Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. Let R be the relation on the set R of all real numbers defined by a R b if a  b\ ≤ 1. Then R is
a) Reflexive and symmetric
b) Symmetric only
c) Transitive only
d) Antisymmetric only
2. If n(A) = 4, n(B) = 3, n(A x B x C) = 24, then n(C) =
a) 288
b) 1
c) 12
d) 17
e) 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 z_{1}.z_{2} and z_{3}, z_{4} are two pairs of conjugate complex numbers, then $arg\left (\frac{z_{1}}{z_{4}} \right )$ + $arg\left (\frac{z_{2}}{z_{3}} \right )$ equals
a) 0
b) $\frac{\pi}{2}$
c) $\frac{3\pi}{2}$
d) π
2. PQ and PR are two infinite rays. QAR is an arc. Point lying in the shaded region excluding the boundary satisfies
a) z  1>2;arg(z  1)<$\frac{\pi}{4}$
b) z  1>2;arg(z  1)<$\frac{\pi}{2}$
c) z + 1>2;arg(z + 1)<$\frac{\pi}{4}$
d) z + 1>2;arg(z + 1)<$\frac{\pi}{2}$

6. Linear Inequalities  Quiz

7. Permutations and Combinations  Quiz
1. Let X be a bionomial random variable and X = [0,1,2,….n]. For r = 0, 1,2,…..n, which of the following holds
a) P(X = r) = ^{n}P_{r}p^{r}q^{nr}
b) P(X = r) = ^{n}C_{r}p^{r}q^{nr}
c) P(X = r) = ^{n}C_{r}p^{r}
d) P(X = r) = ^{n}C_{r}p^{nr}
2. If ^{n}P_{r} = 720. ^{n}C_{r}, then r is equal to
a) 6
b) 5
c) 4
d) 7

8. Binomial Theorem  Quiz
1. The approximate value of (1.0002)^{3000} is
a) 1.6
b) 1.4
c) 1.8
d) 1.2
2. The sum of the coefficients in the expansion of (x + y)^{n} is 4096. The greatest coefficient in the expansion is
a) 1024
b) 924
c) 824
d) 724

9. Sequences and Series  Quiz

10. Straight Lines  Quiz
1. If a and b are two arbitrary constants, then the straight line (a  2b)x + (a + 3b)y + 3a + 4b = 0 will pass through
a) (1,2)
b) (1,2)
c) (2,3)
d) (2,3)
2. The length of perpendicular from a point (1,2) to the straight line 3x + 4y + 4 = 0 is
a) 5
b) 3
c) 7/5
d) None of these

11. Conic Sections  Quiz
1. At what point on the parabola y^{2} = 4x, the normal makes equal angles with the coordinates axes
a) (4,4)
b) (9,6)
c) (4,4)
d) (1,2)
2. The condition that the straight line lx + my = n may be a normal to the hyperbola b^{2}x^{2}  a^{2}y^{2} = a^{2}b^{2} is given by
a) $\frac{a^{2}}{l^{2}}  \frac{b^{2}}{m^{2}}$ = $\frac{\left (a^{2} + b^{2} \right )^{2}}{n^{2}}$
b) $\frac{1^{2}}{a^{2}}  \frac{m^{2}}{b^{2}}$ = $\frac{\left (a^{2} + b^{2} \right )^{2}}{n^{2}}$
c) $\frac{a^{2}}{l^{2}}+ \frac{b^{2}}{m^{2}}$ = $\frac{\left (a^{2}  b^{2} \right )^{2}}{n^{2}}$
d) $\frac{1^{2}}{a^{2}} + \frac{m^{2}}{b^{2}}$ = $\frac{\left (a^{2}  b^{2} \right )^{2}}{n^{2}}$

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. Let p be the proposition : Mathematics is a interesting and let q be the propositions that Mathematics is difficult, then the symbol P ^ q means
a) Mathematics is interesting implies that Mathematics is difficult
b) Mathematics is interesting implies and is implied by Mathematics is difficult
c) Mathematics is interesting and Mathematics is difficult
d) Mathematics is interesting or Mathematics is difficult

15. Statistics  Quiz
1. A rough plane is 100ft long and is inclined to the horizon at an angle sin^{1}(3/5), the cofficient of friction being 1/2, and a body slides down it from rest at the highest point, the velocity on reaching the bottom would be
a) 16/$\sqrt{5}$ ft/sec
b) 16 ft/sec
c) 16$\sqrt{5}$ft/sec
d) 16/$\sqrt{7}$ ft/sec
2. If a couple is acting on 2 particles of mass 1kg attached with a rigid rod of length 4m, fixed at centre, acting at the end and the angular acceleration of system about centre is 1rad/s^{2}, then magnitude of force is
a) 2N
b) 4N
c) 1N
d) None of these

16. Probability  Quiz

17. Quadratic Equation and Inequation  Quiz
1. If α , β, γ are roots of equation x^{3} + ax^{2} + bx + c = 0, then α^{1} + β^{1} + γ^{1} =
a) a/c
b) b/c
c) b/a
d) c/a
2. If b > a, then the equation (x  a)(x  b) = 1 has
a) Both roots in [a,b]
b) Both roots in (∞,a)
c) Both roots in (b,+ ∞)
d) One root in (∞,a) and the other in (b,+∞)

18. Progression  Quiz
1. If $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are in H.P. , then
a) a^{2}b, c^{2}a,b^{2}c are in A.P.
b) a^{2}b,b^{2}c,c^{2}a are in H.P.
c) a^{2}b,b^{2}c,c^{2}a are in G.P.
d) None of these
2. The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is
a) 1
b) 8
c) 4
d) 6

19. Exponential and Logarithmic Series  Quiz
1. $\sum_{k = 1}^{\infty}\frac{1}{k!}\left (\sum_{n = 1}^{k} 2^{n1} \right )$ is equal to
a) e
b) e^{2} + e
c) e^{2}
d) e^{2}  e
2. The sum of the infinite series $\frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + \frac{4}{5!} + ....$ is
a) e  1
b) $\frac{2}{3}e  1$
c) 1
d) 3/2

20. Trigonometric Ratio, Function and Identities  Quiz
1. $tan\theta sin\left (\frac{\pi}{2} + \theta \right )cos\left (\frac{\pi}{2}  \theta \right )$ =
a) 1
b) 0
d) None of these
2. $\sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}$ is equal to
a) $cos7\frac{1}{2}^{0}$
b) $sin7\frac{1}{2}^{0}$
c) sin15^{0}
d) cos15^{0}

21. Trigonometric Equation and Inequation  Quiz
1. In a ΔABC, if $\frac{sinA}{sinC}$ = $\frac{sin\left (A  B \right )}{sin\left (B  C \right )}$, then a^{2} , b^{2}, c^{2} are in
a) A.P.
b) G.P.
c) H.P.
d) None of these
2. In a ΔABC a, c, A are given and b_{2},b_{2} are given and b_{1},b_{2} are two values of the third side b such that b_{2} = 2b_{1}. Then sinA =
a) $\sqrt{\frac{9a^{2}  c^{2}}{8a^{2}}}$
b) $\sqrt{\frac{9a^{2}  c^{2}}{8c^{2}}}$
c) $\sqrt{\frac{9a^{2} + c^{2}}{8a^{2}}}$
d) None of these

22. Hyperbolic Function  Quiz
1. 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) $\frac{1}{2}sin2xsinh2y$
2. cosh^{1}x =
a) $log\left (x + \sqrt{ x^{2} + 1} \right )$
b) $log\left (x  \sqrt{ x^{2} + 1} \right )$
c) $log\left (x  \sqrt{ x^{2}  1} \right )$
d) $log\left (x + \sqrt{ x^{2}  1} \right )$

23. Rectangular Cartesian Coordinate  Quiz
1. The vertices of a triangle are $\left [at_{1}t_{2}, a\left (t_{1} + t_{2} \right ) \right ], \left [at_{2}t_{3}, a\left (t_{2}  t_{3} \right ) \right ], \left [at_{3}t_{1},a\left (t_{3} + t_{1} \right ) \right ]$, then the coordination of its orthocentre are
a) $\left [a,a\left (t_{1} + t_{2} + t_{3} + t_{1}t_{2}t_{3} \right ) \right ]$
b) $\left [a,a\left (t_{1} + t_{2} + t_{3} + t_{1}t_{2}t_{3} \right ) \right ]$
c) $\left [a\left (t_{1} + t_{2} + t_{3} + t_{1}t_{2}t_{3} \right ),a \right ]$
d) None of these
2. 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

24. Circle and System of Circle  Quiz
1. A circle touches the xaxis and also touches the circle with centre at (0,3) and radius 2. The locus of the centre of the circle is
a) A hyperbola
b) A parabola
c) An ellipse
d) A circle
2. Let f(x,y) = 0 be the equation of a circle . If f(0, λ) = 0 equals roots λ = 1,1 and f(λ,0) = 0 has roots λ = $\frac{1}{2}$, 2 , then the centre of the circle is
a) (1,$\frac{1}{2}$)
b) ($\frac{5}{4}$,1)
c) (5,4)
d) ($\frac{1}{2}$,1)

25. Pair of Straight Line  Quiz
1. The condition of representing the coincident lines by the general quadratic equation f(x,y) = 0, is
a) Δ = 0 and h^{2} = ab
b) Δ = 0 and a + b = 0
c) Δ = 0 and h^{2} = ab, g^{2} = ac, f^{2} = bc
d) h^{2} = ab, g^{2} = ac and f^{2} = bc
2. The circumcentre of the triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0
a) (0,0)
b) (2,2)
c) (1,1)
d) (1,2)