Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. 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. If X = {8^{n}  7n  1 : n ε N} and Y = {49(n  1) : n ε N}, then
a) X ⊆ Y
b) Y ⊆ X
c) X = Y
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 z = $\frac{1 + i\sqrt{3}}{\sqrt{3} + i}$, then $\left (\bar{z} \right )^{100}$ lies in
a) I quadrant
b) II quadrant
c) III quadrant
d) IV quadrant
2. If the amplitude of z  2  3i is π/4, then the locus of z = x + iy is
a) x + y  1 = 0
b) x  y 1 = 0
c) x + y + 1 = 0
d) x  y + 1 = 0

6. Linear Inequalities  Quiz

7. Permutations and Combinations  Quiz
1. How many words of 4 consonants and 3 vowels can be formed form 6 consonants and 5 vowels
a) 75000
b) 756000
c) 75600
d) None of these
2. The number of different words that can be formed out of the letters of the word MORADABAD taken four at a time is
a) 500
b) 600
c) 620
d) 626

8. Binomial Theorem  Quiz
1. The value of x in the expansion [x + x^{log10(x)}]^{5}, if the third term in the expansion is 10,00,000
a) 10
b) 11
c) 12
d) None of these
2. Coefficient of x^{11} in the expansion of (1 + x^{2})^{4}(1 + x^{3})^{7}(1 + x^{4})^{12} is
a) 1051
b) 1106
c) 1113
d) 1120

9. Sequences and Series  Quiz

10. Straight Lines  Quiz
1. The length of perpendicular from the point (a cosα , asinα) upon the straight line y = xtanα + c, c > 0 is
a) c cosα
b) c sin^{2}α
c) c sec^{2}α
d) c cos^{2}α
2. The line joining A(bcosα, bsinα) and B(acosβ,asinβ), where a ≠ b, is produced to the point , M(x,y) so that AM : MB = b : a Then $xcos\frac{\alpha + \beta}{2} + ysin\frac{\alpha + \beta}{2}$ is equal to
a) 0
b) 1
c) 1
d) a^{2} + b^{2}

11. Conic Sections  Quiz
1. Lines x + y = 1 and 3y = x + 3 intersect the ellipse x^{2} + 9y^{2} = 9 at the points P,Q,R. The area of triangle PQR is
a) $\frac{36}{5}$
b) $\frac{18}{5}$
c) $\frac{9}{5}$
d) $\frac{1}{5}$
2. The equation of the tangent parallel to y = x drawn to $\frac{x^{2}}{3}  \frac{y^{2}}{2}$ = 1 , is
a) x y  1 = 0
b) x  y + 2 = =
c) x + y  1 = 0
d) x + y + 2 = 0

12. Introduction to Three Dimensional Geometry  Quiz

13. Limits and Derivatives  Quiz

14. Mathematical Reasoning  Quiz
1. The statement p → (q → p) is equivalent to
a) p → (p ∨ q)
b) p → (p ^ q)
c) p → (p ↔ q)
d) p → (p → q)
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. If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1:2, then the magnitude of the resultant is
a) $\frac{P^{2} + Q^{2}}{P}$
b) $\frac{P^{2} + Q^{2}}{Q}$
c) $\frac{P^{2}  Q^{2}}{P}$
d) $\frac{P^{2}  Q^{2}}{Q}$
2. A stop is dropped from an aeroplane which is rising with acceleration f and t seconds after this another stone is dropped. The distance between the two stones at time T after the second stone is dropped is
a) $\frac{1}{2}\left (g + f \right )\left (t + T \right )t$
b) $\frac{1}{2}\left (g + f \right )\left (t + 2T \right )t$
c) $\frac{1}{2}\left (g + f \right )\left (2t + T \right )t$
d) $\frac{1}{2}\left (g  f \right )\left (t + 2T \right )t$

16. Probability  Quiz

17. Quadratic Equation and Inequation  Quiz
1. If b_{1}b_{2} = 2(c_{1} + c_{2}), then at least one of the equations x^{2} + b_{1}x + c_{1} = 0 and x^{2} + b_{2}x + c_{2} = has
a) Real roots
b) Purely imaginary roots
c) Imaginary roots
d) None of these
2. Let a,b,c be real numbers a ≠ 0. If α is a root a^{2}x^{2} + bx + c = 0, β is a root of a^{2}x^{2}  bx  c = 0 and 0 < α < β, then the equation a^{2}x^{2} + 2bx + 2c = 0 has a root γ that always satisfies
a) γ = $\frac{\alpha + \beta}{2}$
b) γ = α + $\frac{\beta}{2}$
c) γ = α
d) α < γ < β

18. Progression  Quiz
1. In the altitudes of a triangle are in A.P. , then the sides of the triangle are in
a) A.P.
b) H.P.
c) G.P.
d) Arithmeticogeometric progression
2. If a,b,c,d are any four consecutive coefficients of any expanded bionomial, then $\frac{a + b}{a}, \frac{b + c}{b}, \frac{c + d}{c}$ are in
a) A.P.
b) G.P.
c) H.P.
d) None of these

19. Exponential and Logarithmic Series  Quiz
1. $\frac{1}{3!} + \frac{2}{5!} + \frac{3}{7!} + ....$ =
a) e^{1}/2
b) e
c) e/4
d) e/6
2. The sum of the series $1 + \frac{1}{4.2!} + \frac{1}{16.4!} + \frac{1}{64.6!} + ....$ and inf. Is
a) $\frac{e  1}{2\sqrt{e}}$
b) $\frac{e + 1}{2\sqrt{e}}$
c) $\frac{e  1}{\sqrt{e}}$
d) $\frac{e + 1}{\sqrt{e}}$

20. Trigonometric Ratio, Function and Identities  Quiz
1. If $tan\frac{\theta}{2}$ = t, then $\frac{1  t^{2}}{1 + t^{2}}$ is equal to
a) cosθ
b) sinθ
c) secθ
d) cos2θ
2. $sin\left (\frac{\pi}{10} \right )sin\left (\frac{3\pi}{10} \right )$ =
a) 1/2
b) 1/2
c) 1/4
d) 1

21. Trigonometric Equation and Inequation  Quiz
1. cosθ = sin2θ(θ ≠ nπ, n is interger), if θ =
a) 45^{0} and 60^{0}
b) 45^{0} and 90^{0}
c) 45^{0} omly
d) 90^{0} only
2. In a triangle ABC, if a sinA = bsinB, then the nature of the sides of triangle is
a) a > b
b) a < b
c) a = b
d) a + b + c

22. Hyperbolic Function  Quiz
1. sin^{2}(ix) + cosh^{2}x is equal to
a) 1
b) 1
c) 2cosh^{2}x
d) cosh2x
2. sech^{1}(sinx) equals
a) $logcot\frac{x}{2}$
b) $logtan\frac{x}{2}$
c) log cotx
d) None of these

23. Rectangular Cartesian Coordinate  Quiz
1. The point of trisection of the line joining the point (0,3) and (6,3) are
a) (2,0) and (4,  1)
b) (2,  1 ) and (4,  1)
c) (3, 1 ) and (4,  1 )
d) (2,1) and (4,  1)
2. If the three points (3q,0), (0,3p) and (1,1) are collinear, then which one is true
a) $\frac{1}{p}  \frac{1}{q}$ = 1
b) $\frac{1}{p} + \frac{1}{q}$ = 1
c) $\frac{1}{p} + \frac{1}{q}$ = 3
d) $\frac{1}{p} + \frac{3}{q}$ = 3

24. Circle and System of Circle  Quiz
1. The condition that the line x cosα + ysinα = p may touch the circle x^{2} + y^{2} = a^{2} is
a) p = acosα
b) p = a tanα
c) p^{2} = a^{2}
d) psinα = a
2. the area of the curve x^{2} + y^{2} = 2ax is
a) πa^{2 b) 2πa2 c) 4πa2d) $\frac{1}{2}$πa2 } 
25. Pair of Straight Line  Quiz
1. The lines represented by the equation ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 will be equidistant from the origin, if
a) f^{2} + g^{2} = c(b  a)
b) f^{4} + g^{4} = c(bf^{2} + ag^{2})
c) f^{4}  g^{4}4 = c(bf^{2}  ag^{2})
d) f^{2} + g^{2} = af^{2} + bg^{2}
2. The equation x^{2} + k_{1}y^{2} + k_{2}xy = 0 represents a pair of perpendicular lines, if
a) k_{1} = 1
b) k_{1} = 2k_{2}
c) 2k_{1} = k_{2}
d) None of these