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 $tan\left [sin^{-1}\left (\frac{3}{5} \right ) + cos^{-1}\left (\frac{3}{\sqrt{13}} \right ) \right ]$ is
    a) $\frac{6}{17}$
    b) $\frac{6}{\sqrt{13}}$
    c) $\frac{\sqrt{13}}{5}$
    d) $\frac{17}{6}$

    2. Th greatest and the least value of (sin-1x)3 + (cos-1x)3 are
    a) $-\frac{\pi}{2}, \frac{\pi}{2}$
    b) $-\frac{\pi^{3}}{8}, \frac{\pi^{3}}{8}$
    c) $\frac{7\pi^{3}}{8}, \frac{\pi^{3}}{32}$
    d) None of these

  • 3. Matrices - Quiz

  • 4. Determinants and Matrices - Quiz

    1. 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

    2. The value of $\begin{bmatrix} 41&42 &43 \\ 44& 45&46 \\ 47&48& 49 \end{bmatrix}$
    a) 2
    b) 4
    c) 0
    d) 1

  • 5. Continuity and Differentiability - Quiz

    1. If f(x) = $\left\{\begin{matrix} \frac{1 - sinx}{\pi - 2x}, & x \ne \frac{\pi}{2}\\ \lambda, &x = \frac{\pi}{2} \end{matrix}\right.$, be continuous at x = π/2, then value of λ is
    a) -1
    b) 1
    c) 0
    d) 2

    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 y = $\frac{e^{x} + e^{-x}}{e^{x} - e^{-x}}$ then $\frac{dy}{dx}$is equal to
    a) sech2x
    b) cosech2x
    c) -sech2x
    d) -cosech2x

    2. If xy = ex-y, then $\frac{dy}{dx}$ =
    a) logx.[log(ex)]-2
    b) logx.[log(ex)]2
    c) logx.log(ex)2
    d) None of these

  • 7. Integrals - Quiz

  • 8. Application of Integrals - Quiz

    1. The solution for x of the equation $\int_{\sqrt{2}}^{x}\frac{dt}{t\sqrt{t^{2} - 1}}$ = $\frac{\pi}{12}$dx, is
    a) 2
    b) π
    c) $\frac{\sqrt{3}}{2}$
    d) 2$\sqrt{2}$

    2. 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

  • 9. Differential Equations - Quiz

    1. A solution of the differential equation $\left (\frac{dy}{dx} \right )^{2} - x\frac{dy}{dx} + y$ = 0 is
    a) y = 2
    b) y = 2x
    c) y = 2x - 4
    d) y = 2x2 - 4

    2. Solution of the differential equation $sin\frac{dy}{dx}$ = a with y(0) = 1 is
    a) $sin^{-1}\frac{\left (y - 1 \right )}{x}$ = a
    b) $sin\frac{\left (y - 1 \right )}{x}$ = a
    c) $sin^{-1}\frac{\left (1 - y \right )}{\left (1 + x \right )}$ = a
    d) $sin^{-1}\frac{y}{\left (x + 1 \right )}$ =a

  • 10. Vector Algebra - Quiz

    1. A vector of magnitude 14 lies in the xy-plane and makes an angle of 600 with x-axis . The components of the vector in the direction of x-axis and y-axis are
    a) 7,7$\sqrt{3}$
    b) 7$\sqrt{3}$, 7
    c) 14$\sqrt{3}$, 14/$\sqrt{3}$
    d) 14/$\sqrt{3}$, 14$\sqrt{3}$

    2. A vector of magnitude 5 and perpendicular to $\hat{i} - 2\hat{j} + \hat{k}$ and $\left (2\hat{i} + \hat{j} - 3\hat{k} \right )$ is
    a) $\frac{5\sqrt{3}}{3}\left (\hat{i} + \hat{j} - \hat{k} \right )$
    b) $\frac{5\sqrt{3}}{3}\left (\hat{i} + \hat{j} + \hat{k} \right )$
    c) $\frac{5\sqrt{3}}{3}\left (\hat{i} - \hat{j} + \hat{k} \right )$
    d) $\frac{5\sqrt{3}}{3}\left (-\hat{i} + \hat{j} + \hat{k} \right )$

  • 11. Three Dimensional Geometry - Quiz

    1. Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2 . If L makes an angle α with the positive x-axis , then cosα equals
    a) $\frac{1}{\sqrt{3}}$
    b) $\frac{1}{2}$
    c) 1
    d) $\frac{1}{\sqrt{2}}$

    2. The direction cosines 1,m,n of two lines are perpendicular are connected by the relation 1 - 5m + 3n = 0 and 7l2 + 5m2 - 3n2 = 0 the angle between them is
    a) $\frac{5}{\sqrt{84}}$
    b) $\frac{6}{\sqrt{84}}$
    c) $\frac{7}{\sqrt{84}}$
    d) $\frac{9}{\sqrt{84}}$

  • 12. Linear Programming - Quiz

    1. By graphical method, the solution of linear programming problem
    Maximize z = 3x1 + 5x2
    Subject to 3x1 + 2x2 ≤ 18 , x1 ≤ 4, x2 ≤ 6, x1 ≥ 0, x2 ≥ 0 is
    a) x1 = 2, x2 = 0, z = 6
    b) x1 = 2, x2 = 6, z = 36
    c) x1 = 4, x2 = 3, z = 27
    d) x1 = 4, x2 = 6, z = 42

    2. Inequations 3x - y ≥ 3 and 4x - y > 4
    a) Have solution for positive x and y
    b) Havo no solution for positive x and y
    c) Have solution for all x
    d) Have solution for all y

  • 13. Probability - Quiz

    1. If P(S) = 0.3, P(T) = 0.4. S and T are independent events, then P(S/T)
    a) 0.2
    b) 0.3
    c) 0.13
    d) 0.4

    2. The probability distribution of a random variable X is given as
    x -5 -4 -3 -2 -1 0 1 2 3 4 5
    p(X = x) p 2p 3p 4p 5p 7p 8p 9p 10p 11p 12p
    0
    The value of p is
    a) $\frac{1}{72}$
    b) $\frac{3}{73}$
    c) $\frac{5}{72}$
    d) $\frac{1}{74}$
    e) $\frac{1}{73}$

  • 14. Statistics and Dynamics - Quiz

  • 15. Indefinite Integration - Quiz

    1. $\int \frac{sin^{-1}x}{\sqrt{1 - x^{2}}}dx$ is equal to
    a) $log\left (sin^{-1}x \right ) + c$
    b) $\frac{1}{2}\left (sin^{-1}x \right )^{2} + c$
    c) $log\left (\sqrt{1 - x^{2}} \right ) + c$
    d) sin(cos-1x) + c

    2. $\int \frac{secx}{\sqrt{sin\left (2x + \alpha \right ) + sin\alpha}}dx$ 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

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

    1. If for a real number y, [y] is the greatest integer less than or equal to y, then the value of integral $\int_{\pi/2}^{3\pi/2}\left [2 sinx \right ]dx$ is
    a) -π
    b) 0
    c) $-\frac{\pi}{2}$
    d) $\frac{\pi}{2}$

    2. The follwing integral $\int_{\frac{\pi}{2}}^{\frac{\pi}{2}}\left (2cosec x \right )^{17}dx$ is equal to
    a) $\int_{0}^{log\left (1 + \sqrt{2} \right )}2\left (e^{u} + e^{-u} \right )^{16}du$
    b) $\int_{0}^{log\left (1 + \sqrt{2} \right )}2\left (e^{u} + e^{-u} \right )^{17}du$
    c) $\int_{0}^{log\left (1 + \sqrt{2} \right )}2\left (e^{u} - e^{-u} \right )^{17}du$
    d) $\int_{0}^{log\left (1 + \sqrt{2} \right )}2\left (e^{u} - e^{-u} \right )^{16}du$