Class/Course  Class XI
Subject  Math
Total Number of Question/s  3865
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1. Sets  Quiz
1. Let r be a relation for R (set of real numbers) to R defined by r = {a,b)a,b ε R and a  b + $\sqrt{3}$ is an irrational number }. The relation r is
a) An equivalence relation
b) Reflexive only
c) Symmetric only
d) Transitive only
2. Let R and S be two nonvoid relations on a set A. Which of the following statements is false
a) R and S are transitive ⇒ R ∪ S is transitive
b) R and S are transitive ⇒ R ∩ S is transitive
c) R and S are symmetric ⇒ R ∪ S is symmetric
d) R and S are reflexive ⇒ R ∩ S is reflexive

2. Relations and Functions  Quiz

3. Trigonometric Functions  Quiz

4. Principle of Mathematical Induction  Quiz

5. Complex Numbers and Quadratic Equations  Quiz
1. If $\left (\frac{1  i}{1 + i} \right )^{100}$ = a + ib, then
a) a = 2, b = 1
b) a = 1, b = 0
c) a = 0, b = 1
d) a = 1, b = 2
2. Let z and ω be two complex numbers such that z ≤ 1, ω ≤ 1 and z + iω = $\left  z  i\bar{\omega } \right $ = 2. Then z is equal to
a) 1 or i
b) i or i
c) 1 or 1
d) i or 1

6. Linear Inequalities  Quiz

7. Permutations and Combinations  Quiz
1. All the letters of the word EAMCET are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is
a) 360
b) 114
c) 72
d) 54
2. In how many ways can 6 persons be selected from 4 officers and 8 constables, if at least one officer is to be included
a) 224
b) 672
c) 896
d) None of these

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. Coefficient of middle term in expansion (1 + x)^{2n}
a) $\frac{2^{n}\left (2n  1 \right )\left (2n  3 \right )....3.1}{n\left (n  1 \right )\left (n  2 \right ).....3.2.1}$
b) 2^{n}(2n  1)(2n  3)….3.1
c) n(n + 1)(n + 2)….3.2.1
d) $\frac{2^{2n}\left (2n  1 \right )\left (2n  3 \right )....3.1}{n\left (n  1 \right )\left (n  2 \right ).....3.2.1}$

9. Sequences and Series  Quiz

10. Straight Lines  Quiz
1. The equations of the lines through (1,1) and making angles of 45^{0} with the line x + y = 0
a) x  1 = 0, x  y = 0
b) x  y = 0, y  1 = 0
c) x + y  2 = 0, y  1 = 0
d) x  1 = 0, y  1 = 0
2. The medians AD and BE of a triangle with vertices A(0,b) , B(0,0) and C(a,0) are perpendicular to each other if,
a) a = $\sqrt{2}$b
b) a = $\sqrt{2}$b
c) Both (a) and (b)
d) None of these

11. Conic Sections  Quiz
1. If the chord joining the points $\left (a_{1}^{2}, 2at_{1} \right )$ and $\left (at_{2}^{2}, 2at_{2} \right )$ of the parabola y^{2} = 4ax passes through the focus of the parabola, then
a) t_{1}t_{2} = 1
b) t_{1}t_{2} = 1
c) t_{1} + t_{2} = 1
d) t_{1}  t_{2} = 1
2. The condition that the straight line lx + my = n may be a normal to the hyperbola b^{2}x^{2}  a^{2}y^{2} = a^{2}b^{2} 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. Let p:7 is not greater than 4 and q : Paris in France be two statements . Then, ∼ (p ∨ q) is the statement
a) 7 is greater than 4 or Paris is not in Frtance
b) 7 is not greater than 4 and Paris is not in France
c) 7 is not greater than 4 and Paris is in France
d) 7 is not greater than 4 or Paris is not in France
e) 7 is greater than 4 and Paris is not in France
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 ball impinges directly upon another ball at rest and is itself reduced to rest by the imapct. If half of the K.E. is destroyed in the collision, the coefficient of restitution, is
a) $\frac{1}{4}$
b) $\frac{1}{3}$
c) $\frac{3}{4}$
d) $\frac{1}{2}$
2. At what height from the base of a vertical pillar, a string of length 6 metres be tied, so that a man sitting on the ground and pulling the other end of the string has to apply minimum force to overtum the pillar
a) 1.5 metres
b) 3$\sqrt{2}$ metres
c) 3$\sqrt{3}$ metres
d) 4$\sqrt{2}$ metres

16. Probability  Quiz

17. Quadratic Equation and Inequation  Quiz
1. If the roots of equation x^{2} + a^{2} = 8x + 6a are real , then
a) a ε [2,8]
b) a ε [2,8]
c) a ε (2,8)
d) a ε (2,8)
2. Let p and q be real numbers such that p ≠ 0, p^{2} ≠ q and p^{3} ≠ q. If α and β are non zero complex number satisfyiong α + β = p and α^{3} + β^{3} = q, then a quadratic equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is
a) $\left (p^{3} + q \right )x^{2}  \left (p^{3} + 2q \right )x + \left (p^{3} + q \right )$ = 0
b) $\left (p^{3} + q \right )x^{2}  \left (p^{3}  2q \right )x + \left (p^{3} + q \right )$ = 0
c) $\left (p^{3}  q \right )x^{2}  \left (5p^{3}  2q \right )x + \left (p^{3}  q \right )$ = 0
d) $\left (p^{3}  q \right )x^{2}  \left (5p^{3} + 2q \right )x + \left (p^{3}  q \right )$ = 0

18. Progression  Quiz
1. If a,b,c be in H.P., then
a) a^{2} + c^{2} > b^{2}
b) a^{2} + b^{2} > 2c^{2}
c) a^{2} + c^{2} > 2b^{2}
d) a^{2} + b^{2} > c^{2}
2. If a, b, c are in G.P., then
a) a^{2}, b^{2}, c^{2} are in G.P.
b) a^{2}(b + c), c^{2}(a + b), b^{2}(a + c) are in G.P.
c) $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$
d) None of the above

19. Exponential and Logarithmic Series  Quiz
1. $1 + xlog_{e}a + \frac{x^{2}}{2!}\left (log_{e}a \right )^{2} + \frac{x^{3}}{3!}\left (log_{e}a \right )^{3} + ....$ =
a) a^{x}
b) x
c) a^{logax}
d) a
2. The coefficient of x^{3} in the expansion of e^{2x+3} as a series in powers of x is
a) e^{3}
b) $\frac{3}{4}e^{3}$
c) $\frac{4}{3}e^{3}$
d) None of these

20. Trigonometric Ratio, Function and Identities  Quiz
1. If cos^{6}α + sin^{6}α + Ksin^{2}2α = 1, then K =
a) $\frac{4}{3}$
b) $\frac{3}{4}$
c) $\frac{1}{2}$
d) 2
2. The least value of 2sin^{2}θ + 3cos^{2}θ is
a) 1
b) 2
c) 3
d) 5

21. Trigonometric Equation and Inequation  Quiz
1. Let PQR be a triangle of area Δ will a = 2, b = $\frac{7}{2}$ and c = $\frac{5}{2}$, where a, b and c are the lengths of the sides of the triangle opposite to the angles at P,Q and R respectively. Then $\frac{2sinP  sin2P}{2sinP + sin2P}$ equals
a) $\frac{3}{4\Delta}$
b) $\frac{45}{4\Delta}$
c) $\left (\frac{3}{4\Delta} \right )^{2}$
d) $\left (\frac{45}{4\Delta} \right )^{2}$
2. If tanθ = $\frac{1}{\sqrt{3}}$ and sinθ = $\frac{1}{2}$,cosθ = $\frac{\sqrt{3}}{2}$, then the principal value of θ will be
a) $\frac{\pi}{6}$
b) $\frac{5\pi}{6}$
c) $\frac{7\pi}{6}$
d) $\frac{\pi}{6}$

22. Hyperbolic Function  Quiz
1. If cos(u + iv) + x + iy, then x^{2} + y^{2} + 1 is equal to
a) cos^{2}u + sinh^{2}v
b) sin^{2}u + cosh^{2}v
c) cos^{2}u + cosh^{2}v
d) sin^{2}u + sinh^{2}v
2. sin^{2}(ix) + cosh^{2}x is equal to
a) 1
b) 1
c) 2cosh^{2}x
d) cosh2x

23. Rectangular Cartesian Coordinate  Quiz
1. Let A(2,3) and B(2,1) be vertices of a triangle ABC . If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
a) 3x  2y = 3
b) 2x  3y =7
c) 3x + 2y =5
d) 2x + 3y =9
2. The orthocentre of the triangle by the lines x + y = 1, 2x + 3y = 6 and 4x  y + 4 = 0 lies in quadrant
a) First
b) Second
c) Third
d) Fourth

24. Circle and System of Circle  Quiz
1. If the chord y = mx + 1 of the circle x^{2} + y^{2} = 1 subtends an angle measures 45^{0} at the major segment of the circle then value of m is
a) 2
b) 2
c) 1
d) None of these
2. The number of common tangents to the circles x^{2} + y^{2}  x = 0, x^{2} + y^{2} + x = 0 is
a) 2
b) 1
c) 4
d) 3

25. Pair of Straight Line  Quiz
1. The equation of one of the line represented by the equation pq(x^{2}  y^{2}) + (p^{2}  q^{2})xy = 0 , is
a) px + qy = 0
b) px  qy = 0
c) p^{2}x + q^{2}y = 0
d) q^{2}x  p^{2}y = 0
2. The angle between the lines represented by the equation x^{2}  2pxy + y^{2} = 0, is
a) sec^{1}p
b) cos^{1} p
c) tan^{1}p
d) None of these