Total Number of Question/s - 3865

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  • 1. Sets - Quiz


    SAMPLE QUESTIONS


    1. If X = {8n - 7n - 1 : n ε N} and Y = {49(n - 1) : n ε N}, then
    a) X ⊆ Y
    b) Y ⊆ X
    c) X = Y
    d) None of these

    2. If A = [(x,y) : x2 + y2 = 25]
    and B = [(x,y) : x2 + 9y2 = 144], then A ∩ B contains
    a) One point
    b) Three points
    c) Two points
    d) Four points

  • 2. Relations and Functions - Quiz


    SAMPLE QUESTIONS


  • 3. Trigonometric Functions - Quiz


    SAMPLE QUESTIONS


  • 4. Principle of Mathematical Induction - Quiz


    SAMPLE QUESTIONS


  • 5. Complex Numbers and Quadratic Equations - Quiz


    SAMPLE QUESTIONS


    1. If z = 1 + i, then the multiplicative inverse of z2 is (where I = $\sqrt{-1}$)
    a) 2i
    b) 1 - i
    c) -i/2
    d) i/2

    2. The number of solutions of the system of equations Re(z2 = 0, |z| = 2 is
    a) 4
    b) 3
    c) 2
    d) 1

  • 6. Linear Inequalities - Quiz


    SAMPLE QUESTIONS


  • 7. Permutations and Combinations - Quiz


    SAMPLE QUESTIONS


    1. 20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table. If the two particular persons are to be seated on either side of the host
    a) 20!
    b) 2 . 18!
    c) 18!0
    d) None of these

    2. The total number of natural numbers of six digits that can be made with digits 1,2,3,4, if all digits are to appear in the same number at least once is
    a) 1560
    b) 840
    c) 1080
    d) 480

  • 8. Binomial Theorem - Quiz


    SAMPLE QUESTIONS


    1. $\binom{n}{0} + 2\binom{n}{1} + 2^{2}\binom{n}{2} + .... + 2^{n \binom{n}{n}}$ is equal to
    a) 2n
    b) 0
    c) 3n
    d) None of these

    2. For r = 0,1,…..,10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the expansion of (1+x)10 , (1 + x)20 and (1 + x)30. Then , $\sum_{r = 1}^{10} A_{r}\left (B_{10}B_{r} - C_{10}A_{r} \right )$ is equal to
    a) B10 - C10
    b) A10($B_{10}^{2}$ - C10A10)
    c) 0
    d) C10 - B10

  • 9. Sequences and Series - Quiz


    SAMPLE QUESTIONS


  • 10. Straight Lines - Quiz


    SAMPLE QUESTIONS


    1. The coordinates of the foot of the perpendicular from (0,0) upon the line x + y = 2 are
    a) (2,-1)
    b) (-2,1)
    c) (1,1)
    d) (1,2)

    2. Equation of angle bisectors between x and y axes are
    a) y = ± x
    b) y = ±3x
    c) $x = \pm\frac{1}{\sqrt{2}}x$
    d) y = ±3x

  • 11. Conic Sections - Quiz


    SAMPLE QUESTIONS


    1. A tangent to a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}$ = 1 intercepts a length of unity from each if the co-ordinate axes, then the point (a,b) lies on the rectanglar hyperbola.
    a) x2 - y2 = 2
    b) x2 -y2 = 1
    c) x2 - y2 = -1
    d) None of these

    2. If the area of the auxillary circle of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1(a > b) is twice the area of the ellipse , then the eccentricity of the ellipse is
    a) $\frac{1}{\sqrt{2}}$
    b) $\frac{\sqrt{3}}{2}$
    c) $\frac{1}{\sqrt{3}}$
    d) $\frac{1}{2}$

  • 12. Introduction to Three Dimensional Geometry - Quiz


    SAMPLE QUESTIONS


  • 13. Limits and Derivatives - Quiz


    SAMPLE QUESTIONS


  • 14. Mathematical Reasoning - Quiz


    SAMPLE QUESTIONS


    1. Let p : roses and q : the sun is a star. Then the verbal translation is (∼) ∨ q is:
    a) Roses are not real and the sun is not a star
    b) It is not true that roses are red or the sun is not a star
    c) It is not true that roses are red and the sun is not a star
    d) Roses are not red or the sun is a star
    e) It is not true that roses are red and the sun is a star

    2. Let S be a non-empty subset of R. consider the following statement.
    p : There is a rational number x ε S such that x > 0 .
    Which of the following statements is the negation of the statement p
    a) There is a rational number x ε S such that x ≤ 0
    b) There is no rational number x ε S such that x ≤ 0
    c) Every rational number x ε S satisfies x ≤ 0
    d) x ε S and x ≤ 0 ⇒ is not rationsl

  • 15. Statistics - Quiz


    SAMPLE QUESTIONS


    1. Forces M and N acting at a point P makes an angle 1500 . Their resultant acts at O magnitude 2 unit and is perpendicular to M. Then, in the same unit, the magnitudes of M and N are
    a) 2$\sqrt{3}$,4
    b) $\sqrt{\frac{3}{2}}$,2
    c) 3,4
    d) 4.5

    2. If the time taken in slipping down on smooth inclined plane is twice to the time taken in falling from the vertical height of that plane, the inclination ofp lane will be
    a) 450
    b) 600
    c) 750
    d) 300

  • 16. Probability - Quiz


    SAMPLE QUESTIONS


  • 17. Quadratic Equation and Inequation - Quiz


    SAMPLE QUESTIONS


    1. The value of a and b for which equation x4 - 4x3 + ax2 + bx + 1 = 0 have four real roots
    a) -6, -4
    b) -6,5
    c) -6,4
    d) 6,-4

    2. For k > 0 , the set of all values of k for which kex - x = 0 has two distinct roots is
    a) $\left (0, \frac{1}{e} \right )$
    b) $\left (\frac{1}{e} , 1\right )$
    c) $\left (\frac{1}{e} , \infty \right )$
    d) (0,1)

  • 18. Progression - Quiz


    SAMPLE QUESTIONS


    1. nth term of the series $1 + \frac{4}{5}+ \frac{7}{5^{2}} + \frac{10}{5^{3}} + .....$ will be
    a) $\frac{3n + 1}{5^{n-1}}$
    b) $\frac{3n - 1}{5^{n}}$
    c) $\frac{3n - 2}{5^{n-1}}$
    d) $\frac{3n + 2}{5^{n-1}}$

    2. If a, ,b, c, d be in H.P. then
    a) a2 + c2 > b2 + d2
    b) a2 + d2 > b2 + c2
    c) ac + bd > b2 + c2
    d) ac + bd > b2 + d2

  • 19. Exponential and Logarithmic Series - Quiz


    SAMPLE QUESTIONS


    1. In the expansion of $\frac{a + bx}{e^{x}}$ , the coefficient of xr is
    a) $\frac{a - b}{r!}$
    b) $\frac{a - br}{r!}$
    c) $\left (-1 \right )^{r}\frac{a - br}{r!}$
    d) None of these

    2. The coefficient of xn in the expansion of loge(1+x) is
    a) $\frac{\left (-1 \right )^{n - 1}}{n}$
    b) $\frac{\left (-1 \right )^{n - 1}}{n}log_{a}e$
    c) $\frac{\left (-1 \right )^{n - 1}}{n}log_{e}a$
    d) $\frac{\left (-1 \right )^{n}}{n}log_{a}e$

  • 20. Trigonometric Ratio, Function and Identities - Quiz


    SAMPLE QUESTIONS


    1. In any triangle ABC, $sin^{2}\frac{A}{2} + sin^{2}\frac{B}{2} + sin^{2}\frac{C}{2}$ is equal to
    a) $1 - 2cos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$
    b) $1 - 2sin\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$
    c) $1 - 2sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
    d) $1 - 2cos\frac{A}{2}cos\frac{B}{2}sin\frac{C}{2}$

    2. If sinθ + cosθ = x, then s6θ + cos6θ = $\frac{1}{4}\left [4 - 3\left (x^{2} - 1 \right )^{2} \right ]$ for
    a) All real x
    b) x2 ≤ 2
    c) x2 ≥ 2
    d) None of these

  • 21. Trigonometric Equation and Inequation - Quiz


    SAMPLE QUESTIONS


    1. The value of n ε Z for which the function f(x) = $\frac{sin nx}{sin\left (x/n \right )}$ has 4π as its period , is
    a) 2
    b) 3
    c) 4
    d) 5

    2. In a triangle with one angle of 1200 the lengths of the sides form an A.P. .If the length of the greatest side is 7cm then, the area triangle is
    a) $\frac{3\sqrt{15}}{4}cm^{2}$
    b) $\frac{15\sqrt{3}}{4}cm^{2}$
    c) $\frac{15}{4}cm^{2}$
    d) $\frac{3\sqrt{3}}{4}cm^{2}$

  • 22. Hyperbolic Function - Quiz


    SAMPLE QUESTIONS


    1. If sinx coshy = cosθ and cosx sinhy = sinθ, then sinh2y equals
    a) sin2x
    b) cosh2x
    c) cos2x
    d) 1

    2. sin2(ix) + cosh2x is equal to
    a) 1
    b) -1
    c) 2cosh2x
    d) cosh2x

  • 23. Rectangular Cartesian Coordinate - Quiz


    SAMPLE QUESTIONS


    1. The following points A(2a,4a), B(2a,6a) and C(2a, $\sqrt{3}a$,5a), (a>0) are the vertices of
    a) An acute angled triangle
    b) A right angles triangle
    c) An isosceles triangle
    d) None of these

    2. Point Q is symmetric to P(4,-1) with respect to the bisector of the first quadrant. The length of PQ is
    a) 3$\sqrt{2}$
    b) 5$\sqrt{2}$
    c) 7$\sqrt{2}$
    d) 9$\sqrt{2}$

  • 24. Circle and System of Circle - Quiz


    SAMPLE QUESTIONS


    1. The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is
    a) (x - 5)2 + (y + 5)2 = 25
    b) (x + 4)2 + (y + 4)2 = 25
    c) (x + 6)2 + (y + 6)2 = 25
    d) (x + 5)2 + (y + 5)2 = 25

    2. The equation of the circle with origin as centre passing through the vertices of an equilateral triangle whose median is of length 3a is
    a) x2 + y2 = 9a2
    b) x2 + y2 = 16a2
    c) x2 + y2 = a2
    d) None of these

  • 25. Pair of Straight Line - Quiz


    SAMPLE QUESTIONS


    1. The joint equation of the straight lines x + y = 1 and x - y = 4 is
    a) x2 - y2 = -4
    b) x2 - y2 = 4
    c) (x + y - 1)(x - y - 4) = 0
    d) (x + y + 1)(x - y + 4) = 0

    2. Two of the lines represented by the equation ay4 + bxy3 + cx2y2 + dx3y + ex4 = - will be perpendicular, then
    a) (b + d)(ad + be) + (e - a)2(a + c + e) = 0
    b) (b + d)(ad + be) + (e + a)2(a + c + e) = 0
    c) (b - d)(ad - be) + (e - a)2(a + c + e) = 0
    d) (b - d)(ad - be) + (e + a)2(a + c + e) = 0