Class/Course - Class XI

Subject - Math

Total Number of Question/s - 3865


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  • 1. Sets - Quiz

    1. 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. Let R and S be two non-void relations on a set A. Which of the following statements is false
    a) R and S are transitive ⇒ R ∪ S is transitive
    b) R and S are transitive ⇒ R ∩ S is transitive
    c) R and S are symmetric ⇒ R ∪ S is symmetric
    d) R and S are reflexive ⇒ R ∩ S is reflexive

  • 2. Relations and Functions - Quiz

  • 3. Trigonometric Functions - Quiz

  • 4. Principle of Mathematical Induction - Quiz

  • 5. Complex Numbers and Quadratic Equations - Quiz

    1. ω is an imaginary cube root of unity . If (1 + ω2)m = (1 + ω4)m, then least positive integral value of m is
    a) 6
    b) 5
    c) 4
    d) 3

    2. If ω is a complex cube root of unity, then
    225 + (3ω + 8ω2)2 + (3ω2 + 8ω2) =
    a) 72
    b) 192
    c) 200
    d) 248

  • 6. Linear Inequalities - Quiz

  • 7. Permutations and Combinations - Quiz

    1. The greatest possible number of points of intersection of 8 straight lines and 4 circleds is
    a) 32
    b) 64
    c) 76
    d) 104

    2. The product r consecutive intergers is divisible by
    a) r!
    b) (r - 1)!
    c) (r + 1)!
    d) None of these

  • 8. Binomial Theorem - Quiz

    1. The coefficient of x5 in the expansion of (x + 3)6 is
    a) 18
    b) 6
    c) 12
    d) 10

    2. Term independent of x in $\left (\sqrt{x} + \frac{m}{x^{2}} \right )^{10}$ is 405, m =
    a) 2
    b) 9
    c) 3
    d) -3

  • 9. Sequences and Series - Quiz

  • 10. Straight Lines - Quiz

    1. If the three points A(1,6), B(3,-4) and C(x,y) are collinear , then the equation satisfying by x and y is
    a) 5x + y - 11= 0
    b) 5x + 13y + 5 = 0
    c) 5x - 13y + 5 = 0
    d) 5x - 13y + 5 = 0
    e) 13x - 5y + 5 = 0

    2. The points (1,3) and (5,1) are the opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then the value of c will be
    a) 4
    b) -4
    c) 2
    d) -2

  • 11. Conic Sections - Quiz

    1. The equation of the hyperbola whose foci are the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9}$ = 1 and the eccentricity is 2 is
    a) $\frac{x^{2}}{4} + \frac{y^{2}}{12}$ = 1
    b) $\frac{x^{2}}{4} - \frac{y^{2}}{12}$ = 1
    c) $\frac{x^{2}}{12}+ \frac{y^{2}}{4}$ = 1
    d) $\frac{x^{2}}{12} - \frac{y^{2}}{4}$ = 1

    2. For the ellipse 25x2 + 9y2 - 150x - 90y + 225 = 0 the eccentricity e =
    a) 2/5
    b) 3/5
    c) 4/5
    d) 1/5

  • 12. Introduction to Three Dimensional Geometry - Quiz

  • 13. Limits and Derivatives - Quiz

  • 14. Mathematical Reasoning - Quiz

    1. An AND gate is the Boolean function defined by
    a) f(x1,x2) = x1.x2, x1x2 ε {0,1}
    b) f(x1,x2) = x1 + x2, x1x2 ε {0,1}
    c) f(x1,x2) = x1, x1x2 ε {0,1}
    d) f(x1,x2) = x2, x1x2 ε {0,1}

    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

    1. A body is projected through an angle α from vertical so that its range is half of maximum range, α is
    a) 600
    b) 750
    c) 300
    d) 22.50

    2. A particle is dropped under gravity from rest from a height h(g = 9.8m/sec2) and then it travels a distance $\frac{9h}{25}$ in the last second. The height h is
    a) 100 metre
    b) 122.5 metre
    c) 145 metre
    d) 167.5 metre

  • 16. Probability - Quiz

  • 17. Quadratic Equation and Inequation - Quiz

    1. If ax2 + bx + c = 0, then x =
    a) $\frac{b \pm \sqrt{b^{2} - 4ac}}{2a}$
    b) $\frac{-b \pm \sqrt{b^{2} - ac}}{2a}$
    c) $\frac{2c}{-b \pm \sqrt{b^{2} - 4ac}}$
    d) None of these

    2. If b1b2 = 2(c1 + c2), then at least one of the equations x2 + b1x + c1 = 0 and x2 + b2x + c2 = has
    a) Real roots
    b) Purely imaginary roots
    c) Imaginary roots
    d) None of these

  • 18. Progression - Quiz

    1. The sum of the series
    $\frac{1}{1 + 1^{2} + 1^{4}} + \frac{2}{1 + 2^{2} + 2^{4}} + \frac{3}{1 + 3^{2} + 3^{4}} + .....$ to n terms is
    a) $\frac{n\left (n^{2} + 1 \right )}{n^{2} + n + 1}$
    b) $\frac{n\left (n + 1 \right )}{2\left (n^{2} + n + 1 \right )}$
    c) $\frac{n\left (n^{2} - 1 \right )}{2\left (n^{2} + n + 1 \right )}$
    d) None of these

    2. If a, b, c are in A.P., then 2ax+1, 2bx+1m 2cx+1 , x ≠ 0 are in
    a) A.P.
    b) G.P. only when x > 0
    c) G.P. if x < 0
    d) G.P. for all x ≠ 0

  • 19. Exponential and Logarithmic Series - Quiz

    1. The sum of the series $\frac{1}{1.2} + \frac{1.3}{1.2.3.4} + \frac{1.3.5}{1.2.3.4.5.6} + .... \infty$ is
    a) 15e
    b) e1/2 + 2
    c) e1/2 - 1
    d) e1/2 - e

    2. The coefficient of x3 in the expansion of e2x+3 as a series in powers of x is
    a) e3
    b) $\frac{3}{4}e^{3}$
    c) $\frac{4}{3}e^{3}$
    d) None of these

  • 20. Trigonometric Ratio, Function and Identities - Quiz

    1. $\frac{sin3\theta + sin5\theta + sin7\theta + sin9\theta}{cos3\theta + cos5\theta + cos7\theta + cos9\theta}$ =
    a) tan3θ
    b) cos3θ
    c) tan6θ
    d) cot6θ

    2. If f(x) = cos2x + sec2x , then
    a) f(x) < 1
    b) f(x) = 1
    c) 1 < f(x) < 2
    d) f(x) ≥ 2

  • 21. Trigonometric Equation and Inequation - Quiz

    1. A tower is situated on horizontal plane. From two points, the line joining three points passes through the base and which are a and b distance from the base. The angle of elevation of the top are α and 900 - α and θ is that angle which two points joining the line makes at the top, the height of tower will be
    a) $\frac{a + b}{a - b}$
    b) $\frac{a - b}{a + b}$
    c) $\sqrt{ab}$
    d) (ab)1/3

    2. The only value of x for which 2sinx + 2cosx > 21-(1/$\sqrt{2}$) holds is,
    a) $\frac{5\pi}{4}$
    b) $\frac{3\pi}{4}$
    c) $\frac{\pi}{2}$
    d) All values of x

  • 22. Hyperbolic Function - Quiz

    1. The value of tan-1(2-1) is
    a) log 2
    b) log 2-1
    c) log $\sqrt{3}$
    d) None of these

    2. coth-1x equals
    a) $\frac{1}{2}log\left (\frac{1 + \sqrt{1 + x^{2}}}{x} \right )$
    b) $\frac{1}{2}log\left (\frac{1 + \sqrt{1 - x^{2}}}{x} \right )$
    c) $\frac{1}{2}log\left (\frac{1 - \sqrt{1 - x^{2}}}{x} \right )$
    d) $\frac{1}{2}log\left (\frac{1 - \sqrt{1 + x^{2}}}{x} \right )$

  • 23. Rectangular Cartesian Coordinate - Quiz

    1. Three vertices of a parallelogram taken in order are (-1,-6), (2,-5) and (7,2). The fourth vertex is
    a) (1,4)
    b) (4,1)
    c) (1,1)
    d) (4,4)

    2. The points (1,1), (0, sec2 θ), (cosec2θ,0) are collinear for
    a) θ = $\frac{n\pi}{2}$
    b) θ ≠ $\frac{n\pi}{2}$
    c) θ = nπ
    d) None of these

  • 24. Circle and System of Circle - Quiz

    1. A circle with centre (a,b) passes through the origin. The equation of the tangent to the circle at the origin is
    a) ax - by = 0
    b) ax + by = 0
    c) bx - ay = 0
    d) bx + ay = 0

    2. Equation to the circles which touch the lines 3x - 4y + 1 = 0, 4x + 3y - 7 = 0 and pass through (2,3) are
    a) (x - 2)2 + (y - 8)2 = 25
    b) 5x2 + 5y2 - 12x - 24y + 31 = 0
    c) Both (a) and (b)
    d) None of these

  • 25. Pair of Straight Line - Quiz

    1. 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

    2. The lines represented by the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 will be equidistant from the origin, if
    a) f2 + g2 = c(b - a)
    b) f4 + g4 = c(bf2 + ag2)
    c) f4 - g44 = c(bf2 - ag2)
    d) f2 + g2 = af2 + bg2