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. For the equation cos-1x + cos-12x + π = 0, the number of real solution is
    a) 1
    b) 2
    c) 0
    d) ∞

    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

  • 4. Determinants and Matrices - Quiz

    1. If $\begin{bmatrix} sin^{2}\alpha &cos^{2}\alpha \\ cos^{2}\alpha& sin^{2}\alpha \end{bmatrix}$ = 0, α ε (0,π), then the values of α are
    a) $\frac{\pi}{2}$ and $\frac{\pi}{12}$
    b) $\frac{\pi}{2}$ and $\frac{\pi}{6}$
    c) $\frac{\pi}{4}$ and $\frac{3\pi}{4}$
    d) $\frac{\pi}{6}$ and $\frac{\pi}{3}$
    e) $\frac{\pi}{2}$ and $\frac{\pi}{3}$

    2. If matrix A = $\begin{bmatrix} 1 & 0 & -1\\ 3& 4 &5 \\ 0 & 6 & 7 \end{bmatrix}$ and its inverse is denoted by A-1 = $\begin{bmatrix} a_{11} & a_{12} &a_{13}\\ a_{21}& a_{22} &a_{23} \\ a_{31} &a_{32} & a_{33} \end{bmatrix}$, then the value of a23 =
    a) $\frac{21}{20}$
    b) $\frac{1}{5}$
    c) $-\frac{1}{5}$
    d) $\frac{2}{5}$

  • 5. Continuity and Differentiability - Quiz

    1. The function f(x) = [x]2 - [x2], (where [y] is the greatest integer less than or equal to y), is discontinuous at
    a) All integers
    b) All integers except 0 and 1
    c) All integers except 0
    d) All integers except 1

    2. A = {1,2,3,4}, B = {1,2,3,4,5,6} are two sets and function f : A → B is defined by f(x) = x + 2, ∀ x ε A, then the function f is
    a) Bijective
    b) Onto
    c) One-one
    d) Many-one

  • 6. Differentiation and Application of Derivatives - Quiz

    1. f(x) = x5 - 5x4 + 5x3 + 1 has
    a) Two maximum and two minimum value
    b) Two maximum and one minimum value
    c) One maximum and one minimum value
    d) None of these

    2. If y = $tan^{-1}\left (\frac{cosx}{1 + sinx} \right )$, then $\frac{dy}{dx}$ is equal to
    a) $\frac{1}{2}$
    b) 2
    c) -2
    d) $\frac{-1}{2}$
    e) -1

  • 7. Integrals - Quiz

  • 8. Application of Integrals - Quiz

    1. $int_{\pi/4}^{3\pi/4}\frac{dx}{1 + cosx}$ is equal to
    a) 2
    b) 2
    c) $\frac{1}{2}$
    d) $-\frac{1}{2}$

    2. If [x] is the greatest integer function not greater than x, then $\int_{0}^{11}\left [x \right ]dx$ =
    a) 55
    b) 45
    c) 66
    d) 35

  • 9. Differential Equations - Quiz

    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. 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

  • 10. Vector Algebra - Quiz

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

    2. If a and b are two unit vectors such that a + 2b and 5a - 4b are perpendicular to each other, then the angle between a and b is
    a) 450
    b) 600
    c) $cos^{-1}\left (\frac{1}{3} \right )$
    d) $cos^{-1}\left (\frac{2}{7} \right )$

  • 11. Three Dimensional Geometry - Quiz

    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. The equation of the plane containing the lines
    $\frac{x - 1}{2}$ = $\frac{y + 1}{-1}$= $\frac{z}{3}$ and $\frac{x}{2}$ = $\frac{y - 2}{-1}$ = $\frac{z + 1}{3}$ is
    a) 8x - y + 5z - 8 = 0
    b) 8x + y - 5z - 7 = 0
    c) x - 8y + 3z + 6 = 0
    d) 8x + y - 5z + 7 = 0
    e) x + y + z - 6 = 0

  • 12. Linear Programming - Quiz

    1. For the following shaded area, the linear constraints except x ≥ 0 and y ≥ 0, are

    a) 2x + y ≤ 2, x - y ≤ 1, x + 2y ≤ 8
    b) 2x + y ≥ 2, x - y ≤ 1, x + 2y ≤ 8
    c) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≤ 8
    d) 2x + y ≥ 2, x - y ≥ 1, x + 2y ≥ 8

    2. The L.P. problem MaxZ = x1 + x2 such that -2x1 + x2 ≤ 1 , x1 ≤ 2, x1 + x2 ≤ 3 and x1, x2 ≥ 0 has
    a) One solution
    b) Three solution
    c) An infinite no. of solution
    d) None of these

  • 13. Probability - Quiz

    1. Among 15 players, 8 are batsman and 7 are bowlers . Find the probability that a team is chosen of 6 batsman and 5 bowlers
    a) $\frac{^{8}C_{6} \times ^{7}C_{5}}{^{15}C_{11}}$
    b) $\frac{^{8}C_{6} + ^{7}C_{5}}{^{15}C_{11}}$
    c) $\frac{15}{28}$
    d) None of these

    2. An unbiased coin is tossed. If the result is a head, a pait of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked andt he number on the card is noted. The probability that the noted number is either 7 or 8 is
    a) 0.24
    b) 0.244
    c) 0.024
    d) None of these

  • 14. Statistics and Dynamics - Quiz

  • 15. Indefinite Integration - Quiz

    1. If $\int \frac{1}{x + x^{5}}dx$ = f(x) + c, then the value of $\int \frac{x^{4}}{x + x^{5}}dx$ is
    a) logx - f(x) + c
    b) f(x) + logx + c
    c) f(x) - logx + c
    d) None of these

    2. $\int \frac{x + sinx}{1 + cosx}dx$ is equal to
    a) $-xtan\frac{x}{2}+ c$
    b) $xtan\frac{x}{2}+ c$
    c) xtanx + c
    d) $\frac{1}{2}xtanx + c$

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

    1. The intercepts on x-axis made by tangents to the curve, y = $\int_{0}^{x}|t| dt, x \epsilon R$, which are parallel to the line y = 2x, are equal to
    a) ±1
    b) ±2
    c) ±3
    d) ±4

    2. Let a,b,c be non-zero real numbers such that $\int_{0}^{3}\left (3ax^{2} + 2bx + c \right )dx$ = $\int_{1}^{3}\left (3ax^{2} + 2bx + c \right )dx$, then
    a) a + b + c = 3
    b) a + b + c = 1
    c) a + b + c = 0
    d) a + b + c = 2