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. If sin-1x + sin-1y = $\frac{2\pi}{3}$, then cos-1x + cos-1y =
    a) $\frac{2\pi}{3}$
    b) $\frac{\pi}{3}$
    c) $\frac{\pi}{6}$
    d) π/2

    2. $2tan^{-1\left (\frac{1}{3} \right )} + tan^{-1}\left (\frac{1}{7} \right )$ =
    a) $tan^{-1}\left (\frac{49}{29} \right )$
    b) $\frac{\pi}{2}$
    c) 0
    d) π/4

  • 3. Matrices - Quiz

  • 4. Determinants and Matrices - Quiz

    1. If the system of equations x+ay, az + y = 0 and ax + z = 0 has infinite solutions, then the value of a is
    a) -1
    b) 1
    c) 0
    d) No real values

    2. If $\begin{vmatrix} a &b&0 \\ 0& a &b \\ b& 0 & a \end{vmatrix}$ = 0, then
    a) a is one of the cube roots of unity
    b) b is one of the cube roots of unity
    c) $\left ( \frac{a}{b} \right )$ is one of the cube roots of unity
    d) $\left ( \frac{a}{b} \right )$ is one of the cube roots of -1

  • 5. Continuity and Differentiability - Quiz

    1. If f is strictly increasing function, then $lim_{0 \rightarrow 0}\frac{f\left (x^{2} \right ) - f\left (x \right )}{f\left (x \right ) - f\left (0 \right )}$ is equal to
    a) 0
    b) 1
    c) -1
    d) 2

    2. If f(x) = $\frac{x - 1}{x + 1}$, then f(2x) is
    a) $\frac{f\left (x \right ) + 1}{f\left (x \right ) + 3}$
    b) $\frac{3f\left (x \right ) + 1}{f\left (x \right ) + 3}$
    c) $\frac{f\left (x \right ) + 3}{f\left (x \right ) + 1}$
    d) $\frac{f\left (x \right ) + 3}{3f\left (x \right ) + 1}$

  • 6. Differentiation and Application of Derivatives - Quiz

    1. The equation of the tangent to the curve x = 2cos3θ and y = 3sin3θ at the point θ = π/4 is
    a) 2x + 3y = 3$\sqrt{2}$
    b) 2x - 3y = 3$\sqrt{2}$
    c) 3x - 2y = 3$\sqrt{2}$
    d) 2x - 2y = 3$\sqrt{2}$

    2. If y = $sin^{-1}\sqrt{x}$, then $\frac{dy}{dx}$ =
    a) $\frac{2}{\sqrt{x}\sqrt{1 - x}}$
    b) $\frac{-2}{\sqrt{x}\sqrt{1 - x}}$
    c) $\frac{1}{2\sqrt{x}\sqrt{1 - x}}$
    d) $\frac{1}{\sqrt{1 - x}}$

  • 7. Integrals - Quiz

  • 8. Application of Integrals - Quiz

    1. The function L(x) = $\int_{1}^{x}\frac{dt}{t}$ satisfies the equation
    a) L(x+y) = L(x) + L (y)
    b) $L\left (\frac{x}{y} \right )$ = $L\left (x \right ) + L\left (y \right )$
    c) L(xy) = L(x) + L(y)
    d) None of these

    2. The sin and cosine curves intersects infinitely many times giving bounded regions of equal areas. They area of one of such region is
    a) $\sqrt{2}$
    b) $2\sqrt{2}$
    c) $3\sqrt{2}$
    d) $4\sqrt{2}$

  • 9. Differential Equations - Quiz

    1. The differential equation satisfied by the family of curves y = $axcos\left (\frac{1}{x} + b \right )$, where a,b are parameters, is
    a) x2y2 + y = 0
    b) x4y2 + y = 0
    c) xy2 - y = 0
    d) x4y2 - y = 0

    2. Solution of the differential equation $\frac{dy}{dx} + \frac{y}{x}$ = sinx is
    a) x(y + cosx) =+ sinx + c
    b) x(y - cosx) = sinx + c
    c) x(y . cosx) = sinx + c
    d) x(y - cosx) = cosx + c
    e) x(y + cosx) = cosx + c

  • 10. Vector Algebra - Quiz

    1. A and B are two points . The position vector of A is 6b - 2a . A point P divides the line AB in the ratio 1:2. If a-b is the position vector of P, then the position vector of B is given by
    a) 7a - 15b
    b) 7a + 15b
    c) 15a - 7b
    d) 15a + 7b

    2. If the resultant of two vectors equals in magnitude to one of them and perpendicular to it in direction , the magnitude of the other vector is
    a) Same as that of the first
    b) $\sqrt{2}$ times that of the first
    c) Twice that of the first
    d) None of these

  • 11. Three Dimensional Geometry - Quiz

    1. The angle between the pair of lines with direction ratios (1,1,2) and ($\sqrt{3}$ - 1, -$\sqrt{3}$ - 1,4) is
    a) 300
    b) 450
    c) 600
    d) 900

    2. The radius of the circle in which the sphere x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2x + 7 = 0 is
    a) 1
    b) 2
    c) 3
    d) 4

  • 12. Linear Programming - Quiz

    1. Variables of the objective function of the linear programming problem are
    a) Zero
    b) Zero or positive
    c) Negative
    d) Zero or negative

    2. The objective function P(x,y) = 2x + 3y is maximized subject to the constraints x + y ≤ 30, x - y ≥ 0, 3 ≤ y ≤ 12, 0 ≥ x ≤ 20. The function attains the maximum value at the point
    a) (12,18)
    b) (18,12)
    c) (15,15)
    d) None of these

  • 13. Probability - Quiz

    1. A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$. If the signal received at station B is green, then the probability that the original signal was green is
    a) $\frac{3}{5}$
    b) $\frac{6}{7}$
    c) $\frac{20}{23}$
    d) $\frac{9}{20}$

    2. If P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28 , P(ABC) = 0.09, P(A + B + C) ≥ 0.75 and P(BC) = x, then
    a) 0.23 ≤ x ≤ 0.48
    b) 0.32 ≤ x ≤ 0.84
    c) 0.25 ≤ x ≤ 0.73
    d) None of these

  • 14. Statistics and Dynamics - Quiz

  • 15. Indefinite Integration - Quiz

    1. $\int e^{x}sin\left (e^{x} \right )dx$ =
    a) -cosex + c
    b) cosex + c
    c) -cosecex + c
    d) None of these

    2. $\int \frac{1}{1 + cosx + sinx}dx$ =
    a) $log \left | 1 + tan\frac{x}{2} \right | + c$
    b) $\frac{1}{2} log \left | 1 + tan\frac{x}{2} \right | + c$
    c) $2log \left | 1 + tan\frac{x}{2} \right | + c$
    d) $\frac{1}{2} log \left | 1 - tan\frac{x}{2} \right | + c$

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

    1. $\int_{-1}^{0}\frac{dx}{x^{2} + 2x + 2}$ =
    a) 0
    b) π/4
    c) π/2
    d) -π/4

    2. The value of the integral $\int_{0}^{1}x\left (1 - x \right )^{5}dx$ is equal to
    a) $\frac{1}{6}$
    b) $\frac{1}{7}$
    c) $\frac{6}{7}$
    d) $\frac{5}{6}$
    e) $\frac{1}{42}$