## 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 non-void 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) 2n(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 450 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 y2 = 4ax passes through the focus of the parabola, then
a) t1t2 = -1
b) t1t2 = 1
c) t1 + t2 = -1
d) t1 - t2 = 1

2. The condition that the straight line lx + my = n may be a normal to the hyperbola b2x2 - a2y2 = a2b2 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 x2 + a2 = 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, p2 ≠ q and p3 ≠ -q. If α and β are non zero complex number satisfyiong α + β = -p and α3 + β3 = 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) a2 + c2 > b2
b) a2 + b2 > 2c2
c) a2 + c2 > 2b2
d) a2 + b2 > c2

2. If a, b, c are in G.P., then
a) a2, b2, c2 are in G.P.
b) a2(b + c), c2(a + b), b2(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) ax
b) x
c) alogax
d) a

2. The coefficient of x3 in the expansion of e2x+3 as a series in powers of x is
a) e3
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 cos6α + sin6α + Ksin22α = 1, then K =
a) $\frac{4}{3}$
b) $\frac{3}{4}$
c) $\frac{1}{2}$
d) 2

2. The least value of 2sin2θ + 3cos2θ 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 x2 + y2 + 1 is equal to
a) cos2u + sinh2v
b) sin2u + cosh2v
c) cos2u + cosh2v
d) sin2u + sinh2v

2. sin2(ix) + cosh2x is equal to
a) 1
b) -1
c) 2cosh2x
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 x2 + y2 = 1 subtends an angle measures 450 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 x2 + y2 - x = 0, x2 + y2 + 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(x2 - y2) + (p2 - q2)xy = 0 , is
a) px + qy = 0
b) px - qy = 0
c) p2x + q2y = 0
d) q2x - p2y = 0

2. The angle between the lines represented by the equation x2 - 2pxy + y2 = 0, is
a) sec-1p
b) cos-1 p
c) tan-1p
d) None of these