## 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) Anti-symmetric 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 z1.z2 and z3, z4 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) = nPrprqn-r
b) P(X = r) = nCrprqn-r
c) P(X = r) = nCrpr
d) P(X = r) = nCrpn-r

2. If nPr = 720. nCr, 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 y2 = 4x, the normal makes equal angles with the co-ordinates 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 b2x2 - a2y2 = a2b2 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/s2, 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 x3 + ax2 + 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) a2b, c2a,b2c are in A.P.
b) a2b,b2c,c2a are in H.P.
c) a2b,b2c,c2a 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. $\sum_{k = 1}^{\infty}\frac{1}{k!}\left (\sum_{n = 1}^{k} 2^{n-1} \right )$ is equal to
a) e
b) e2 + e
c) e2
d) e2 - 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) sin150
d) cos150

• 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 a2 , b2, c2 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 b2,b2 are given and b1,b2 are two values of the third side b such that b2 = 2b1. 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 sin2(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-1x =
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 x-axis 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 h2 = ab
b) Δ = 0 and a + b = 0
c) Δ = 0 and h2 = ab, g2 = ac, f2 = bc
d) h2 = ab, g2 = ac and f2 = 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)