Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. If A = [(x,y) : x^{2} + y^{2} = 25]
and B = [(x,y) : x^{2} + 9y^{2} = 144], then A ∩ B contains
a) One point
b) Three points
c) Two points
d) Four points
2. Let R and S be two nonvoid 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 + ω^{2})^{m} = (1 + ω^{4})^{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 + 8ω^{2})^{2} + (3ω^{2} + 8ω^{2}) =
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 x^{5} 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 25x^{2} + 9y^{2}  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(x_{1},x_{2}) = x_{1}.x_{2}, x_{1}x_{2} Îµ {0,1}
b) f(x_{1},x_{2}) = x_{1} + x_{2}, x_{1}x_{2} Îµ {0,1}
c) f(x_{1},x_{2}) = x_{1}, x_{1}x_{2} Îµ {0,1}
d) f(x_{1},x_{2}) = x_{2}, x_{1}x_{2} Îµ {0,1}
2. Let S be a nonempty 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) 60^{0}
b) 75^{0}
c) 30^{0}
d) 22.5^{0}
2. A particle is dropped under gravity from rest from a height h(g = 9.8m/sec^{2}) 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 ax^{2} + 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 b_{1}b_{2} = 2(c_{1} + c_{2}), then at least one of the equations x^{2} + b_{1}x + c_{1} = 0 and x^{2} + b_{2}x + c_{2} = 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 2^{ax+1}, 2^{bx+1}m 2^{cx+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) e^{1/2} + 2
c) e^{1/2}  1
d) e^{1/2}  e
2. The coefficient of x^{3} in the expansion of e^{2x+3} as a series in powers of x is
a) e^{3}
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) = cos^{2}x + sec^{2}x , 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 90^{0}  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 2^{sinx} + 2^{cosx} > 2^{1(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^{1}x 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, sec^{2} θ), (cosec^{2}θ,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) 5x^{2} + 5y^{2}  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 ay^{4} + bxy^{3} + cx^{2}y^{2} + dx^{3}y + ex^{4} =  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 ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 will be equidistant from the origin, if
a) f^{2} + g^{2} = c(b  a)
b) f^{4} + g^{4} = c(bf^{2} + ag^{2})
c) f^{4}  g^{4}4 = c(bf^{2}  ag^{2})
d) f^{2} + g^{2} = af^{2} + bg^{2}