Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. Let a relation R is defined by R = {(4,5); (1,4); (4,6); (7,6); (3,7)} then R^{1}oR is
a) {(1,1), (4,4), (4,7), (7,4),(7,7), (3,3)}
b) {(1,1), (4,4), (7,7), (3,3)}
c) {(1,5), (1,6), (3,6)}
d) None of these
2. Let R = {(1,3), (2,2), (3,2)} and S = {(2,1), (3,2), (2,3)} be two relations on set A = {1,2,3}. Then RoS =
a) {(1,3), (2,2), (3,2), (2,1), (2,3)}
b) {(3,2), (1,3)}
c) {(2,3), (3,2), (2,2)}
d) {(2,3), (3,2)}

2. Relations and Functions  Quiz

3. Trigonometric Functions  Quiz

4. Principle of Mathematical Induction  Quiz

5. Complex Numbers and Quadratic Equations  Quiz
1. If 8 + z + z  8 = 16 where z is a complex number, then the point z will lie on
a) A circle
b) An ellipse
c) A straight line
d) None of these
2. The argument of the complex number $\frac{13  5i}{4  9i}$ is
a) $\frac{\pi}{3}$
b) $\frac{\pi}{4}$
c) $\frac{\pi}{5}$
d) $\frac{\pi}{6}$

6. Linear Inequalities  Quiz

7. Permutations and Combinations  Quiz
1. In ^{n}p_{r} = 30240 and ^{n}C_{r} = 252, then the ordered pair (n,r) is equal to
a) (12,6)
b) (10,5)
c) (9,4)
d) (16,7)
2. A parallelogram is cut by two sets of m lines parallel to its sides. The number of parallelgrams thus formed is
a) (^{m}C_{2})^{2}
b) (^{m+1}C_{2})
c) (^{m+2}C_{2})^{2}
d) None of these

8. Binomial Theorem  Quiz
1. If the coefficient of x^{7} in $\left (ax^{2} + \frac{1}{bx} \right )^{11}$ is equal to the coefficient of x^{7} in $\left (ax  \frac{1}{bx^{2} } \right )^{11}$, then ab =
a) 1
b) 1/2
c) 2
d) 3
2. The sum of coefficients in the expansion of (x + 2y + 3z)^{8} is
a) 3^{8}
b) 5^{8}
c) 6^{8}
d) None of these

9. Sequences and Series  Quiz

10. Straight Lines  Quiz
1. The lines a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are perpendicular to each other, if
a) a_{1}b_{2}  b_{1}a_{2} = 0
b) a_{1}a_{2} + b_{1}b_{2} = 0
c) $a_{1}^{2}b_{2} + b_{1}^{2}a_{2}$ = 0
d) a_{1}b_{1} + a_{2}b_{2} = 0
2. The medians AD and BE of a triangle with vertices A(0,b) , B(0,0) and C(a,0) are perpendicular to each other if,
a) a = $\sqrt{2}$b
b) a = $\sqrt{2}$b
c) Both (a) and (b)
d) None of these

11. Conic Sections  Quiz
1. The equation of common tangents to the parabola y^{2} = 8x and hyperbola 3x^{2}  y^{2} = 3, is
a) 2x ± y + 1 = 0
b) 2x ± y  1 = 0
c) x ± 2y + 1 = 0
d) x + 2y  1 = 0
2. If a ≠ 0 and the line abx + 3cy + 4d = 0 passes through the points of intersection of the parabola y^{2} = 4ax and x^{2} = 4ay, then
a) d^{2} + (3b  2c)^{2} = 0
b) d^{2} + (3b  2c)^{2} = 0
c) d^{2} + (2b  3c)^{2} = 0
d) d^{2} + (2b + 3c)^{2} = 0

12. Introduction to Three Dimensional Geometry  Quiz

13. Limits and Derivatives  Quiz

14. 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. Negation of the proposition : If we control population growth, we prosper
a) If we do not control population growth , we propsper
b) Itf we control population growth, we do not prosper
c) We control population but we do not prosper
d) We do not control population, but we prosper

15. Statistics  Quiz
1. Two trains A and B, 100 kms apart, are travelling to each other with starting speed of 50km/hr for both . The train A is accelerating at 18km/hr^{2} and B is decelerating at 18 km/hr^{2}. The distance where the engines cross each other from the initial position of A is
a) 50 kms
b) 68 kms
c) 32 kms
d) 59 kms
2. What will be that force when applying along any inclination plane will stop 10kilogram weight , it is given that force reaction of plane and weight of body are in arithmetic series
a) 4kgwt
b) 6kgwt
c) 8kgwt
d) 7kgwt

16. Probability  Quiz

17. Quadratic Equation and Inequation  Quiz
1. If k ε (∞, 2) ∪ (2,∞), then the roots of the equation x^{2} + 2kx + 4 = 0 are
a) Complex
b) Real and Unequal
c) Real and equal
d) One real and one imaginary
2. If one root of the equation ax^{2} + bx + c = 0 the square of the other, then a(c  b)^{3} = cX, where X is
a) a^{3} + b^{3}
b) (a  b)^{3}
c) a^{3}  b^{3}
d) None of these

18. Progression  Quiz
1. If a, ,b,c, d are in H.P., then ab + bc + cd is equal to
a) 3ad
b) (a + b)(c + d)
c) 3ac
d) None of these
2. If three real numbers a, ,b, c are in harmonic progression, then which of the following is true
a) $\frac{1}{a}, b, \frac{1}{c}$ are in A.P.
b) $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$ are in H.P.
c) ab,bc, ca are in H.P.
d) $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are in H.P.

19. Exponential and Logarithmic Series  Quiz
1. If S = $\frac{1}{1.2}  \frac{1}{2.3} + \frac{1}{3.4}  \frac{1}{4.5} + .... + \infty$, then e^{S} =
a) $log_{e}\left (\frac{4}{e} \right )$
b) $\frac{4}{e}$
c) $log_{e}\left (\frac{e}{4} \right )$
d) $\frac{e}{4}$
2. $\frac{1}{3!} + \frac{2}{5!} + \frac{3}{7!} + ....$ =
a) e^{1}/2
b) e
c) e/4
d) e/6

20. Trigonometric Ratio, Function and Identities  Quiz
1. Let f_{k}(x) = $\frac{1}{k}\left (sin^{k}x + cos^{k}x \right )$ where x ε R and k ≥ 1. Then f_{4}(x)  f_{0}(x) equals
a) $\frac{1}{4}$
b) $\frac{1}{12}$
c) $\frac{1}{6}$
d) $\frac{1}{3}$
2. If α, β are solution of 6cosθ + 8 sinθ = 9, then sin(α + β) =
a) $\frac{3}{5}$
b) $\frac{4}{5}$
c) $\frac{24}{25}$
d) $\frac{12}{13}$

21. Trigonometric Equation and Inequation  Quiz
1. Two straight roads intersect at an angle of 60^{0}, A bus on one road is 2km away from the intersection and a car on the other road is 3km away from the intersection. Then the direct distance between the two vehivles is
a) 1 km
b) $\sqrt{2}$ km
c) 4 km
d) $\sqrt{7}$ km
2. If the sides of the triangle are 5K, 6K, 5K and radius of incircle is 6 then value of K is equal to
a) 4
b) 5
c) 6
d) 7

22. Hyperbolic Function  Quiz
1. The imaginary part of tan^{1}(cosθ + isinθ) is
a) tanh^{1}(sinθ)
b) tanh^{1}(∞)
c) 1/2tanh^{1}(sinθ)
d) None of these
2. sinh^{1}x =
a) $log\left (x + \sqrt{1  x^{2}} \right )$
b) $log\left (x + \sqrt{ x^{2} + 1} \right )$
c) $log\left (x + \sqrt{ x^{2}  1} \right )$
d) None of these

23. Rectangular Cartesian Coordinate  Quiz
1. If the three points (0,1), (0,1) and (x,0) are vertices of an equilateral triangle, then the values of x are
a) $\sqrt{3},\sqrt{2}$
b) $\sqrt{3}, \sqrt{3}$
c) $\sqrt{5}, \sqrt{3}$
d) $\sqrt{2}, \sqrt{2}$
e) $\sqrt{5}, \sqrt{5}$
2. If the vertices of a triangle are A(1,4), B(3,0) and C(2,1) , then the length of the median passing through C is
a) 1
b) 2
c) $\sqrt{2}$
d) $\sqrt{3}$

24. Circle and System of Circle  Quiz
1. The locus of a point which divides the join of A(1,1) and variable point P on the circle x^{2} + y^{2} = 4 in the ratio 3:2 is
a) 25(x^{2} + y^{2}) + 20(x  y) + 28 = 0
b) 25(x^{2} + y^{2}) + 20(x  y)  28 = 0
c) 20(x^{2} + y^{2}) + 25(x  y) + 28 = 0
d) None of these
2. The locus of centre of the circle which cuts the circles x^{2} + y^{2} + 2g_{1}x + 2f_{1}y + c_{1} = 0 x^{2} + y^{2} + 2g_{2}x + 2f_{2}y + c_{2} = 0 orthogonally is
a) An ellipse
b) The radical axis of the given circles
c) A conic
d) Another circle

25. Pair of Straight Line  Quiz
1. The area (in square units) of the quadrilateral formed by the two pairs of lines l^{2}x^{2}  m^{2}y^{2}  n(lx + my) = 0 and l^{2}x^{2  m2y2 + n(lx  my) = 0 is a) $\frac{n^{2}}{2\left  lm \right }$ b) $\frac{n^{2}}{\left  m \right }$ c) $\frac{n}{2\left  m \right }$d) $\frac{n^{2}}{4\left  m \right }$ 2. The pair of lines represented by 3ax2 + 5xy + (a2  2)y2 = 0 are perpendicular to each other for a) Two values of a b) ∀a c) For one value of ad) For no value of a }