## Class/Course - Class XI

### Subject - Math

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

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• 1. Sets - Quiz

1. If A = [(x,y) : x2 + y2 = 25]
and B = [(x,y) : x2 + 9y2 = 144], then A ∩ B contains
a) One point
b) Three points
c) Two points
d) Four points

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. ω is an imaginary cube root of unity . If (1 + ω2)m = (1 + ω4)m, then least positive integral value of m is
a) 6
b) 5
c) 4
d) 3

2. If ω is a complex cube root of unity, then
225 + (3ω + 8ω2)2 + (3ω2 + 8ω2) =
a) 72
b) 192
c) 200
d) 248

• 6. Linear Inequalities - Quiz

• 7. Permutations and Combinations - Quiz

1. The greatest possible number of points of intersection of 8 straight lines and 4 circleds is
a) 32
b) 64
c) 76
d) 104

2. The product r consecutive intergers is divisible by
a) r!
b) (r - 1)!
c) (r + 1)!
d) None of these

• 8. Binomial Theorem - Quiz

1. The coefficient of x5 in the expansion of (x + 3)6 is
a) 18
b) 6
c) 12
d) 10

2. Term independent of x in $\left (\sqrt{x} + \frac{m}{x^{2}} \right )^{10}$ is 405, m =
a) 2
b) 9
c) 3
d) -3

• 9. Sequences and Series - Quiz

• 10. Straight Lines - Quiz

1. If the three points A(1,6), B(3,-4) and C(x,y) are collinear , then the equation satisfying by x and y is
a) 5x + y - 11= 0
b) 5x + 13y + 5 = 0
c) 5x - 13y + 5 = 0
d) 5x - 13y + 5 = 0
e) 13x - 5y + 5 = 0

2. The points (1,3) and (5,1) are the opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then the value of c will be
a) 4
b) -4
c) 2
d) -2

• 11. Conic Sections - Quiz

1. The equation of the hyperbola whose foci are the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9}$ = 1 and the eccentricity is 2 is
a) $\frac{x^{2}}{4} + \frac{y^{2}}{12}$ = 1
b) $\frac{x^{2}}{4} - \frac{y^{2}}{12}$ = 1
c) $\frac{x^{2}}{12}+ \frac{y^{2}}{4}$ = 1
d) $\frac{x^{2}}{12} - \frac{y^{2}}{4}$ = 1

2. For the ellipse 25x2 + 9y2 - 150x - 90y + 225 = 0 the eccentricity e =
a) 2/5
b) 3/5
c) 4/5
d) 1/5

• 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. Let S be a non-empty subset of R. consider the following statement.
p : There is a rational number x ε S such that x > 0 .
Which of the following statements is the negation of the statement p
a) There is a rational number x ε S such that x ≤ 0
b) There is no rational number x ε S such that x ≤ 0
c) Every rational number x ε S satisfies x ≤ 0
d) x ε S and x ≤ 0 ⇒ is not rationsl

• 15. Statistics - Quiz

1. A body is projected through an angle α from vertical so that its range is half of maximum range, α is
a) 600
b) 750
c) 300
d) 22.50

2. A particle is dropped under gravity from rest from a height h(g = 9.8m/sec2) and then it travels a distance $\frac{9h}{25}$ in the last second. The height h is
a) 100 metre
b) 122.5 metre
c) 145 metre
d) 167.5 metre

• 16. Probability - Quiz

• 17. Quadratic Equation and Inequation - Quiz

1. If ax2 + bx + c = 0, then x =
a) $\frac{b \pm \sqrt{b^{2} - 4ac}}{2a}$
b) $\frac{-b \pm \sqrt{b^{2} - ac}}{2a}$
c) $\frac{2c}{-b \pm \sqrt{b^{2} - 4ac}}$
d) None of these

2. If b1b2 = 2(c1 + c2), then at least one of the equations x2 + b1x + c1 = 0 and x2 + b2x + c2 = has
a) Real roots
b) Purely imaginary roots
c) Imaginary roots
d) None of these

• 18. Progression - Quiz

1. The sum of the series
$\frac{1}{1 + 1^{2} + 1^{4}} + \frac{2}{1 + 2^{2} + 2^{4}} + \frac{3}{1 + 3^{2} + 3^{4}} + .....$ to n terms is
a) $\frac{n\left (n^{2} + 1 \right )}{n^{2} + n + 1}$
b) $\frac{n\left (n + 1 \right )}{2\left (n^{2} + n + 1 \right )}$
c) $\frac{n\left (n^{2} - 1 \right )}{2\left (n^{2} + n + 1 \right )}$
d) None of these

2. If a, b, c are in A.P., then 2ax+1, 2bx+1m 2cx+1 , x ≠ 0 are in
a) A.P.
b) G.P. only when x > 0
c) G.P. if x < 0
d) G.P. for all x ≠ 0

• 19. Exponential and Logarithmic Series - Quiz

1. The sum of the series $\frac{1}{1.2} + \frac{1.3}{1.2.3.4} + \frac{1.3.5}{1.2.3.4.5.6} + .... \infty$ is
a) 15e
b) e1/2 + 2
c) e1/2 - 1
d) e1/2 - e

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. $\frac{sin3\theta + sin5\theta + sin7\theta + sin9\theta}{cos3\theta + cos5\theta + cos7\theta + cos9\theta}$ =
a) tan3θ
b) cos3θ
c) tan6θ
d) cot6θ

2. If f(x) = cos2x + sec2x , then
a) f(x) < 1
b) f(x) = 1
c) 1 < f(x) < 2
d) f(x) ≥ 2

• 21. Trigonometric Equation and Inequation - Quiz

1. A tower is situated on horizontal plane. From two points, the line joining three points passes through the base and which are a and b distance from the base. The angle of elevation of the top are α and 900 - α and θ is that angle which two points joining the line makes at the top, the height of tower will be
a) $\frac{a + b}{a - b}$
b) $\frac{a - b}{a + b}$
c) $\sqrt{ab}$
d) (ab)1/3

2. The only value of x for which 2sinx + 2cosx > 21-(1/$\sqrt{2}$) holds is,
a) $\frac{5\pi}{4}$
b) $\frac{3\pi}{4}$
c) $\frac{\pi}{2}$
d) All values of x

• 22. Hyperbolic Function - Quiz

1. The value of tan-1(2-1) is
a) log 2
b) log 2-1
c) log $\sqrt{3}$
d) None of these

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

• 23. Rectangular Cartesian Coordinate - Quiz

1. Three vertices of a parallelogram taken in order are (-1,-6), (2,-5) and (7,2). The fourth vertex is
a) (1,4)
b) (4,1)
c) (1,1)
d) (4,4)

2. The points (1,1), (0, sec2 θ), (cosec2θ,0) are collinear for
a) θ = $\frac{n\pi}{2}$
b) θ ≠ $\frac{n\pi}{2}$
c) θ = nπ
d) None of these

• 24. Circle and System of Circle - Quiz

1. A circle with centre (a,b) passes through the origin. The equation of the tangent to the circle at the origin is
a) ax - by = 0
b) ax + by = 0
c) bx - ay = 0
d) bx + ay = 0

2. Equation to the circles which touch the lines 3x - 4y + 1 = 0, 4x + 3y - 7 = 0 and pass through (2,3) are
a) (x - 2)2 + (y - 8)2 = 25
b) 5x2 + 5y2 - 12x - 24y + 31 = 0
c) Both (a) and (b)
d) None of these

• 25. Pair of Straight Line - Quiz

1. Two of the lines represented by the equation ay4 + bxy3 + cx2y2 + dx3y + ex4 = - will be perpendicular, then
a) (b + d)(ad + be) + (e - a)2(a + c + e) = 0
b) (b + d)(ad + be) + (e + a)2(a + c + e) = 0
c) (b - d)(ad - be) + (e - a)2(a + c + e) = 0
d) (b - d)(ad - be) + (e + a)2(a + c + e) = 0

2. The lines represented by the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 will be equidistant from the origin, if
a) f2 + g2 = c(b - a)
b) f4 + g4 = c(bf2 + ag2)
c) f4 - g44 = c(bf2 - ag2)
d) f2 + g2 = af2 + bg2