Total Number of Question/s - 3005

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  • 1. Sets, Relations and Functions - Quiz


    SAMPLE QUESTIONS


    1. A real valued function f(x) satisfies the functional equation
    f(x-y) = f(x)f(y) - f(a-x)f(a+y) where a is a given constant and f(0) = 1, f(2a-x) is equal to
    a) f(-x)
    b) f(a) + f(a-x)
    c) f(x)
    d) -f(x)

    2. Let R be the set of real numbers.
    Statement I A = {(x,y) ε R x R : y - x is an integer} is an equivalent relation on R.
    Statement II B = {(x,y) ε R x R : x = αy for some rational number α } is an equivalence relation on R.
    a) Statement I is true, Statement II is true ; Statement II is not a correct explantion for Statement I.
    b) Statement I is true, Statement II is false
    c) Statement I is false, Statement II is true.
    d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

  • 2. Complex Numbers and Quadratic Equations - Quiz


    SAMPLE QUESTIONS


    1. The conjugate of a complex number is $\frac{1}{i - 1}$. Then that compolex number is
    a) $\frac{1}{i - 1}$
    b) $-\frac{1}{i - 1}$
    c) $\frac{1}{i +1}$
    d) $-\frac{1}{i + 1}$

    2. If the roots of the equation x2 - bx + x = 0, be two consecutive integers, then b2 - 4c equals
    a) 1
    b) 2
    c) 3
    d) -2

  • 3. Matrices and Determinants - Quiz


    SAMPLE QUESTIONS


    1. If l , m , n are the pth, qth and rth terms of an GP and all positive, then $\begin{bmatrix} 1 & \omega^{n} &\omega^{2n} \\ \omega^{n} & \omega^{2n} &1 \\ \omega^{2n} &1 & \omega^{n} \end{bmatrix}$ equals
    a) 3
    b) 2
    c) 1
    d) 0

    2. Let A and b be two symmetric matrices of order 3.
    Statement I A (BA) and (AB) A are symmetric matrices.
    Statement II AB is symmetric matrix, if matrix multiplication of A and B is communitative.
    a) Statement 1 is true, Statement II is true; Statement II is not a correct explanation for Statement I.
    b) Statement I is true, Statement II is false.
    c) Statement I is false, Statement II is true.
    d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

  • 4. Permutations and Combinations - Quiz


    SAMPLE QUESTIONS


    1. A student is to ansewr 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
    a) 140
    b) 196
    c) 280
    d) 346

    2. In a shop there are five types of ice-creams available. A child buys six ice-cream available. A child buys six ice-creams
    Statement I The number of different ways the child can buy the six ice-creams is 10C5.
    Statement II The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6A's and 4B's in a row.
    a) Statement I is false, Statement II is true
    b) Statement I is true, Statement II is true; Statement II is a 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

  • 5. Mathematical Induction - Quiz


    SAMPLE QUESTIONS


    1. Let s(k) = 1 + 3 + 5 + ...... + (2k - 1) = 3 + k2. Then which of the following is true?
    a) S(1) is correct
    b) s(k) ⇒ S(k+1)
    c) S(k) ⇒ S(k+1)
    d) Principle of mathematical induction can be used to prove the formula.

    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. If |x| < 1, then the coefficient of xn in expansion of (1 + x + x2 + x3 + .......)2 is
    a) n
    b) n-1
    c) n+2
    d) n+1

    2. For natural numbers m,n if (1 - y)m(1+y)n = 1 + a1y + a2y2 + .... and a1 = a2 = 10, then (m,n) is
    a) (35,20)
    b) (45,35)
    c) (35,45)
    d) (20,45)

  • 7. Sequences and Series - Quiz


    SAMPLE QUESTIONS


    1. The sum of the series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - .......$ upto ∞ is equal to
    a) 2loge2
    b) loge 2-1
    c) log2e
    d) log2$\left (\frac{4}{e} \right )$

    2. The sum of the first n terms of the series $1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2} + 2.6^{2} + ........$ is $\frac{n\left (n+1 \right )^{2}}{2}$ when n is even. When n is odd the sum is
    a) $\frac{3n\left (n+1 \right )}{2}$
    b) $\frac{n^{2}\left (n+1 \right )}{2}$
    c) $\frac{n\left (n+1 \right )^{2}}{4}$
    d) $\left [\frac{n\left (n+1 \right )}{2} \right ]^{2}$

  • 8. Limits, Continuity and Differentiabilty - Quiz


    SAMPLE QUESTIONS


    1. How many solutions does the equation
    $x^{7} + 14x^{5} + 16x^{3} + 30x - 560$ = 0
    have?
    a) 5
    b) 7
    c) 1
    d) 3

    2. For ∈ R, $lim_{x \rightarrow \infty}\left (\frac{x - 3}{x + 2} \right )^{x}$ is equal to
    a) e
    b) e-1
    c) e-5
    d) e5

  • 9. Integral Calculas - Quiz


    SAMPLE QUESTIONS


    1. $\int_{0}^{2}\left [x^{2} \right ]dx$ is
    a) $2- \sqrt{2}$
    b) $2+ \sqrt{2}$
    c) $\sqrt{2}$ - 1
    d) $-\sqrt{2} - \sqrt{3} + 5$

    2. If (a + b -x) = f(x) , then $\int_{a}^{b}x f\left (x \right )dx$ is equal to
    a) $\frac{a + b}{2}\int_{a}^{b}f\left (b - x \right )dx$
    b) $\frac{a + b}{2}\int_{a}^{b}f\left ( x \right )dx$
    c) $\frac{b - a}{2}\int_{a}^{b}f\left (x \right )dx$
    d) $\frac{a + b}{2}\int_{a}^{b}f\left (a + b + x \right )dx$

  • 10. Differential Equations - Quiz


    SAMPLE QUESTIONS


    1. If <$\frac{dy}{dx}$ = y(log y - logx + 1), then the solution of the equation is
    a) $log\left (\frac{x}{y} \right )$ = cy
    b) $log\left (\frac{y}{x} \right )$ = cx
    c) $xlog\left (\frac{y}{x} \right )$ = cy
    d) $ylog\left (\frac{x}{y} \right )$ = cx

    2. The differential equation representating the family of curves y2 = 2c(x + $\sqrt{c}$ ), where c > 0, is a parameter, is of order and degree as follows
    a) order 2, degree 2
    b) order 1, degree 3
    c) order 1, degree 1
    d) order 1, degree 2

  • 11. Coordinate Geometry - Quiz


    SAMPLE QUESTIONS


    1. The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB . Equation of the circle on AB as a diameter is
    a) x2 + y2 - x - y = 0
    b) x2 + y2 - x + y = 0
    c) x2 + y2
    d) x2 + y2 + x - y = 0

    2. If non numbers, a, b , c are in HP, then the straight line $\frac{x}{a} + \frac{y}{a} + \frac{1}{c}$ = 0 always passes through a fixed point. That point is
    a) $\left (1, -\frac{1}{2} \right )$
    b) (1,-2)
    c) (-1,-2)
    d) (-1,2)

  • 12. Three Dimensional Geometry - Quiz


    SAMPLE QUESTIONS


    1. A parallelopiped is formed by planes drawn through the coordinate planes. The length of a diagonal of the parallelopiped is
    a) 7 unit
    b) $\sqrt{38}unit$
    c) $\sqrt{155}unit$
    d) None of these

    2. The centre of the circle given by $\vec{r}.\left (\hat{i} + 2\hat{j} + 2\hat{k} \right )$ = 15 and $\left |\vec{r} - \left (\hat{j} + 2\hat{k} \right ) \right |$ = 4 is
    a) (0,1,2)
    b) (1,3,4)
    c) (-1.3.4)
    d) None of these

  • 13. Vector Algebra - Quiz


    SAMPLE QUESTIONS


    1. Let $\vec{u}, \vec{v}, \vec{w}$ be such that $\left | \vec{u} \right | $= 1, $\left | \vec{v} \right | $= 2, $\left | \vec{u} \right |$ = 3 . If the projection $\vec{v}$ along $\vec{u}$ is equal to that of $\vec{w}$ along $\vec{u}$ and $\vec{v},\vec{w}$ are perpendicular to each other, then $\left | \vec{u} - \vec{v} + \vec{w} \right |$ are equals
    a) 2
    b) $\sqrt{7}$
    c) $\sqrt{14}$
    d) 14

    2. For any vector $\frac{10}{3\sqrt{3}}$ , the value of $\left (\vec{a} \times \hat{i} \right )^{2} + \left (\vec{a} \times \hat{j} \right )^{2} + \left (\vec{a} \times \hat{k} \right )^{2}$ is equal to
    a) $4\vec{a}^{2}$
    b) $2\vec{a}^{2}$
    c) $\vec{a}^{2}$
    d) $3\vec{a}^{2}$

  • 14. Statistics and Probabilty - Quiz


    SAMPLE QUESTIONS


    1. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event the number obtained is less than S. Then P(A ∪ B) is
    a) $\frac{2}{5}$
    b) $\frac{3}{5}$
    c) 0
    d) 1

    2. Consider he following statements
    (1) Mode can be compound from histogram
    (2) Median is not independent of change of scale
    (3) Varience is independent of change of origin and scale
    Which of these is/are correct?
    a) Only (1)
    b) Only (2)
    c) Only (1) and (2)
    d) (1), (2) and (3)

  • 15. Trigonometry - Quiz


    SAMPLE QUESTIONS


    1. A triangular park is enclosed on two sides by a fence and on the third side by a strength river bank. The two sides having fence are of same length x. the maximum area enclosed by the park is
    a) $\frac{x^{3}}{8}$
    b) $\frac{1}{2}x^{2}$
    c) πx2
    d) $\frac{3}{2}x^{2}$

    2. In a δABC, $tan\frac{A}{2}$ = $\frac{5}{6}, tan \frac{C}{2}$ = $\frac{2}{5}$, then
    a) a, c, b are in AP
    b) a, b , c are in AP
    c) b, a, c are in AP
    d) a, b, c are in GP

  • 16. Mathematical Reasoning - Quiz


    SAMPLE QUESTIONS


    1. The statement p → (q → p) is equivalent to
    a) p → (p ↔ q)
    b) p → (p → q)
    c) p → (p ∨ q)
    d) p → (p ∧ q)

    2. Statement I $\sim$ (p ↔ ∼ q) is equivalent to p ↔ q.
    Statement II ∼ (p ↔ ∼ q) is a tautology.
    a) Statement I is true, Statement II is true; Statement II is true; Statement II is a correct explanation for Statement I.
    b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
    c) Statement I is true, Statement II is false.
    d) Statement I is false, Statement II is true.