Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. Let L denote the set of all straight lines in a place. Let a relation R be defined by αRβ ⇔ α⊥β,α, β εL. Then R is
a) Reflexive
b) Symmetric
c) Transitive
d) None of these
2. Let R = {(3,3), (6,9), (9,9), (12,12), (6,12), (3,9), (3,12),(3,6)} be a relation on the set A = {3,6,9,12} . The relation is
a) An equivalence relation
b) Reflexive and symmeteric only
c) Reflexive and transitive only
d) Reflexive only

2. Relations and Functions  Quiz

3. Trigonometric Functions  Quiz

4. Principle of Mathematical Induction  Quiz

5. Complex Numbers and Quadratic Equations  Quiz
1. For three complex numbers 1i, i , 1 + i which of the following is true
a) They form a right triangle
b) They are collinear
c) They form an equilateral triangle
d) They form an isosceles triangle
2. If z = r(cosθ + isinθ), then the value of $\frac{z}{\bar{z}} + \frac{\bar{z}}{z}$ is
a) cos2θ
b) 2 cos2θ
c) 2 cosθ
d) 2 sinθ
e) 2 sin 2θ

6. Linear Inequalities  Quiz

7. Permutations and Combinations  Quiz
1. There is a rectangular sheet of dimension (2m  1) x (2n  1), (where , m > 0 , n > 0). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length
a) (m + n + 1)^{2}
b) mn(m + 1)(n + 1)
c) 4^{m+n2}
d) m^{2}n^{2}
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
1. If the coefficient of the middle term in the xpansion of (1 + x)^{2n+2} is p and the coefficients of middle terms in the expansion of (1 + x)^{2n+1} are q and r, then
a) p + q = r
b) p + r = q
c) p = q + r
d) p + q + r = 0
2. Coefficient of x^{2} in the expansion of $\left (x  \frac{1}{2x} \right )^{8}$ is
a) $\frac{1}{7}$
b) $\frac{1}{7}$
c) 7
d) 7

9. Sequences and Series  Quiz

10. Straight Lines  Quiz
1. The equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2,1). The length of the side of the triangle is
a) $\sqrt{3/2}$
b) $\sqrt{2}$
c) $\sqrt{2/3}$
d) None of these
2. The line L given by $\frac{x}{5} + \frac{y}{b}$ = 1 passes through the point (13,32). The line K is parallel to L and has the equation $\frac{x}{c} + \frac{y}{3}$ = 1. Then, the distance between L and K is
a) $\frac{23}{\sqrt{15}}$
b) $\sqrt{17}$
c) $\frac{17}{\sqrt{15}}$
d) $\frac{23}{\sqrt{17}}$

11. Conic Sections  Quiz
1. The common tangents to the circle x^{2} + y^{2} = 2 and the parabola y^{2}8x touch the circle at the points P, Q and the parabola at the points R,S. Then the area of the quadrilateral PQRS is
a) 3
b) 6
c) 9
d) 15
2. The ends of the latus rectum of the conic x^{2} + 10x  16y + 25 = 0 are
a) (3,4),(13,4)
b) (3,4), (13,4)
c) (3,4), (13,4)
d) (5,8) (5,8)

12. Introduction to Three Dimensional Geometry  Quiz

13. Limits and Derivatives  Quiz

14. Mathematical Reasoning  Quiz
1. The negation of P ∨ ∼ q) ^ q is
a) (∼p ∨ q)^ ∼ q
b) (p ^ ∼q) ∨ q
c) (∼p ^ q) ∨ ∼ q
d) (p^∼q)∨∼q
e) (∼ p^ ∼q) ^ ∼q
2. The statement p → (∼q) is equivalent to
a) q → p
b) ∼ q ∨ ∼ p
c) p ^ ∼ q
d) ∼ → p

15. Statistics  Quiz
1. A sphere impinges directly on an equal sphere which is at rest. Then original kinetic energy lost is equal to
a) $\frac{1 + e^{2}}{2}$ times the initial K.E.
b) $\frac{1  e^{2}}{2}$
c) $\frac{1  e^{2}}{2}$ times the initial K.E.
d) None of these
2. A stone is dropped slowly from the top of the wall and it reaches the surface of the water with the velocity 3924 cm/sec, if sound of aplash is heard after $4\frac{109}{475}$ seconds, then the velocity of sound will be
a) 312 metre/sec
b) 302 metre/sec
c) 321 metre/sec
d) 342 metre/sec

16. Probability  Quiz

17. Quadratic Equation and Inequation  Quiz
1. If Α and β , &alpha and γ α and δ are the roots of the equations ax^{2} + 2bx + c = 0, 2bx^{2} + cx + a = 0 and cx^{2} + ax + 2b = 0 respectively, where a,b and c are positive real numbers, then α + α^{2} =
a) 1
b) 0
c) abc
d) a + 2b + c
e) None of these
2. Let α, &beta be the roots x^{2}  x + p = 0 and γ , δ be the roots of x^{2}  4x + q = 0. If α, β, γ, δ are in G.P., then integral values of p,q are respectively
a) 2, 32
b) 2,3
c) 6,3
d) 6,32

18. Progression  Quiz
1. If n geometric means between a and b G_{1}, G_{2}, ….G_{n} and a geometric mean be G, then the true relation is
a) G_{1}.G_{2} ….. G_{n} = G
b) G_{1}.G_{2}…….G_{n} = G^{1/n}
c) G_{1}.G_{2} …..G_{n} = G^{n}
d) G_{1}.G_{2} …. G_{n} = G^{2/n}
2. If a,b,c are three unequal numbers such that a, b, c are in A.P. and b  a, c  b, a are in G.P. , then a : b : c is
a) 1:2:3
b) 2:3:1
c) 1:3:2
d) 3:2:1

19. Exponential and Logarithmic Series  Quiz
1. If n = (1999)! Then $\sum_{x=1}^{1999}log_{n}x$ is equal to
a) 1
b) 0
c) $\sqrt[1999]{1999}$
d) 1
2. The value of $log_{e}\left (1 + ax^{2} + a^{2} + \frac{a}{x^{2}}\right )$ is
a) $a\left (x^{2}  \frac{1}{x^{2}} \right )  \frac{a^{2}}{2}\left (x^{4}  \frac{1}{x^{4}} \right ) + \frac{a^{3}}{3}\left (x^{6}  \frac{1}{x^{6}} \right )  ....$
b) $a\left (x^{2} + \frac{1}{x^{2}} \right )  \frac{a^{2}}{2}\left (x^{4} + \frac{1}{x^{4}} \right ) + \frac{a^{3}}{3}\left (x^{6} + \frac{1}{x^{6}} \right )  ....$
c) $a\left (x^{2} + \frac{1}{x^{2}} \right ) + \frac{a^{2}}{2}\left (x^{4} + \frac{1}{x^{4}} \right ) + \frac{a^{3}}{3}\left (x^{6} + \frac{1}{x^{6}} \right ) + ....$
d) $a\left (x^{2}  \frac{1}{x^{2}} \right ) + \frac{a^{2}}{2}\left (x^{4}  \frac{1}{x^{4}} \right ) + \frac{a^{3}}{3}\left (x^{6}  \frac{1}{x^{6}} \right ) + ....$

20. Trigonometric Ratio, Function and Identities  Quiz
1. sin12^{0}sin24^{0sin480sin840 = a) cos200cos400cos600cos800 b) sin200sin400sin600sin800 c) $\frac{3}{15}$d) None of these 2. In a triangle the sum of two sides is x and the product of the same two sides is y. If x2  c2 = y, where c is the third side of the triangle, then the ratio of the inradius to the circumradius of the triangle is a) $\frac{3y}{2x\left (x + c \right )}$ b) $\frac{3y}{2c\left (x + c \right )}$ c) $\frac{3y}{4x\left (x + c \right )}$d) $\frac{3y}{4c\left (x + c \right )}$ } 
21. Trigonometric Equation and Inequation  Quiz
1. If the two angles on the base of a triangle are $\left (22\frac{1}{2} \right )^{0}$ and $\left (11\frac{1}{2} \right )^{0}$, then the ratio of the height of the triangle to the length of the base is
a) 1:2
b) 2:1
c) 2:3
d) 1:1
2. If the median of ΔABC through A is perpendicular to AB, then
a) tanA + tanB = 0
b) 2tanA + tanB = 0
c) tanA + 2tanB = 0
d) None of these

22. Hyperbolic Function  Quiz
1. 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) $\frac{1}{2}log\left (\frac{1  \sqrt{1 + x^{2}}}{x} \right )$
2. The imaginary part of sin^{2}(x + iy) is
a) $\frac{1}{2}cosh2xcos2y$
b) $\frac{1}{2}cos2xcosh2y$
c) $\frac{1}{2}sinh2xsin2y$
d) $\frac{1}{2}sin2xsinh2y$

23. Rectangular Cartesian Coordinate  Quiz
1. If (0,β) lies on a inside the triangle with sides y + 3x + 2 = 0, 3y  2x  5 = 0 and 4y + x  14 = 0, then
a) $0 \le \beta \le \frac{7}{2}$
b) $0 \le \beta \le \frac{5}{2}$
c) $\frac{5}{3} \le \beta \le \frac{7}{2}$
d) None of these
2. If coordinates of the point A and B are (2,4) and (4,2) respectively and point M is such that AMB also AB = 3 AM, then the coordinates of M are
a) $\left(\frac{8}{3}, \frac{10}{3} \right )$
b) $\left (\frac{10}{3}, \frac{14}{4}\right )$
c) $\left (\frac{10}{3}, \frac{6}{3}\right )$
d) $\left (\frac{13}{4}, \frac{10}{4}\right )$

24. Circle and System of Circle  Quiz
1. If θ_{1}, θ_{2} be the inclination of tangents drawn from the point P to the circle x^{2} + y^{2} = a^{2} with xaxis , then the locus of P, if given that cotθ_{1} + cotθ_{2} = c is
a) c(x^{2}  a^{2}) = 2xy
b) c(x^{2}  a^{2}) = y^{2}  a^{2}
c) c(y^{2}  a^{2}) = 2xy
d) None of these
2. The centre of the circle passing through (0,0) and (1,0) and touching the circle x^{2} + y^{2} = 9 is
a) $\left (\frac{1}{2}, \frac{1}{2} \right )$
b) $\left (\frac{1}{2}, \sqrt{2} \right )$
c) $\left (\frac{3}{2}, \frac{1}{2} \right )$
d) $\left (\frac{1}{2}, \frac{3}{2} \right )$

25. Pair of Straight Line  Quiz
1. The equation of one of the line represented by the equation x^{2} + 2xycotθ  y^{2} = 0, is
a) x  ycotθ = 0
b) x + ytanθ
c) x sinθ + y(cosθ + 1) = 0
d) xcosθ + y(sinθ + 1) = 0
2. The equation x^{2} + ky^{2} + 4xy = 0 represents two coincident lines, if k =
a) 0
b) 1
c) 4
d) 16