## 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 1-i, 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) 4m+n-2
d) m2n2

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 x2 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 x2 + y2 = 2 and the parabola y28x 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 x2 + 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 ax2 + 2bx + c = 0, 2bx2 + cx + a = 0 and cx2 + ax + 2b = 0 respectively, where a,b and c are positive real numbers, then α + α2 =
a) -1
b) 0
c) abc
d) a + 2b + c
e) None of these

2. Let α, &beta be the roots x2 - x + p = 0 and γ , δ be the roots of x2 - 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 G1, G2, ….Gn and a geometric mean be G, then the true relation is
a) G1.G2 ….. Gn = G
b) G1.G2…….Gn = G1/n
c) G1.G2 …..Gn = Gn
d) G1.G2 …. Gn = G2/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. sin120sin240sin480sin840 =
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 in-radius to the circum-radius 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-1x 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 sin2(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 A-M-B 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 θ1, θ2 be the inclination of tangents drawn from the point P to the circle x2 + y2 = a2 with x-axis , then the locus of P, if given that cotθ1 + cotθ2 = c is
a) c(x2 - a2) = 2xy
b) c(x2 - a2) = y2 - a2
c) c(y2 - a2) = 2xy
d) None of these

2. The centre of the circle passing through (0,0) and (1,0) and touching the circle x2 + y2 = 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 x2 + 2xycotθ - y2 = 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 x2 + ky2 + 4xy = 0 represents two coincident lines, if k =
a) 0
b) 1
c) 4
d) 16