Class/Course - Engineering Entrance

Subject - Mathematics

Total Number of Question/s - 3005


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  • 1. Sets, Relations and Functions - Quiz

    1. Let f : N → Y be a function defined as f(x) = 4x + 3 where
    Y = { y ∈ N : y = 4x + 3 for some x ∈ N}.
    Show that f is invertible and its inverse is
    a) g(y) = $\frac{y-3}{4}$
    b) g(y) = $\frac{3y+4}{3}$
    c) g(y) = $4 + \frac{y+3}{4}$
    d) g(y) = $\frac{y+3}{4}$

    2. Let R = {(1.3), (4,2), (4,2), (2,4), (2,3), (3,1)} be relation on the set A = {1,2,3,4} . The relation of R is
    a) a function
    b) transitive
    c) not symmetric
    d) reflexive

  • 2. Complex Numbers and Quadratic Equations - Quiz

    1. The number of the real solutions of the equation x2 - 3|x| + 2 = 0
    a) 2
    b) 4
    c) 1
    d) 3

    2. If (1-p) is a root of quadratic equation x2 + px + (1-p) = 0, then its roots are
    a) 0,1
    b) -1,1
    c) 0,-1
    d) -1, 2

  • 3. Matrices and Determinants - Quiz

    1. 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.

    2. If 1, ω, ω2 are the cube roots of unity, then Δ = $\begin{bmatrix} 1 & \omega^{n} & \omega^{2n} \\ \omega^{n} & \omega^{2n} &1 \\ \omega^{2n}& 1 & \omega^{n} \end{bmatrix}$ is equal to
    a) 0
    b) 1
    c) ω
    d) ω2

  • 4. Permutations and Combinations - Quiz

    1. The number of ways of distributing 8 identical balls in distinct boxes, so that none of the boxes is empty, is
    a) 5
    b) 21
    c) 38
    d) 8C3

    2. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary , then the word SACHIN appears at serial number
    a) 602
    b) 603
    c) 600
    d) 601

  • 5. Mathematical Induction - Quiz

    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 every natural number n ≥ 2
    $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + .......... + \frac{1}{\sqrt{n}}$ > $\sqrt{n}$
    statement II For every natural number $n \ge 2. \sqrt{n\left (n + 1 \right )} < + 1$
    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

    1. Statement I $\sum_{r = 0}^{n}\left (r + 1 \right ),^{n}C_{r}$ = $\left (n+2 \right )2^{n-1}$
    Statement II $\sum_{r=0}^{n}\left (r+1 \right )^{n}C_{r}.x^{r}$ = $\left (1+x \right )^{n} + nx\left (1+x \right )^{n+1}$
    a) Statement I is false, Statement II is true.
    b) Statement I is true, Statement II is true; Statement II is a correct explanations of 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.

    2. If Sn = $\sum_{r = 0}^{n}\frac{1}{^{n}C_{r}} \ and \ t_{n}= \sum_{r=0}^{n}\frac{r}{^{n}C_{r}} \ then \ \frac{t_{n}}{S_{n}}$ is equal to
    a) $\frac{n}{2}$
    b) $\frac{n}{2}$ - 1
    c) n-1
    d) $\frac{2n-1}{2}$

  • 7. Sequences and Series - Quiz

    1. If 1, $log_{3}\sqrt{\left (3^{1-x} + 2 \right )}, log_{3}\left (4.3^{x} - 1 \right )$ are in, Ap. Then x equals
    a) log34
    b) 1 - log34
    c) 1 - log43
    d) log43

    2. If a1, a2 , .....,an are in HP. Then the expression a1a2 + a2a3 + .... + an-1an is equal to
    a) (n-1)(a1 - an)
    b) na1an
    c) (n-1)a1 - a2
    d) n(a1 - an)

  • 8. Limits, Continuity and Differentiabilty - Quiz

    1. Let f(x) = x|x| and g(x) = sin x
    Statement I gof is differentiable at x = 0 and its derivative is continuous at that point.
    Statement II gof is twice differentiable at x = 0.
    a) Statement I is false, Statement II is true.
    b) Statement I is true, Statement II is 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.

    2. The function f : R/(0) → R given by
    f(x) = $\frac{1}{x} - \frac{2}{e^{2x} - 1}$
    can be made continuous at x = 0 by defining f(0) as
    a) 2
    b) -1
    c) 0
    d) 1

  • 9. Integral Calculas - Quiz

    1. $\int_{0}^{10x}\left | sin x\right|$ is
    a) 20
    b) 8
    c) 10
    d) 18

    2. Let F(x) = f(x) + $f\left (\frac{1}{x} \right )$ , where f(x) = $\int_{1}^{x}\frac{log t}{1 + t}dt$. Then , F(e) equals
    a) $\frac{1}{2}$
    b) 0
    c) 1
    d) 2

  • 10. Differential Equations - Quiz

    1. The solution of the differential equation
    $\left (1 + y^{2} \right ) + \left (x - e^{tan^{-1}y} \right )\frac{dy}{dx}$ = 0 is
    a) $\left (x - 2 \right )$= $ce^{-2tan^{-1}y}$
    b) $2xe^{tan^{-1}y}$ = $2^{tan^{-1}y} + c$
    c) $xe^{tan^{-1}y}$ = $tan^{-1}y + c$
    d) $xe^{2tan^{-1}y}$ = $e^{tan^{-1}y} + c$

    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

    1. A variable circle passes through the fixed point A(p,q) and touches x-axis. The locus of the other end of the diameter through A is
    a) (x - p)2 = 4qy
    b) (x - q)2 = 4py
    c) (y - p)2 = 4qx
    d) (y - q)2 = 4px

    2. The equation of the chord joining two points (x1, y1) and (x2,y2) on the rectangular hyperbola xy = c2 is
    a) $\frac{x}{x_{1} + x_{2}} + \frac{y}{y_{1} + y_{2}}$ = 1
    b) $\frac{x}{x_{1} - x_{2}} + \frac{y}{y_{1} - y_{2}}$ = 1
    c) $\frac{x}{y_{1} + y_{2}} + \frac{y}{x_{1} + x_{2}}$ = 1
    d) $\frac{x}{y_{1} - y_{2}} + \frac{y}{x_{1} - x_{2}}$ = 1

  • 12. Three Dimensional Geometry - Quiz

    1. The line $\frac{x-2}{1}$=$\frac{y-3}{1}$=$\frac{z-4}{-k}$ and $\frac{x-1}{k}$=$\frac{y-4}{2}$=$\frac{z-4}{1}$ are coplanar, if
    a) k = 0 or -1
    b) k = 1 or -1
    c) k = 0 or -3
    d) k = 3 or -3

    2. Statement I The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$
    Statement II The line the line segment joining $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining A(1,0,7) and B(1,6,3).
    a) Statement I 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.

  • 13. Vector Algebra - Quiz

    1. Let $\vec{a}$ = $\hat{i} - \hat{k}$ , $\vec{b}$ = $x\hat{i} + \hat{j} + \left (1 - x \right )k^{2}$ and $\vec{c}$ = $y\hat{i} + x\hat{j} + \left (1 + x - y \right )\hat{k}$ . Then $\left [\vec{a}\vec{b}\vec{c} \right ]$ depends on
    a) neither x notr y
    b) both x and y
    c) only x
    d) only y

    2. If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and λ be a real number, then the vectors $\vec{a} + 2\vec{b} + 3\vec{c}, \lambda \vec{b} + 4\vec{c}$ and $\left (2\lambda - 1 \right )\vec{c}$ are non-coplanar for
    a) all value of λ
    b) all except one value of λ
    c) all except two values of λ
    d) no value of λ

  • 14. Statistics and Probabilty - Quiz

    1. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?
    a) 73
    b) 65
    c) 68
    d) 74

    2. A pair of fair dice is thrown in independently three times. The probability of getting a score of exactly 9 is twice is
    a) 1/729
    b) 8/9
    c) 8/729
    d) 8/243

  • 15. Trigonometry - Quiz

    1. The possible values of &thet; € (0,π) such that sin(θ) + sin(4θ) + sin(7θ) = 0 are
    a) $\frac{2\pi }{9},\frac{\pi }{4},\frac{4\pi }{9},\frac{\pi}{2},\frac{3\pi}{4},\frac{8\pi}{9}$
    b) $\frac{\pi }{4},\frac{5\pi }{12},\frac{\pi }{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{9}$
    c) $\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi}{2},\frac{3\pi}{4},\frac{35\pi}{36}$
    d) $\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{9}$

    2. If f : R → S, defined by
    f(x) = $sin x - \sqrt{3} cosx + 1$, is onto, then the interval of S is
    a) [0,3]
    b) [-1,1]
    c) [0,1]
    d) [-1,3]

  • 16. Mathematical Reasoning - Quiz

    1. 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

    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.