## Class/Course - Class XI

### Subject - Math

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

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• 1. Sets - Quiz

1. Let A = {x,y,z) and B = {a,b,c,d}. Which one of the following is not a relation form A to B
a) {(x,a), (x,c)}
b) {(y,c), (y,d)}
c) {(z,a), (z,d)}
d) {(z,b), (y,b), (a,d)}
e) {(x,c)}

2. Which of the following is a true statement
a) {a} ε {a,b,c}
b) {a} ⊆ {a,b,c}
c) φ ε {a,b,c}
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. sinh ix is
a) i sin(ix)
b) i sin x
c) -i sinx
d) sin(ix)

2. A wan walks a distance of 3 units from the origin towards the north-east (N 450E direction. From there, he walks a distance of 4 units towards the north-west (N 450W) direction to reach a point P. Then the position of P in the Argand plane is
a) 3eiπ/4 + 4i
b) (3 - 4i)eiπ/4
c) (4 + 3i)eiπ/4
d) (3 + 4i)eiπ/4

• 6. Linear Inequalities - Quiz

• 7. Permutations and Combinations - Quiz

1. A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, then the number of ways in which the car can be filled is
a) 10
b) 20
c) 30
d) None of these

2. The number of ways in which 10 persons can go in two boats so that there may be 5 on each boat, supposing that two particular will not go in the same boat is
a) $\frac{1}{2}\left (^{10}C_{5} \right )$
b) 2(8C4)
c) $\frac{1}{2}\left (^{8}C_{5} \right )$
d) None of these

• 8. Binomial Theorem - Quiz

1. In the expansion of $\left (2x^{2} - \frac{1}{x} \right )^{12}$, the term independent of x is
a) 10th
b) 9th
c) 8th
d) 7th

2. The value of $\binom{30}{0}\binom{30}{0} - \binom{30}{1}\binom{30}{11} + \binom{30}{2}\binom{30}{12} + ....... + \binom{30}{20}\binom{30}{30}$
a) 60C20
b) 30C10
c) 60C30
d) 40C30

• 9. Sequences and Series - Quiz

• 10. Straight Lines - Quiz

1. If the line px - qy = r intersects the co-ordinate axes at (a,0) and (0,b), then value of a + b is equal to
a) $r\left (\frac{q + p}{pq} \right )$
b) $r\left (\frac{q - p}{pq} \right )$
c) $r\left (\frac{p - q}{pq} \right )$
d) $r\left (\frac{p + q}{q - p} \right )$
e) $r\left (\frac{p - q}{q + p} \right )$

2. The vertices of a triangle are (2,1), (5,2) and (4,4). The lengths of the perpendicular from the vertices on the opposite sides are
a) $\frac{7}{\sqrt{5}}, \frac{7}{\sqrt{13}}, \frac{7}{\sqrt{6}}$
b) $\frac{7}{\sqrt{6}}, \frac{7}{\sqrt{8}}, \frac{7}{\sqrt{10}}$
c) $\frac{7}{\sqrt{5}}, \frac{7}{\sqrt{8}}, \frac{7}{\sqrt{15}}$
d) $\frac{7}{\sqrt{5}}, \frac{7}{\sqrt{13}}, \frac{7}{\sqrt{10}}$

• 11. Conic Sections - Quiz

1. The line xcosα + ysinα = p will be a tangent to the conic $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 , if
a) p2 = a2sin2α + b2cos2α
b) p2 = a2 + b2
c) p2 = b2sin2α + a2cos2α
d) None of these

2. Let P be a variable point on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 with foci F1 and F2. If A is the area of the triangle PF1F2, then maximum value of A is
a) ab
b) abe
c) $\frac{e}{ab}$
d) $\frac{ab}{e}$

• 12. Introduction to Three Dimensional Geometry - Quiz

• 13. Limits and Derivatives - Quiz

• 14. Mathematical Reasoning - Quiz

1. ∼ p ^ q is logically equivalent to
a) p → q
b) q → p
c) ∼ (p → q)
d) ∼(q → p)

2. Which of the following is the inverse of the proposition : If a number is a prime then it is odd.
a) If a number is not a prime then it is odd
b) If a number is not a prime then it is not odd
c) If a number is not odd then it is not a prime
d) If a number is not odd then it is a prime

• 15. Statistics - Quiz

1. A glass marble, whose mass is (1/10)kg falls from a height of 2.5 m and rebounds to a height of 1.6m. Then the average force between the marble and the floor , if the time during which they are in contact be one-tenth of a second, is
a) 10.58 N
b) 11.58 N
c) 12.58 N
d) 13.58N

2. The resultant of the forces 4,3,4 and 3 unit acting along the lines AB, BC, CD and DA of a square ABCD of side a respectively is
a) A force 5$\sqrt{2}$ through the centre of the square
b) A couple of moment 7a
c) A null force
d) None of these

• 16. Probability - Quiz

• 17. Quadratic Equation and Inequation - Quiz

1. If the roots of the equation x2 - 5x + 16 = 0 are α, β and the roots of equation x2 + px + q = 0 are α2 + β2 , $\frac{\alpha\beta}{2}$, then
a) p = 1, q = -56
b) p = -1, q = -56
c) p = 1, q = 56
d) p = -1, q = 56

2. If the roots of equation $\frac{x^{2} - bx}{ax - c}$ = $\frac{m - 1}{m + 1}$ are equal but opposite in sign, then the value of m will be
a) $\frac{a - b}{a + b}$
b) $\frac{b - a}{a + b}$
c) $\frac{a + b}{a - b}$
d) $\frac{b + a}{b - a}$

• 18. Progression - Quiz

1. The sum of three decreasing numbers in A.P. is 27. If -1,-1,3 are added to them respectively, the resulting series is in G.P. The numbers are
a) 5, 9, 13
b) 15, 9, 3
c) 13, 9 , 5
d) 17, 9 , 1

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. $1 + \frac{4^{2}}{3!} + \frac{4^{4}}{5!} + .... \infty$ =
a) $\frac{e^{4} + e^{-4}}{4}$
b) $\frac{e^{4} - e^{-4}}{4}$
c) $\frac{e^{4} + e^{-4}}{8}$
d) $\frac{e^{4} - e^{-4}}{8}$

2. $\frac{1}{1.3} + \frac{1}{2.5} + \frac{3.7}{} + \frac{1}{4.9} + ...$ is equal to
a) 2loge2 - 2
b) 2 - loge 2
c) 2loge4
d) loge4

• 20. Trigonometric Ratio, Function and Identities - Quiz

1. If A, B, C are angles of a triangle, then sin2A + sin2B - sin2C is equal to
a) 4sinA cosB cosC
b) 4cosA
c) 4sinAcosA
d) 4cosAcosBcosC

2. $cos^{2}\left (\frac{\pi}{6} + \theta\right ) - sin^{2}\left (\frac{\pi}{6} - \theta \right )$ =
a) $\frac{1}{2}cos2\theta$
b) 0
c) -$\frac{1}{2}cos2\theta$
d) $\frac{1}{2}$

• 21. Trigonometric Equation and Inequation - Quiz

1. The most general value of θ satisfying the equations tanθ = -1 and cosθ = $\frac{1}{\sqrt{2}}$ is
a) $n\pi + \frac{7\pi}{4}$
b) $n\pi + \left (-1 \right )^{n}\frac{7\pi}{4}$
c) $2n\pi + \frac{7\pi}{4}$
d) None of these

2. In a ΔABC, r1 < r2 < r3 , then
a) a < b < c
b) a > b > c
c) b < a < c
d) a < c < b

• 22. Hyperbolic Function - Quiz

1. If cosecθ = cothx, then the value of tanθ is
a) coshx
b) sinhx
c) tanhx
d) cosechx

2. The value of $2coth^{-1}\left (\frac{z}{2} \right )$ is
a) $log\left (\frac{z - 2}{z + 2} \right )$
b) $\frac{1}{2}$$log\left (\frac{z - 1}{z + 1} \right ) c) \frac{1}{2}$$log\left (\frac{z + 1}{z - 1} \right )$
d) -$log\left (\frac{z - 2}{z + 2} \right )$

• 23. Rectangular Cartesian Coordinate - Quiz

1. ABC is an isosceles triangle. If the coordinates of the base are B(1,3) and C(-2,7), the coordination of vertex A can be
a) (1,6)
b) $\left (-\frac{1}{2},5 \right )$
c) $\left (\frac{5}{6},6 \right )$
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. The two circles which passes through (0, a) and (0,-a) and touch the line y = mx + c will intersect each other at right angle, if
a) a2 = c2(2m + 1)
b) a2 = c2(2 + m2)
c) c2 = a2(2 + m2)
d) c2 = a2(2m + 1)

2. The line L passes through the points of intersection of the circles x2 + y2 = 25 and x2 + y2 - 8x + 7 = 0. The length of perpendicular from centre of second circle onto the line L, is
a) 4
b) 3
c) 1
d) 0

• 25. Pair of Straight Line - Quiz

1. The area enclosed bounded by the angle bisectors of the lines x2 - y2 + 2y = 1 and the line x + y = 3, is
a) 2
b) 3
c) 4
d) 6

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