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 2sin-1x - cos-1x = $\frac{\pi}{2}$, then x is equal to
    a) 1/$\sqrt{2}$
    b) -1/$\sqrt{2}$
    c) $-\sqrt{3/2}$
    d) $\sqrt{3}2$
    e) 1/2

    2. The solution of sin-1x - sin-12x = $\frac{\pm \pi}{3}$ 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


    SAMPLE QUESTIONS


  • 4. Determinants and Matrices - Quiz


    SAMPLE QUESTIONS


    1. If a ≠ p, b ≠ 1, c ≠ r and $\begin{vmatrix} p& q& r\\ p+a& q+b &2c \\ a & b &r \end{vmatrix}$ = 0, then $\frac{p}{p - a} + \frac{q}{q - b} + \frac{r}{r - c}$ =
    a) 3
    b) 2
    c) 1
    d) 0

    2. l,m,n are the pth, qth and rth term of a G.P. , all positive then $\begin{vmatrix} log l & p &1 \\ logm& q & 1\\ log n& r& 1 \end{vmatrix}$ equals
    a) -1
    b) 2
    c) 1
    d) 0

  • 5. Continuity and Differentiability - Quiz


    SAMPLE QUESTIONS


    1. The value of $lim_{x \rightarrow 0}\frac{\sqrt{x^{2} + 1} - 1}{\sqrt{x^{2} + 9} - 3}$ is
    a) 3
    b) 4
    c) 1
    d) 2

    2. The function f(x) = $\frac{1 - sinx + cosx}{1 + sin x cosx}$ is not defined at x = π. The value of f(π) , so that f(x) is continuous at x = π, is
    a) -1/2
    b) 1/2
    c) -1
    d) 1

  • 6. Differentiation and Application of Derivatives - Quiz


    SAMPLE QUESTIONS


    1. The maximum value of xe-x is
    a) $-\frac{1}{e}$
    b) e
    c) $\frac{1}{e}$
    d) -e

    2. The derivative of f(x) = |x2 - x| at x = 2 is
    a) -3
    b) 0
    c) 3
    d) Not defined

  • 7. Integrals - Quiz


    SAMPLE QUESTIONS


  • 8. Application of Integrals - Quiz


    SAMPLE QUESTIONS


    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 the definite integral $\int_{0}^{1}\frac{xdx}{x^{3} + 16}$ lies in the interval [a,b]. The smallest such interval is
    a) $\left [0,\frac{1}{17} \right ]$
    b) [0,1]
    c) $\left [0,\frac{1}{27} \right ]$
    d) None of these

  • 9. Differential Equations - Quiz


    SAMPLE QUESTIONS


    1. Solution of $\frac{dy}{dx}$ = $\frac{xlogx^{2} + x}{siny + ycosy}$ is
    a) ysiny = x2logx + c
    b) ysiny = x2 + c
    c) ysiny = x2 + logx + c
    d) ysiny = xlogx + c

    2. The order and degree of the differential equation $x\left (\frac{d^{3}y}{dx^{3}} \right )^{2} + y\left (\frac{dy}{dx} \right )^{4} + y^{2}$ = 0 is
    a) Order2, degree 3
    b) Order 3, degree 2
    c) Order 2, degree 2
    d) None of these

  • 10. Vector Algebra - Quiz


    SAMPLE QUESTIONS


    1. If the position vectors of A, B, C, D are 2i + j, i - 3j, 3i + 2j and i + λj respectively and $\overrightarrow{AB}$ || $\overrightarrow{CD}$, then λ will be
    a) -8
    b) -6
    c) 8
    d) 6

    2. If ABCDEF is regular hexagon, then $\overrightarrow{AD}$ + $\overrightarrow{EB}$ + $\overrightarrow{FC}$ =
    a) 0
    b) 2$\overrightarrow{AB}$
    c) $3\overrightarrow{AB}$
    d) $4\overrightarrow{AB}$

  • 11. Three Dimensional Geometry - Quiz


    SAMPLE QUESTIONS


    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. From a point P(λ, λ, λ) perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x , z = -1. If P is such that ∠QPR is a right angle, then the possible value (s) of λ is (are)
    a) $\sqrt{2}$
    b) 1
    c) -1
    d) $-\sqrt{2}$

  • 12. Linear Programming - Quiz


    SAMPLE QUESTIONS


    1. The point which provides the solution of the linear programming problem Max. (45x + 55y) subject to constraint x,y ≥ 0.6x + 4y ≥ 120 . 3x + 10y ≤ 180 is
    a) (15,10)
    b) (10,15)
    c) (0,18)
    d) (20,0)

    2. The maximum value of z = 4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10 ; x , y ≥ 0 is
    a) 36
    b) 40
    c) 20
    d) None of these

  • 13. Probability - Quiz


    SAMPLE QUESTIONS


    1. One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls . A balls is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is
    a) 8/17
    b) 40/153
    c) 5/9
    d) 4/9

    2. Let A and B be events for which P(A) = x, P(B) = y, P(A ∩ B) = z, then P($\bar{A}$ ∩ B) equals
    a) (1 - x)y
    b) 1 - x + y
    c) y - z
    d) 1 - x + y - z

  • 14. Statistics and Dynamics - Quiz


    SAMPLE QUESTIONS


  • 15. Indefinite Integration - Quiz


    SAMPLE QUESTIONS


    1. $\int \frac{\sqrt{x}}{1 + x}dx$ =
    a) $\sqrt{x} - tan^{-1}\sqrt{x} + c$
    b) $2\left (\sqrt{x} - tan^{-1}\sqrt{x} \right ) + c$
    c) $2\left (\sqrt{x} + tan^{-1}\sqrt{x} \right ) + c$
    d) $\sqrt{1 + x}+ c$

    2. $\int \frac{cos2x + x + 1}{x^{2} + sin2x + 2x}dx$ =
    a) $log\left (x^{2} + sin2x + 2x \right ) + c$
    b) $-log\left (x^{2} + sin2x + 2x \right ) + c$
    c) $\frac{1}{2}log\left (x^{2} + sin2x + 2x \right ) + c$
    d) None of these

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


    SAMPLE QUESTIONS


    1. The value of the integral $\int_{-\pi/2}^{\pi/2}\left (x^{2} + ln\frac{\pi + x}{\pi - x} \right )cosx dx$ is
    a) 0
    b) $\frac{\pi^{2}}{2} - 4$
    c) $\frac{\pi^{2}}{2} + 4$
    d) $\frac{\pi^{2}}{2}$

    2. The area of the region between the curves y = $\sqrt{\frac{1 + sinx}{cosx}}$ and y = $\sqrt{\frac{1 - sinx}{cosx}}$ bounded by the lines x = 0 and x = $\frac{\pi}{4}$ is
    a) $\int_{0}^{\sqrt{2}-1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
    b) $\int_{0}^{\sqrt{2}-1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
    c) $\int_{0}^{\sqrt{2}+1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
    d) $\int_{0}^{\sqrt{2}+1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$