Class/Course - Class XII

Subject - Math

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. Interested person may contact us at info@justexam.in


  • 1. Relations and Functions - Quiz

  • 2. Inverse Trigonometric Functions - Quiz

    1. The value of $sin^{-1}\left (\frac{\sqrt{3}}{2} \right ) - sin^{-1}\left (\frac{1}{2} \right )$ is
    a) 450
    b) 900
    c) 150
    d) 300
    2. The equation 2cos-1x + sin-1 = $\frac{11\pi}{6}$ has
    a) No solution
    b) Only one solution
    c) Two solutions
    d) Three solutions
  • 3. Matrices - Quiz

  • 4. Determinants and Matrices - Quiz

    1. If A = [aij]2x2, where $a_{ij} = \left\{\begin{matrix} i +j, if \ i \ne j\\ i^{2} - 2j, if \ i = j \end{matrix}\right.$, then A01 is equal to
    a) $\frac{1}{9}\begin{bmatrix} 4 &1 \\ -1& 2 \end{bmatrix}$
    b) $\frac{1}{9}\begin{bmatrix} 0 &-3 \\ -3& -1 \end{bmatrix}$
    c) $\frac{1}{9}\begin{bmatrix} 0 &3 \\ 3& 1 \end{bmatrix}$
    d) None of these
    2. The values of x,y,z in order of the system of equations 3x + y + 2z = 3, 2x - 3y - z = -3, x + 2y + z = 4, are
    a) 2,1,5
    b) 1,1,1
    c) 1,-2,-1
    d) 1,2,-1
  • 5. Continuity and Differentiability - Quiz

    1. If f(x) = x($\sqrt{x}$ - $\sqrt{x-1}$), then
    a) f(x) is continuous but non-differentiable at x = 0
    b) f(x) is differentiable at x = 0
    c) f(x) is not differentiable at x = 0
    d) None of these
    2. $lim_{x \rightarrow 0} \frac{sin\left (\pi cos^{2}x \right )}{x^{2}}$ =
    a) -π
    b) π
    c) π/2
    d) 1
  • 6. Differentiation and Application of Derivatives - Quiz

    1. If y = sinx + ex, then $\frac{d^{2}y}{dy^{2}}$ =
    a) (-sinx + ex)-1
    b) $\frac{sinx - e^{x}}{\left (cosx + e^{x} \right )}^{2}$
    c) $\frac{sinx - e^{x}}{\left (cosx + e^{x} \right )}^{3}$
    d) $\frac{sinx + e^{x}}{\left (cosx + e^{x} \right )}^{3}$
    2. If f(x) = $\frac{1}{4x^{2} + 2x + 1}$ , then its maximum value is
    a) 4/3
    b) 2/3
    c) 1
    d) 3/4
  • 7. Integrals - Quiz

  • 8. Application of Integrals - Quiz

    1. The value of $\int_{0}^{0\pi + v}\left | sinx \right |dx$ is
    a) 2n + 1 + cosv
    b) 2n - 1 - cosv
    c) 2n + 1
    d) 2n + cosv
    2. $\int_{0}^{\pi/2}\left (sinx - cosx \right )log\left (sinx + cosx \right )dx$ =
    a) -1
    b) 1
    c) 0
    d) None of these
  • 9. Differential Equations - Quiz

    1. The differential equation of the system of all circles of radius r in the xy-plane, is
    a) $\left [1 + \left (\frac{dy}{dx} \right )^{3} \right ]^{2}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{2}$
    b) $\left [1 + \left (\frac{dy}{dx} \right )^{3} \right ]^{2}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{3}$
    c) $\left [1 + \left (\frac{dy}{dx} \right )^{2} \right ]^{3}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{2}$
    d) $\left [1 + \left (\frac{dy}{dx} \right )^{2} \right ]^{3}$ = $r^{2}\left (\frac{d^{2}y}{dx^{2}} \right )^{3}$
    2. If $\left ( \frac{dy}{dx} \right )$ = e -2y and y = 0 when x = 5, than value of x for y = 3 is
    a) e5
    b) e6 + 1
    c) $\frac{e^{6} + 9}{2}$
    d) loge6
  • 10. Vector Algebra - Quiz

    1. If a of magnitude 50 is collinear with the vector b = 6i - 8j - $\frac{15k}{2}$, and makes an acute angle with the positive direction of z-axis then the vector a is equal to
    a) 24i - 32j + 30k
    b) -24i + 32j + 30k
    c) 16i - 16j - 15k
    d) -12i + 16j - 30k
    2. Let two non-collinear unit vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves so that at any time t the position vector $\overrightarrow{OP}$ (where O is the origin) is given by $\hat{a}cost + \hat{b}sint$. When P is farthest from origin O, let M be the length of $\overrightarrow{OP}$ and $\hat{u}$ be the unit vector along $\overrightarrow{OP}$. Then,
    a) $\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$
    b) $\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$
    c) $\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$
    d) $\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$
  • 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. If the plane 3x + y + 2z + 6 = 0 is parallel to the line $\frac{3x - 1}{2b}$ = 3 - y = $\frac{z - 1}{a}$, then the value of 3a + 3b is
    a) $\frac{1}{2}$
    b) $\frac{3}{2}$
    c) 3
    d) 4
    e) $\frac{5}{2}$
  • 12. Linear Programming - Quiz

    1. Shaded region is represented by

    a) 4x - 2y ≤ 3
    b) 4x - 2y ≤ -3
    c) 4x - 2y ≥ 3
    d) 4x - 2y ≥ -3
    2. The maximum value of z = 5x - 3y subjected to the conditions 3x + 5y ≤ 5x + 2y ≤ 10, x, y ≥ 0 is
    a) $\frac{235}{19}$
    b) $\frac{325}{19}$
    c) $\frac{529}{19}$
    d) $\frac{532}{19}$
  • 13. Probability - Quiz

    1. A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is
    a) $\frac{1}{3}$
    b) $\frac{1}{2}$
    c) $\frac{1}{4}$
    d) None of these
    2. Three numbers are chosen at random without replacement from {1,2,3,…,8}. The probability that their minimum is 3, given that their maximum is 6, is
    a) $\frac{3}{8}$
    b) $\frac{1}{5}$
    c) $\frac{1}{4}$
    d) $\frac{2}{5}$
  • 14. Statistics and Dynamics - Quiz

  • 15. Indefinite Integration - Quiz

    1. Let I = $\int \frac{e^{x}}{e^{4x} + e^{2x} + 1}dx$,J = $\int \frac{e^{-x}}{e^{-4x} + e^{-2x} + 1}dx$. Then, for an arbitrary constant C, the value of J-I equals
    a) $\frac{1}{2}log\left (\frac{e^{4x} - e^{2x} + 1 }{e^{4x} + e^{2x} + 1}\right ) + C$
    b) $\frac{1}{2}log\left (\frac{e^{2x} + e^{x} + 1 }{e^{2x} - e^{x} + 1}\right ) + C$
    c) $\frac{1}{2}log\left (\frac{e^{2x} - e^{x} + 1 }{e^{2x} + e^{x} + 1}\right ) + C$
    d) $\frac{1}{2}log\left (\frac{e^{4x} + e^{2x} + 1 }{e^{4x} - e^{2x} + 1}\right ) + C$
    2. $\int a^{x} dx$ =
    a) $\frac{a^{x}}{log a} + c$
    b) $a^{x}log a + c$
    c) log a + c
    d) ax + c
  • 16. Definite Integration and Area under the curve - Quiz

    1. $\int_{0}^{1}sin\left (2tan^{-1}\sqrt{\frac{1 + x}{1 - x}} \right )dx$ =
    a) π/6
    b) π/4
    c) π/2
    d) π
    2. $\int_{0}^{\infty}\frac{x ln x dx}{\left (1 + x^{2} \right )^{2}}$ is equal to
    a) 0
    b) 1
    c) ∞
    d) None of these