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 : (-1,1) → B, be a function defined by f(x) = $tan^{-1}\left (\frac{2x}{1 - x^{2}} \right )$, the f is both one -one and onto when B is in the interval
    a) $\left (-\frac{\pi}{2}, \frac{\pi}{2} \right )$
    b) $[-\frac{\pi}{2}, \frac{\pi}{2}]$
    c) $[0,\frac{\pi}{2})$
    d) $(0,\frac{\pi}{2})$

    2. Let for a ≠ a1 ≠ 0, f(x) = ax2 = ax2 + bx + c,
    g(x) = a1x2 + b1 x + c1 and p(x) = f(x) - g(x) , If p(x) = 0 only for x = -1 and p(-2) = 2, then the value of p(2) is

    a) 18
    b) 3
    c) 9
    d) 6

  • 2. Complex Numbers and Quadratic Equations - Quiz

    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 complex numbers z such that |z-1| = |z+1| = |z-i| equals
    a) 0
    b) 1
    c) 2
    d) ∞

  • 3. Matrices and Determinants - Quiz

    1. If a1, a2 , ......., an, ....... , are in GP, then the determinant
    Δ = $\begin{vmatrix} log a_{n} & loga_{n+1} &log a_{n+2} \\ log a_{n} + 3& loga_{n + 4} & loga_{n + 5} \\ log a_{n+6} & loga_{n+7} & loga_{n + 8} \end{vmatrix}$
    is equal to
    a) 2
    b) 4
    c) 0
    d) 1

    2. If D = $\begin{vmatrix} 1 & 1 & 1\\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{vmatrix}$ for x ≠ 0, y ≠ 0, then D is
    a) divisible by neither x not y
    b) divisible by both x and y
    c) divisible by x but not y
    d) divisible by y but not x

  • 4. Permutations and Combinations - Quiz

    1. The set S = {1,2,3, .....,12} is to be partitioned into three sets A,B,C of equal size.
    Thus, A ∪ B ∪ C = S,
    A ∩ B = B ∩ C = A ∩ C = φ
    The number of ways to partition S is
    a) 12!/3!(4!)3
    b) 12!/3!(3!)4
    c) 12!/(4!)3
    d) 12!/(3!)4

    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

    1. 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.

    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

    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. The coefficient of x7 in the expansion of (1 - x - x2 + x3)6 is
    a) -132
    b) -144
    c) 132
    d) 144

  • 7. Sequences and Series - Quiz

    1. A person is to count 4500 currently notes. Let a11, denotes the number of notes he counts in the nth minute . If a1 = a2 = .... = a10 = 150 and a10, a11,.... are in AP with common difference -2, then the common difference -2, then the time taken by him to count to count all notes, is
    a) 24 min
    b) 34 min
    c) 125 min
    d) 135 min

    2. Such term of a GP is 2, then the product of its 9 terms is
    a) 256
    b) 512
    c) 1024
    d) None of these

  • 8. Limits, Continuity and Differentiabilty - Quiz

    1. Let f(x) = $\left\{\begin{matrix} \left (x - 1 \right )sin\frac{1}{x-1}, & if \ x \ne 1 \\ 0, & if \ x = 1 \end{matrix}\right.$
    Then which one of the following is true?
    a) f is differentiable at x = 1 but not at x = 0
    b) f is neither differentiable at x = 0 nor at x = 1
    c) f is differentiable at x = 0 and at x = 1
    d) f is differentiable at x = 0 but not at x = 1

    2. A function is matched below against an interval where it is supposed to be increasing . Which of the following pairs is incorrectly matched?
    a) Interval - (-∞, -4), Function = x3 + 6x2 + 6
    b) Interval = $\left (-infty, \frac{1}{3} \right ]$, Function = 3x2 - 2x + 1
    c) Interval = [2,∞), Function = 2x3 - 3x2 - 12x + 6
    d) Interval = (-∞, ∞), Function = x3 - 3x2 + 3x + 3

  • 9. Integral Calculas - Quiz

    1. The value of $\int_{-2}^{3}\left | 1 - x^{2} \right |dx$ is
    a) $\frac{28}{3}$
    b) $\frac{14}{3}$
    c) $\frac{7}{3}$
    d) $\frac{1}{3}$

    2. The value of $\int_{1}^{a}$[x]f'(x) dx , a > 1 where [x] denotes the greatest integer not exceeding x, is
    a) [a]f(a) - {f(1) + f(2) + ....... + f([a])}
    b) [a]f([a]) - {f(1) + f(2) + ...... + f(a)}
    c) af([a]) - {f(1) + f(2) + ..... + f(a)}
    d) af(a) - {f(1) + f(2) + ...... + f([a])}

  • 10. Differential Equations - Quiz

    1. Consider the differential equation y2dx + $\left (x - \frac{1}{y} \right )dy$ = 0. If y(1) = 1, then x is given by
    a) $1 - \frac{1}{y} + \frac{\frac{1}{e^{y}}}{e}$
    b) $4 - \frac{2}{y} + \frac{\frac{1}{e^{y}}}{e}$
    c) $3 - \frac{1}{y} + \frac{\frac{1}{e^{y}}}{e}$
    d) $1 + \frac{1}{y} - \frac{\frac{1}{e^{y}}}{e}$

    2. Solution of the differential equation cos x dy = y(sinx - y)dx, 0 < x < $\frac{\pi}{2}$ , is
    a) sec x = (tan + c) y
    b) y sec x = tan x + c
    c) y tanx = secx + c
    d) tan x = (sec x + c) y

  • 11. Coordinate Geometry - Quiz

    1. A circle touches the x-axis and also touches the circle with centre at (0,3) and radius 2. The locus of the centre of the circle is
    a) a parabola
    b) a hyperbola
    c) a circle
    d) an ellipse

    2. If a circle passes through the point (a,b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
    a) 2ax + 2by - (a2 - b2 + p2) = 0
    b) x2 + y2 - 2ax - 3by + (a2 - b2 - p2) = 0
    c) 2ax + 2by - (a2 - b2 + p2) = 0
    d) x2 + y2 - 3ax - 4by + (a2 + b2 - p2) = 0

  • 12. Three Dimensional Geometry - Quiz

    1. The two lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other, if
    a) aa' + cc' = 1
    b) $\frac{a}{a'} + \frac{c}{c'}$ = -1
    c) $\frac{a}{a'} + \frac{c}{c'}$ = 1
    d) aa' + cc' = -1

    2. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
    a) $\frac{3}{2}$
    b) $\frac{5}{2}$
    c) $\frac{7}{2}$
    d) $\frac{9}{2}$

  • 13. Vector Algebra - Quiz

    1. If $\vec{a} $= $\frac{1}{^{10}}\left ( 3\hat{i} +\hat{k}\right )$ and $\vec{b} $= $\frac{1}{7}\left ( 2\hat{i} + 3\hat{k} - 6\hat{k}\right )$then the value of $\left ( 2\vec{a}-\vec{b} \right )\cdot \left [ \left ( \vec{a}\times \vec{b} \right ) \times \left ( \vec{a}+2\vec{b} \right ) \right ]$ is
    a) -3
    b) 5
    c) 3
    d) -5

    2. If the vectors $\vec{\epsilon}$ = $\hat{i} - \hat{j} + 2\hat{k}, \vec{b}$ = $2\hat{i} + 4\hat{j} + \hat{k}$ and $\vec{c}$ = $\lambda \hat{i} + \hat{j} + \mu\hat{k}$ are mutually orthogonal, then (λ, μ) is equal to
    a) (-3,2)
    b) (2,-3)
    c) (-2,3)
    d) (3,-2)

  • 14. Statistics and Probabilty - Quiz

    1. For two two data sets, each of size, 5 the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is
    a) $\frac{5}{2}$
    b) $\frac{11}{2}$
    c) 6
    d) $\frac{13}{2}$

    2. If the mean deviations about the median of the number a, 2a, .......5a is 50, than |a| equals to
    a) 3
    b) 4
    c) 5
    d) 2

  • 15. Trigonometry - Quiz

    1. If in a triangle ABC
    $a \ cos^{2}\left (\frac{C}{2} \right ) + c \ cos^{2}\left (\frac{A}{2} \right )$ = $\frac{3b}{2}$
    then the sides,a , b and c
    a) are in AP
    b) are in GP
    c) are in HP
    d) satisfy a + b = c

    2. 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) $\sqrt{3}$

  • 16. Mathematical Reasoning - Quiz

    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. 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)