## Class/Course - Class XI

### Subject - Math

#### Total Number of Question/s - 3865

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• 1. Sets - Quiz

1. 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. For any two sets A and B if A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X , then
a) A - B = A ∩ B
b) A = B
c) B - A = A ∩ B
d) None of these

• 2. Relations and Functions - Quiz

• 3. Trigonometric Functions - Quiz

• 4. Principle of Mathematical Induction - Quiz

• 5. Complex Numbers and Quadratic Equations - Quiz

1. If P is the point in the argand diagram corresponding to the complex number $\sqrt{3}$ + i and if OPQ is an isosceles right angled triangle, right angled at O, then Q represents the complex number
a) $\sqrt{3}$ - i or 1 - i$\sqrt{3}$
b) -1 ± i$\sqrt{3}$
c) -1 + i$\sqrt{3}$ or 1 - i$\sqrt{3}$
d) 1 ± i$\sqrt{3}$

2. If z = x + iy and $arg\left (\frac{z - 2}{z + 2} \right )$ = $\frac{\pi}{6}$, then locus of z is
a) A straight line
b) A circle
c) A parabola
d) An ellipse

• 6. Linear Inequalities - Quiz

• 7. Permutations and Combinations - Quiz

1. The value of 20P2 is
a) 20
b) 19
c) 380
d) None of these

2. 20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table. If the two particular persons are to be seated on either side of the host
a) 20!
b) 2 . 18!
c) 18!0
d) None of these

• 8. Binomial Theorem - Quiz

1. In the expansion of (x + a)n, the sum of odd terms is P and sum of even terms is Q, then the value of (P2 - Q2) will be
a) (x2 + a2)n
b) (x2 - a2)n
c) (x - a)2n
d) (x + a)2n

2. The term independent of x in $\left [\sqrt{\frac{x}{3}} + \frac{\sqrt{3}}{x^{2}} \right ]^{10}$ is
a) 2/3
b) 5/3
c) 4/3
d) None of these

• 9. Sequences and Series - Quiz

• 10. Straight Lines - Quiz

1. The equation of the perpendicular bisector of the line segment joining A(-2,3) and B(6,-5) is
a) x - y = -1
b) x - y = 3
c) x + y = 3
d) x + y = 1
e) x + y = -1

2. The equation of the line which bisects the obtuse angle between the lines x - 2y + 4 = 0 and 4x - 3y + 2 = 0, is
a) $\left (4 - \sqrt{5}\right )x - \left (3 -2 \sqrt{5} \right )y + \left (2 - 4\sqrt{5} \right )$ = 0
b) $\left (4 + \sqrt{5}\right )x - \left (3 +2 \sqrt{5} \right )y + \left (2 + 4\sqrt{5} \right )$ = 0
c) $\left (4 + \sqrt{5}\right )x + \left (3 +2 \sqrt{5} \right )y + \left (2 + 4\sqrt{5} \right )$ = 0
d) None of these

• 11. Conic Sections - Quiz

1. The locus of the point of intersection of lines (x + y)t = a and x - y = at, where t is the parameter , is
a) A circle
b) An ellipse
c) A rectangular hyperbola
d) None of these

2. Three normals are drawn to the parabola y2 = x through point (a,0) . Then
a) a = 1/2
b) a = 1/4
c) a = 1/2
d) None of these

• 12. Introduction to Three Dimensional Geometry - Quiz

• 13. Limits and Derivatives - Quiz

• 14. Mathematical Reasoning - Quiz

1. An AND gate is the Boolean function defined by
a) f(x1,x2) = x1.x2, x1x2 Îµ {0,1}
b) f(x1,x2) = x1 + x2, x1x2 Îµ {0,1}
c) f(x1,x2) = x1, x1x2 Îµ {0,1}
d) f(x1,x2) = x2, x1x2 Îµ {0,1}

2. Which of the following is not a proposition
a) $\sqrt{3}$ is a prime
b) $\sqrt{2}$ is irrational
c) Mathematics is interesting
d) 5 is an even integer

• 15. Statistics - Quiz

1. A force $\sqrt{5}$ unit act along the line $\frac{x-3}{2}$ = $\frac{y-4}{-1}$, the moment of the force about point (4,1) along z-axis is
a) 0
b) 5$\sqrt{5}$
c) -$\sqrt{5}$
d) 5

2. A bowler throws a bumper with a speed of 25 m/sec. The moment the ball touches the ground , it losses its energy by 1.5 kgm. If the weight of the ball is 225gm, the speed of the ball at which it hits the bat is
a) 2.22 m/sec
b) 22.2 m/sec
c) 4.44m/sec
d) 44.4 n/sec

• 16. Probability - Quiz

• 17. Quadratic Equation and Inequation - Quiz

1. If the equation anxn + an-1xn-1 + ….. + a1x = 0, a1 ≠ 0, n ≥ 2, has a positive root x = α , then the equation nanxn-1 + (n-1)an-1xn-2 + ..... + a1 = - has a positive root, which is
a) Greater than or equal to α
b) Equal to α
c) Greater than α
d) Smaller than α

2. The condition that x3 - px2 + qx - r = 0 may have two of its roots equal to each other but opposite in sign is
a) r = pq
b) r = 2p3 + pq
c) r = p2q
d) None of these

• 18. Progression - Quiz

1. The sum of the series 5.05 + 1.212 + 0.29088 + …. ∞ is
a) 6.93378
b) 6.87342
c) 6.74384
d) 6.64474

2. A boy goes to school from his home at a speed of x km/hour and comes back at a speed of y km/hour, then the average speed is given by
a) A.M.
b) G.M.
c) H.M.
d) None of these

• 19. Exponential and Logarithmic Series - Quiz

1. If x,y,x are three consecutive positive integers, then $\frac{1}{2}log_{e}x + \frac{1}{2}log_{e}z + \frac{1}{2xz + 1} + \frac{1}{3}\left (\frac{1}{2xz + 1} \right )^{3} + ....$ =
a) logex
b) logey
c) logez
d) None of these

2. If S = $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - \frac{1}{4.5} + .... + \infty$, then eS =
a) $log_{e}\left (\frac{4}{e} \right )$
b) $\frac{4}{e}$
c) $log_{e}\left (\frac{e}{4} \right )$
d) $\frac{e}{4}$

• 20. Trigonometric Ratio, Function and Identities - Quiz

1. If x + y + z = 1800, then cos2x + cos2y - cos2z is equal to
a) 4sinx.siny.sinz
b) 1 - 4sinx.siny.cosz
c) 4sinx.siny.sinz-1
d) cosA.cosB.cosC

2. $sin^{4}\frac{\pi}{8} + sin^{4}\frac{3\pi}{8} + sin^{4}\frac{5\pi}{8} + sin^{4}\frac{7\pi}{8}$ = =
a) $\frac{1}{2}$
b) $\frac{1}{4}$
c) $\frac{3}{2}$
d) $\frac{3}{4}$

• 21. Trigonometric Equation and Inequation - Quiz

1. If a, b,c are the sides of a triangle ABC, then which of the following inequalities is not true
a) 8abc ≤ (a + b)(b + c)(c + a)
b) 2bc ≤ a3 + b3 + c3
c) 6abc ≤ bc(b + c) + ca(c + a) + ab(a + b)
d) abc ≤ (a + b - c)(b + c - a)(c + a - b)

2. In ΔABC, $\frac{1}{a}cos^{2}\frac{A}{2} + \frac{1}{b}cos^{2}\frac{B}{2} + \frac{1}{c}cos^{2}\frac{C}{2}$ =
a) s
b) $\frac{s}{abc}$
c) $\frac{s^{2}}{abc}$
d) $\frac{s^{3}}{abc}$

• 22. Hyperbolic Function - Quiz

1. sin2(ix) + cosh2x is equal to
a) 1
b) -1
c) 2cosh2x
d) cosh2x

2. cosech-1 equals
a) $log\left (\frac{1 + \sqrt{1 + x^{2}}}{x} \right )$
b) $log\left (\frac{1 + \sqrt{1 - x^{2}}}{x} \right )$
c) $log\left (\frac{1 - \sqrt{1 - x^{2}}}{x} \right )$
d) $log\left (\frac{1 - \sqrt{1 + x^{2}}}{x} \right )$

• 23. Rectangular Cartesian Coordinate - Quiz

1. Two vertices of a triangle are (4,-3) and (-2,5) . If the orthocentre of the triangle is at (1,2), then the third vertex is
a) (-33,-26)
b) (33,26)
c) (26,33)
d) None of these

2. The following points A(2a,4a), B(2a,6a) and C(2a, $\sqrt{3}a$,5a), (a>0) are the vertices of
a) An acute angled triangle
b) A right angles triangle
c) An isosceles triangle
d) None of these

• 24. Circle and System of Circle - Quiz

1. Area of the circle in which a cord of length $\sqrt{2}$ makes an angle $\frac{\pi}{2}$ at the centre is
a) $\frac{\pi}{2}$
b) 2π
c) π
d) $\frac{\pi}{4}$

2. The equation of the circle which passes through (1,0) and (0-,1) and has its radius as small as possible , is
a) x2 + y2 - 2x - 2y +1 = 0
b) x2 + y2 - x - y = 0
c) 2x2 + 2y2 - 3x - 3y + 1 = 0
d) x2 + y2 - 3x - 3y + 2 = 0

• 25. Pair of Straight Line - Quiz

1. Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c)(x2 - 5y + 6y2) = 0 represents
a) Four straight lines, when c = 0 and a,b are of the same sign
b) Two straight lines and a circle, when a = b and c is of sign opposite to that of a
c) Two straight line and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
d) A circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a

2. If in general quadratic equation f(x,y) = 0, Δ = 0 and h2 = ab, then the equation represents
a) Two parallel then the equation represents
b) Two perpendicular straight lines
c) Two coincident lines
d) None of these