## Class/Course - Class XI

### Subject - Math

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

Just Exam provide question bank for Class XI standard. Currently number of question's are 3865. We provide this data in all format (word, excel, pdf, sql, latex form with images) to institutes for conducting online test/ examinations. Here we are providing some demo contents. Interested person may contact us at info@justexam.in

• 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 npr = 30240 and nCr = 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
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 eS =
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 fk(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 l2x2 - 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