, latex form with images) to institutes for conducting online test/ examinations. Here we are providing some demo contents.

• 1. Relations and Functions - Quiz

SAMPLE QUESTIONS

• 2. Inverse Trigonometric Functions - Quiz

SAMPLE QUESTIONS

1. If (tan-1 x)2 + (cot-1x)2 = $\frac{5\pi^{2}}{8}$, then x equals
a) -1
b) 1
c) 0
d) None of these

2. If sin-1x = $\frac{\pi}{5}$ for some x ε (-1,1), then the value of cos-1x is
a) $\frac{3\pi}{10}$
b) $\frac{5\pi}{10}$
c) $\frac{7\pi}{10}$
d) $\frac{9s\pi}{10}$

• 3. Matrices - Quiz

SAMPLE QUESTIONS

• 4. Determinants and Matrices - Quiz

SAMPLE QUESTIONS

1. Let M and N be two even order non-singular skew-symmetric matrices such that MN = NM . If PT denotes the transpose of P, then M2N2(MTN)-1(MN-1)T is equal to
a) M2
b) -N2
c) -M2
d) MN

2. The sum of the products of the elements of any row of a determinant A with the co-factor of same row is always equal to
a) 1
b) 0
c) |A|
d) $\frac{1}{2}|A|$

• 5. Continuity and Differentiability - Quiz

SAMPLE QUESTIONS

1. $lim_{n \rightarrow \infty} \left (\frac{n^{2} - 1 + 1}{n^{2} - n - 1} \right )^{n\left (n - 1 \right )}$ =
a) e
b) e2
c) 2-1
d) 1

2. The function f(x) = $log\left (\frac{1 + x}{1 - x} \right )$ satisfies the equation
a) f(x + 2) - 2f(x + 1) + f(x) = 0
b) f(x) + f(x + 1) = f(x(x + 1))
c) f(x) + f(y) = $f\left (\frac{x + y}{1 + xy} \right )$
d) f(x + y) = f(x)f(y)

• 6. Differentiation and Application of Derivatives - Quiz

SAMPLE QUESTIONS

1. The radius of a cylinder is increasing at the rate of 3 m/sec and its altitude is decreasing at the rate of 4m/sec. The rate of change of volume when radius is 4 metres and altitude is 6 metres is
a) 80π cu. m/sec
b) 144π cu.m/sec
c) 80 cu. m/sec
d) 64 cu. m/sec
e) -80-π cu. m/sec

2. If y = $e^{\sqrt{x}}$, then $\frac{dy}{dx}$ equals
a) $\frac{e^{\sqrt{x}}}{2\sqrt{x}}$
b) $\frac{\sqrt{x}}{e^{\sqrt{x}}}$
c) $\frac{x}{e^{\sqrt{x}}}$
d) $\frac{2\sqrt{x}}{e^{\sqrt{x}}}$

• 7. Integrals - Quiz

SAMPLE QUESTIONS

• 8. Application of Integrals - Quiz

SAMPLE QUESTIONS

1. $lim_{n \rightarrow \infty}\frac{1 + 2^{4} + 3^{4} + .... + n^{4}}{n^{5}}$ - $lim_{n \rightarrow \infty} \frac{1 + 2^{3} + 3^{3} + .... + n^{3}}{n^{5}}$ =
a) $\frac{1}{30}$
b) Zero
c) $\frac{1}{4}$
d) $\frac{1}{5}$

2. Let I = $\int_{0}^{1}\frac{sinx}{\sqrt{x}}dx$ and J = $\int_{0}^{1}\frac{cosx}{\sqrt{x}}dx$. Then which one of the following is true
a) I < $\frac{2}{3}$ and J < 2
b) I < $\frac{2}{3}$ and J > 2
c) I > $\frac{2}{3}$ and J < 2
d) I > $\frac{2}{3}$ and J > 2

• 9. Differential Equations - Quiz

SAMPLE QUESTIONS

1. To reduce the differential equation $\frac{dy}{dx}$ + P(x)y = Q(x).yn to the linear form, the substitution is
a) v = $\frac{1}{y^{n}}$
b) v = $\frac{1}{y^{n-1}}$
c) v = yn
d) v = yn-1

2. If the integrating factor of the differential equation $x\frac{dy}{dx}$ + my = x2ex is x-2, the value of m is
a) -1
b) 1
c) 2
d) -2

• 10. Vector Algebra - Quiz

SAMPLE QUESTIONS

1. If a ≠ 0, b ≠ 0 and |a + b| = |a - b|, then the vectors a and b are
a) Parallel to each other
b) Perpendicular to each other
c) Inclined at an angle of 600
d) Neither perpendicular nor parallel

2. If a and b are two non-zero vectors, then the component of b along a is
a) $\frac{\left (a.b \right )a}{b.b}$
b) $\frac{\left (a.b \right )b}{a.a}$
c) $\frac{\left (a.b \right )b}{a.b}$
d) $\frac{\left (a.b \right )a}{a.a}$

• 11. Three Dimensional Geometry - Quiz

SAMPLE QUESTIONS

1. Equation of the plane parallel to the planes x + 2y + 3z - 5 = 0, x + 2y + 3z - 7 = 0 and equidistant from them is
a) x + 2y + 3z - 6 = 0
b) x + 2y + 3z - 1 = 0
c) x + 2y + 3z - 8 = 0
d) x + 2y + 3z - 3 = 0

2. The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + 4x - 2y - 6z = 155 is
a) 26
b) $11\frac{4}{13}$
c) 13
d) 39

• 12. Linear Programming - Quiz

SAMPLE QUESTIONS

1. In LPP, ΔJ for all basic variables is equal to
a) 1
b) -1
c) 0
d) None of these

2. Variables of the objective function of the linear programming problem are
a) Zero
b) Zero or positive
c) Negative
d) Zero or negative

• 13. Probability - Quiz

SAMPLE QUESTIONS

1. A pair of a dice thrown, if appears on at least one of the dice, then the probability that the sum is 10 or greater is
a) $\frac{11}{36}$
b) $\frac{2}{9}$
c) $\frac{3}{11}$
d) $\frac{1}{12}$

2. If n positive integers are taken at random and multiplied together, the probability that the last digit of the product is 2,4,6 or 8, is
a) $\frac{4^{n} + 2^{n}}{5^{n}}$
b) $\frac{4^{n} \times 2^{n}}{5^{n}}$
c) $\frac{4^{n} - 2^{n}}{5^{n}}$
d) None of these

• 14. Statistics and Dynamics - Quiz

SAMPLE QUESTIONS

• 15. Indefinite Integration - Quiz

SAMPLE QUESTIONS

1. $\int \frac{secx}{\sqrt{sin\left (2x + \alpha \right ) + sin\alpha}}dx$ is equal to
a) $\sqrt{2sec\alpha \left (tanx + tan\alpha \right )}$
b) $\sqrt{2sec\alpha \left (tanx - tan\alpha \right )}$
c) $\sqrt{2sec\alpha \left (tan\alpha - tanx \right )}$
d) None of these

2. $\int cos^{-3/7}xsin^{-11/7}xdx$ =
a) $log|sin^{4/7}x| + c$
b) $\frac{4}{7}tan^{4/7}x + c$
c) $\frac{-7}{4}tan^{4/7} x + c$
d) $log |cos^{3/7}x | + c$
e) $\frac{7}{4}tan^{4/7} x + c$

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

SAMPLE QUESTIONS

1. On the interval $\left [\frac{5\pi}{3}, \frac{7\pi}{4} \right ]$ , the greatest value of the function f(x) = $\int_{6\pi/3}^{x}\left (6cost - 2sint \right )dt$ =
a) 3$\sqrt{2}$ + 2$\sqrt{2}$ + 1
b) 3$\sqrt{2}$ - 2$\sqrt{2}$ - 1
c) Does not exist
d) None of these

2. The area bounded by the curves 4y = x2 and 2y = 6 - x2 is
a) 8
b) 6
c) 4
d) 10

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