Total Number of Question/s - 3349

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  • 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