Question Bank for Math in Class XI standard : Just Exam

Class/Course - Class XI

Subject - Math

Total Number of Question/s - 3865

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1. Sets - Quiz

1. Let a relation R is defined by R = {(4,5); (1,4); (4,6); (7,6); (3,7)} then R^-1oR is
a) {(1,1), (4,4), (4,7), (7,4),(7,7), (3,3)}
b) {(1,1), (4,4), (7,7), (3,3)}
c) {(1,5), (1,6), (3,6)}
d) None of these

2. Let R = {(1,3), (2,2), (3,2)} and S = {(2,1), (3,2), (2,3)} be two relations on set A = {1,2,3}. Then RoS =
a) {(1,3), (2,2), (3,2), (2,1), (2,3)}
b) {(3,2), (1,3)}
c) {(2,3), (3,2), (2,2)}
d) {(2,3), (3,2)}
2. Relations and Functions - Quiz
3. Trigonometric Functions - Quiz
4. Principle of Mathematical Induction - Quiz
5. Complex Numbers and Quadratic Equations - Quiz

1. If |8 + z| + |z - 8| = 16 where z is a complex number, then the point z will lie on
a) A circle
b) An ellipse
c) A straight line
d) None of these

2. The argument of the complex number $\frac{13 - 5i}{4 - 9i}$ is
a) $\frac{\pi}{3}$
b) $\frac{\pi}{4}$
c) $\frac{\pi}{5}$
d) $\frac{\pi}{6}$
6. Linear Inequalities - Quiz
7. Permutations and Combinations - Quiz

1. In ⁿp_r = 30240 and ⁿC_r = 252, then the ordered pair (n,r) is equal to
a) (12,6)
b) (10,5)
c) (9,4)
d) (16,7)

2. A parallelogram is cut by two sets of m lines parallel to its sides. The number of parallelgrams thus formed is
a) (^mC₂)²
b) (^m+1C₂)
c) (^m+2C₂)²
d) None of these
8. Binomial Theorem - Quiz

1. If the coefficient of x⁷ in $\left (ax^{2} + \frac{1}{bx} \right )^{11}$ is equal to the coefficient of x⁷ in $\left (ax - \frac{1}{bx^{2} } \right )^{11}$, then ab =
a) 1
b) 1/2
c) 2
d) 3

2. The sum of coefficients in the expansion of (x + 2y + 3z)⁸ is
a) 3⁸
b) 5⁸
c) 6⁸
d) None of these
9. Sequences and Series - Quiz
10. Straight Lines - Quiz

1. The lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are perpendicular to each other, if
a) a₁b₂ - b₁a₂ = 0
b) a₁a₂ + b₁b₂ = 0
c) $a_{1}^{2}b_{2} + b_{1}^{2}a_{2}$ = 0
d) a₁b₁ + a₂b₂ = 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. The equation of common tangents to the parabola y² = 8x and hyperbola 3x² - y² = 3, is
a) 2x ± y + 1 = 0
b) 2x ± y - 1 = 0
c) x ± 2y + 1 = 0
d) x + 2y - 1 = 0

2. If a ≠ 0 and the line abx + 3cy + 4d = 0 passes through the points of intersection of the parabola y² = 4ax and x² = 4ay, then
a) d² + (3b - 2c)² = 0
b) d² + (3b - 2c)² = 0
c) d² + (2b - 3c)² = 0
d) d² + (2b + 3c)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. Negation of the proposition : If we control population growth, we prosper
a) If we do not control population growth , we propsper
b) Itf we control population growth, we do not prosper
c) We control population but we do not prosper
d) We do not control population, but we prosper
15. Statistics - Quiz

1. Two trains A and B, 100 kms apart, are travelling to each other with starting speed of 50km/hr for both . The train A is accelerating at 18km/hr² and B is decelerating at 18 km/hr². The distance where the engines cross each other from the initial position of A is
a) 50 kms
b) 68 kms
c) 32 kms
d) 59 kms

2. What will be that force when applying along any inclination plane will stop 10kilogram weight , it is given that force reaction of plane and weight of body are in arithmetic series
a) 4kg-wt
b) 6kg-wt
c) 8kg-wt
d) 7kg-wt
16. Probability - Quiz
17. Quadratic Equation and Inequation - Quiz

1. If k ε (-∞, -2) ∪ (2,∞), then the roots of the equation x² + 2kx + 4 = 0 are
a) Complex
b) Real and Unequal
c) Real and equal
d) One real and one imaginary

2. If one root of the equation ax² + bx + c = 0 the square of the other, then a(c - b)³ = cX, where X is
a) a³ + b³
b) (a - b)³
c) a³ - b³
d) None of these
18. Progression - Quiz

1. If a, ,b,c, d are in H.P., then ab + bc + cd is equal to
a) 3ad
b) (a + b)(c + d)
c) 3ac
d) None of these

2. If three real numbers a, ,b, c are in harmonic progression, then which of the following is true
a) $\frac{1}{a}, b, \frac{1}{c}$ are in A.P.
b) $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$ are in H.P.
c) ab,bc, ca are in H.P.
d) $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are in H.P.
19. Exponential and Logarithmic Series - Quiz

1. If S = $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - \frac{1}{4.5} + .... + \infty$, then e^S =
a) $log_{e}\left (\frac{4}{e} \right )$
b) $\frac{4}{e}$
c) $log_{e}\left (\frac{e}{4} \right )$
d) $\frac{e}{4}$

2. $\frac{1}{3!} + \frac{2}{5!} + \frac{3}{7!} + ....$ =
a) e^-1/2
b) e
c) e/4
d) e/6
20. Trigonometric Ratio, Function and Identities - Quiz

1. Let f_k(x) = $\frac{1}{k}\left (sin^{k}x + cos^{k}x \right )$ where x ε R and k ≥ 1. Then f₄(x) - f₀(x) equals
a) $\frac{1}{4}$
b) $\frac{1}{12}$
c) $\frac{1}{6}$
d) $\frac{1}{3}$

2. If α, β are solution of 6cosθ + 8 sinθ = 9, then sin(α + β) =
a) $\frac{3}{5}$
b) $\frac{4}{5}$
c) $\frac{24}{25}$
d) $\frac{12}{13}$
21. Trigonometric Equation and Inequation - Quiz

1. Two straight roads intersect at an angle of 60⁰, A bus on one road is 2km away from the intersection and a car on the other road is 3km away from the intersection. Then the direct distance between the two vehivles is
a) 1 km
b) $\sqrt{2}$ km
c) 4 km
d) $\sqrt{7}$ km

2. If the sides of the triangle are 5K, 6K, 5K and radius of incircle is 6 then value of K is equal to
a) 4
b) 5
c) 6
d) 7
22. Hyperbolic Function - Quiz

1. The imaginary part of tan^-1(cosθ + isinθ) is
a) tanh^-1(sinθ)
b) tanh^-1(∞)
c) 1/2tanh^-1(sinθ)
d) None of these

2. sinh^-1x =
a) $log\left (x + \sqrt{1 - x^{2}} \right )$
b) $log\left (x + \sqrt{ x^{2} + 1} \right )$
c) $log\left (x + \sqrt{ x^{2} - 1} \right )$
d) None of these
23. Rectangular Cartesian Coordinate - Quiz

1. If the three points (0,1), (0,-1) and (x,0) are vertices of an equilateral triangle, then the values of x are
a) $\sqrt{3},\sqrt{2}$
b) $\sqrt{3}, -\sqrt{3}$
c) $-\sqrt{5}, \sqrt{3}$
d) $\sqrt{2}, -\sqrt{2}$
e) $\sqrt{5}, -\sqrt{5}$

2. If the vertices of a triangle are A(1,4), B(3,0) and C(2,1) , then the length of the median passing through C is
a) 1
b) 2
c) $\sqrt{2}$
d) $\sqrt{3}$
24. Circle and System of Circle - Quiz

1. The locus of a point which divides the join of A(-1,1) and variable point P on the circle x² + y² = 4 in the ratio 3:2 is
a) 25(x² + y²) + 20(x - y) + 28 = 0
b) 25(x² + y²) + 20(x - y) - 28 = 0
c) 20(x² + y²) + 25(x - y) + 28 = 0
d) None of these

2. The locus of centre of the circle which cuts the circles x² + y² + 2g₁x + 2f₁y + c₁ = 0 x² + y² + 2g₂x + 2f₂y + c₂ = 0 orthogonally is
a) An ellipse
b) The radical axis of the given circles
c) A conic
d) Another circle
25. Pair of Straight Line - Quiz

1. The area (in square units) of the quadrilateral formed by the two pairs of lines l²x² - m²y² - n(lx + my) = 0 and l²x^{2 - m²y² + n(lx - my) = 0 is

a) $\frac{n^{2}}{2\left | lm \right |}$

b) $\frac{n^{2}}{\left | m \right |}$

c) $\frac{n}{2\left | m \right |}$
d) $\frac{n^{2}}{4\left | m \right |}$

2. The pair of lines represented by 3ax² + 5xy + (a² - 2)y² = 0 are perpendicular to each other for

a) Two values of a

b) ∀a

c) For one value of a
d) For no value of a}

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Math [Class XI]

Class/Course - Class XI

Subject - Math

Total Number of Question/s - 3865