Total Number of Question/s - 3005

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  • 1. Sets, Relations and Functions - Quiz


    SAMPLE QUESTIONS


    1. A function f from the set of natural numbers to integers defined by
    f(n) = $\left\{\begin{matrix} \frac{n-1}{2}, & where \ n \ is \ odd \\ -\frac{n}{2},& when \ n \ is \ even \end{matrix}\right.$ is
    a) onle-one but not onlto
    b) onlto but not one-one
    c) one-one and onlto both
    d) neither one-one not onto

    2. The domain of the function f(x) = $\frac{1}{\sqrt{|x| - x}}$ is
    a) (o,∞)
    b) (-∞,0)
    c) (-∞,∞)-{0}
    d) (-∞,∞)

  • 2. Complex Numbers and Quadratic Equations - Quiz


    SAMPLE QUESTIONS


    1. If $\left (\frac{1 + i}{1 - i} \right )^{x}$ = 1 , then
    a) x = 4n, where n is any positive integer
    b) x = 2n, where n in any positive integer
    c) x = 4n + 1, where n is any positive integer
    d) x = 2n + 1, where n is any positive integer

    2. The number of real roots of $3^{2x^{2} - 7x + 7}$ = 9 is
    a) 0
    b) 2
    c) 1
    d) 4

  • 3. Matrices and Determinants - Quiz


    SAMPLE QUESTIONS


    1. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx, and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to
    a) 1
    b) 2
    c) -1
    d) 0

    2. If ω ≠ 1 is the complex cube root of unity and matrix H - $\begin{bmatrix} \omega & 0\\ 0& \omega \end{bmatrix}$ , then H70 is equal to
    a) H
    b) 0
    c) -H
    d) H2

  • 4. Permutations and Combinations - Quiz


    SAMPLE QUESTIONS


    1. At an election , a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is
    a) 6210
    b) 385
    c) 600
    d) 601

    2. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then , the middle of such arrangements is
    a) at least 500 but less than 750
    b) at least 750 but less than 1000
    c) at least 1000
    d) less than 500

  • 5. Mathematical Induction - Quiz


    SAMPLE QUESTIONS


    1. If A = $\begin{bmatrix} 1 &0 \\ 1& 1 \end{bmatrix}$ and I = $\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}$, then which one of the following holds for all n ≥ 1, by the principle of mathematical induction?
    a) $A^{n}$ = $2^{n-1}A + \left (n-1 \right )I$
    b) $A^{n}$ = $nA + \left (n-1 \right )I$
    c) An = $2^{n-1}A-\left (n-1 \right )I$
    d) An = nA - (n-1)I

    2. Statement I For each natural number n,(n+1)7 - n7 - 1 is divisible by 7.
    Statement II For each natural number n, n7 - n is divisible by 7.
    a) Statement I is false , Statement II is true.
    b) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
    c) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
    d) Statement I is true, Statement II is false.

  • 6. Binomial Theorem - Quiz


    SAMPLE QUESTIONS


    1. The value of 50C4 $\sum_{r=1}^{6}$ 56-3C3 is
    a) $^{56}C_{4}$
    b) $^{56}C_{3}$
    c) $^{55}C_{3}$
    d) $^{55}C_{4}$

    2. The coefficient of x5 in (1 + 2x + 3x2 + ......)-3/2 is
    a) 21
    b) 25
    c) 26
    d) None of these

  • 7. Sequences and Series - Quiz


    SAMPLE QUESTIONS


    1. Then sum of the series
    1 + $\frac{1}{4.2!} + \frac{1}{16.4!} + \frac{1}{64.4!} + .... \infty$ is
    a) $\frac{e + 1}{2\sqrt{2}}$
    b) $\frac{e - 1}{2\sqrt{2}}$
    c) $\frac{e + 1}{\sqrt{2}}$
    d) $\frac{e - 1}{\sqrt{2}}$

    2. In p and q are positive real numbers such that p2 + q2 =1, then the maximum value of (p + q) is
    a) 2
    b) $\frac{1}{2}$
    c) $\frac{1}{\sqrt{2}}$
    d) $\sqrt{2}$

  • 8. Limits, Continuity and Differentiabilty - Quiz


    SAMPLE QUESTIONS


    1. If $lim_{x \rightarrow \infty}\left (1 + \frac{a}{x} + \frac{b}{x^{2}} \right )^{2x}$, then the values of a and b are
    a) a ∈ R, b ∈ R
    b) a = 1, b ∈ R
    c) a ∈ R, b = 2
    d) a = 1, b = 2

    2. Let f be a function defined by
    f(x) = $\left\{\begin{matrix} \frac{tan x}{x} ,&x \ne 0 \\ 1,& x = 0 \end{matrix}\right.$
    Statement I x = 0 is point of minima of f.
    Statement II f'(0) = 0
    a) Statement I is false, Statement II is true
    b) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
    c) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
    d) Statement I is true, Statement II is false.

  • 9. Integral Calculas - Quiz


    SAMPLE QUESTIONS


    1. $\int\frac{dx}{x\left (x^{n} + 1 \right )}$ is equal to
    a) $\frac{1}{n}log\left (\frac{x^{n}}{x^{n} + 1} \right ) + c$
    b) $\frac{1}{n}log\left (\frac{x^{n} + 1}{x^{n}} \right ) + c$
    c) $log\left (\frac{x^{n}}{x^{n} + 1} \right ) + c$
    d) None of the above

    2. The area of the region bounded by the curves y = | x - 1| and y = 3 - |x| is
    a) 2 sq unit
    b) 3 sq unit
    c) 4 sq unit
    d) 6 sq unit

  • 10. Differential Equations - Quiz


    SAMPLE QUESTIONS


    1. The differential equation for the family of curves x2 + y2 - 2ay = 0, where a is an arbitrary constant, is
    a) 2(x2 - y2)y' = xy
    b) 2(x2 + y2)y' = xy
    c) (x2 - y2)y' = 2xy
    d) (x2 + y2)y' = 2xy

    2. The solution of the differential equation
    $\frac{dy}{dx}$ = $\frac{x + y}{x}$
    satisfying the condition y(1) = 1 is
    a) y = x log x + x
    b) y = log x + x
    c) y = x log x + x2
    d) y = xe(x-1)

  • 11. Coordinate Geometry - Quiz


    SAMPLE QUESTIONS


    1. If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four times their product, then c has the value
    a) 1
    b) -1
    c) 2
    d) -2

    2. The greater distance of the point P(10,7) from the circle x2 + y2 - 4x - 2y - 20 = 0 is
    a) 10 unit
    b) 15 unit
    c) 5 unit
    d) None of these

  • 12. Three Dimensional Geometry - Quiz


    SAMPLE QUESTIONS


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

    2. If the angle θ between the line $\frac{x + 1}{1}$ = $\frac{y - 1}{2}$ = $\frac{z - 2}{2}$ and the plane 2x - y + $\sqrt{\lambda }z$ + 4 = 0 is such that sinθ = $\frac{1}{3}$. The value of λ is
    a) $-\frac{4}{3}$
    b) $\frac{3}{4}$
    c) $-\frac{3}{5}$
    d) $\frac{5}{3}$

  • 13. Vector Algebra - Quiz


    SAMPLE QUESTIONS


    1. Let $\vec{a}$ = $\hat{i} + \hat{j} + \hat{k} , \vec{b}$ = $\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{c}$ and $x\hat{i} + \left (x - 2 \right )\hat{j} - \hat{k}$ . If the vector $\vec{c}$ lies in the plane of $\vec{a} and \vec{b}$ , then x equals
    a) 0
    b) 1
    c) -4
    d) -2

    2. Let $\vec{a}$ = $\hat{j} - \hat{k} and \vec{c}$ = $\hat{i} - \hat{j} - \hat{k}$ . Then the vector $\vec{b}$ satisfying $\vec{a} \times \vec{b} + \vec{c}$ = 0 and \vec{a}.\vec{b}$ = 3, is
    a) $-\hat{i} + \hat{j} - 2\hat{k}$
    b) $2\hat{i} - \hat{j} + 2\hat{k}$
    c) $\hat{i} - \hat{j} - 2\hat{k}$
    d) $\hat{i} + \hat{j} - 2\hat{k}$

  • 14. Statistics and Probabilty - Quiz


    SAMPLE QUESTIONS


    1. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
    a) is increased by 2
    b) is decreased by 2
    c) is two times the original median
    d) remains the same as that of the original set

    2. If C and D are two events such that the C ⊂ D and P(D) ≠ 0, then the correct statement among the following is
    a) P(C|D) ≥ P(C)
    b) P(C|D) < P(C)
    c) P(C|D) = $\frac{P\left (D \right )}{P\left (C \right )}$
    d) P(C|D) = P(C)

  • 15. Trigonometry - Quiz


    SAMPLE QUESTIONS


    1. A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB = ( = a) subtends an angle of 600 at the foot of the tower and the angles of elevation of the top of the tower A or B is 300. The height of the tower is
    a) $\frac{2a}{\sqrt{3}}$
    b) $2a\sqrt{3}$
    c) $\frac{a}{\sqrt{3}}$
    d) $\sqrt{3}$

    2. If $sin^{-1}\left (\frac{x}{5} \right ) + cosec^{-1}\left (\frac{5}{4} \right )$ = $\frac{\pi}{2}$ , then a value of x is
    a) 1
    b) 3
    c) 4
    d) 5

  • 16. Mathematical Reasoning - Quiz


    SAMPLE QUESTIONS


    1. Consider the following statements
    P : Suman is brilliant.
    Q : Suman is rich.
    R : Suman is honest.
    The negative of the statement. Suman is brilliant and dishonest if and only if Suman is rich can be expressed as
    a) ∼ (Q ↔ (O P ∼ R)
    b) ∼ Q ↔ P ^ R
    c) ∼ (P ^ ∼ R) ↔ Q
    d) ∼ P ^ (Q ↔ ∼ R)

    2. The only statement among the following that is a tautology is
    a) B → ∧ ( A → B)]
    b) A ∧ (A ∨ B)
    c) A ∨ (A ∧ B)
    d) [A ∧ (A → B)] → B