43030 + Interview Questions in Mathematics

1.	Shape of the feasible region formed by the following constraints is x + y ≤ 10, x + y ≥ 6, x ≥ 0, y ≥ 0
Answer» Shape of the feasible region formed by the following constraints is x + y ≤ 10, x + y ≥ 6, x ≥ 0, y ≥ 0

Discussion

2.	∫x+2(x2+3x+3)√x+1dx
Answer» $\int \frac{x + 2}{(x^{2} + 3 x + 3) \sqrt{x + 1}} d x$

Discussion

3.	For x>1, the sum of the series xx+1+x2(x+1)(x2+1)+x4(x+1)(x2+1)(x4+1)+⋯∞ is
Answer» For $x > 1$ , the sum of the series $\frac{x}{x + 1} + \frac{x^{2}}{(x + 1) (x^{2} + 1)} + \frac{x^{4}}{(x + 1) (x^{2} + 1) (x^{4} + 1)} + \dots \infty$ is

Discussion

4.	The inverse of f:R to R+ ; f(x)=x^2 is 1.not on to. 2.not one to one 3.not one to one and on to. 4.not at all a function.
Answer» The inverse of f:R to R+ ; f(x)=x^2 is 1.not on to. 2.not one to one 3.not one to one and on to. 4.not at all a function.

4.

The inverse of f:R to R+ ; f(x)=x^2 is 1.not on to. 2.not one to one 3.not one to one and on to. 4.not at all a function.

Answer»

The inverse of f:R to R+ ; f(x)=x^2 is

1.not on to. 2.not one to one

3.not one to one and on to. 4.not at all a function.

Discussion

5.	In a plane, there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides no three lines pass through one point, no line passes through both points A and B, no two are parallel. Then the number of intersection points the lines have is equal to _____.
Answer» In a plane, there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides no three lines pass through one point, no line passes through both points A and B, no two are parallel. Then the number of intersection points the lines have is equal to _____.

Discussion

6.	How many kids does Sakshi have? I. Roshni is the only sister of Sunder who is the only son of Sakshi. II. Sunder and Roshni have no more siblings
Answer» How many kids does Sakshi have? I. Roshni is the only sister of Sunder who is the only son of Sakshi. II. Sunder and Roshni have no more siblings

6.

How many kids does Sakshi have? I. Roshni is the only sister of Sunder who is the only son of Sakshi. II. Sunder and Roshni have no more siblings

Answer»

How many kids does Sakshi have?

I. Roshni is the only sister of Sunder who is the only son of Sakshi.

II. Sunder and Roshni have no more siblings

Discussion

7.	Find the number of solution of the equation z2 + \|z\|2 = 0.
Answer» Find the number of solution of the equation $z^{2}$ + $\| z \|^{2}$ = 0.

Discussion

8.	If esinx−e−sinx−a=0 has no real solution, then
Answer» If $e^{s i n x} - e^{- s i n x} - a = 0$ has no real solution, then

Discussion

9.	If the set of natural numbers is partitioned into subset S1 = {1},S2= {2,3},S3= {4,5,6} and so on.Then the sum of the terms is S50 is_______.
Answer» If the set of natural numbers is partitioned into subset $S_{1}$ = {1}, $S_{2}$ = {2,3}, $S_{3}$ = {4,5,6} and so on.Then the sum of the terms is $S_{50}$ is_______.

Discussion

10.	If x, y, z ϵ R+ [ R+ denote real positive numbers] Then, aba+b is
Answer» If x, y, z $ϵ$ $R^{+}$ [ $R^{+}$ denote real positive numbers] Then, $\frac{a b}{a + b}$ is

Discussion

11.	Let S={x∈(−π,π):x≠0,±π2}. The sum of all distinct solutions of the equation √3secx+cosec x+2(tanx−cotx)=0 in the set S is equal to:
Answer» Let $S = {x \in (- π, π) : x \neq 0, \pm \frac{π}{2}}$ . The sum of all distinct solutions of the equation $\sqrt{3} sec x + cosec x + 2 (tan x - cot x) = 0$ in the set $S$ is equal to:

Discussion

12.	If α and β are the roots of the equation ax2+bx+c=0 then the equation whose roots are (α2+β2),(1α2+1β2) is
Answer» If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ then the equation whose roots are $(α^{2} + β^{2}), (\frac{1}{α^{2}} + \frac{1}{β^{2}})$ is

Discussion

13.	∫dx(1+x2)√p2+q2(tan−1x)2=
Answer» $\int \frac{d x}{(1 + x^{2}) \sqrt{p^{2} + q^{2} (t a n^{- 1} x)^{2}}} =$

Discussion

14.	Consider the circle c:x2+y2=1 and the line L:y=m(x+2). If line L intersect c at P and Q, then locus of middle point of PQ is
Answer» Consider the circle $c : x^{2} + y^{2} = 1$ and the line $L : y = m (x + 2)$ . If line L intersect c at P and Q, then locus of middle point of PQ is

Discussion

15.	f(x)=Max{sinx,cosx}∀xϵ then Range of f(x) is.
Answer» $f (x) = M a x {s i n x, c o s x} \forall x ϵ t h e n R a n g e o f f (x) i s .$

Discussion

16.	If the sixth term of an increasing A.P. is equal to 2, then the value of the common difference of the A.P. such that the product a1 a4 a5 is greatest, is (the ith term is denoted by ai)
Answer» If the sixth term of an increasing A.P. is equal to 2, then the value of the common difference of the A.P. such that the product $a_{1} a_{4} a_{5}$ is greatest, is (the $i^{t h}$ term is denoted by $a_{i}$ )

Discussion

17.	Two finite ets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of ma and n are respectively.
Answer» Two finite ets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of ma and n are respectively.

Discussion

18.	If z2+z+1=0, where z is complex number, then the value of (z+1z)+(z2+1z2)+(z3+1z3)+⋯+(z6+1z6) is
Answer» If $z^{2} + z + 1 = 0,$ where $z$ is complex number, then the value of $(z + \frac{1}{z}) + (z^{2} + \frac{1}{z^{2}}) + (z^{3} + \frac{1}{z^{3}}) + \dots + (z^{6} + \frac{1}{z^{6}})$ is

Discussion

19.	f(x)=⎧⎨⎩√1+kx−√1−kxx,if −1≤x<02x+1x−1,if 0≤x≤1at x=0 What is the value of k if the function is continuous at all points?
Answer» $f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{\sqrt{1 + k x} - \sqrt{1 - k x}}{x}, & i f - 1 \leq x < 0 \frac{2 x + 1}{x - 1}, & i f 0 \leq x \leq 1 \end{matrix} a t x = 0$ What is the value of k if the function is continuous at all points?

Discussion

20.	Find the intervals in which the function f given by f(x)=4 sin x−2x−x cos x2+cos x is decreasing
Answer» Find the intervals in which the function f given by $f (x) = \frac{4 s i n x - 2 x - x c o s x}{2 + c o s x}$ is decreasing

Discussion

21.	The equation of line passing through (3,4) and parallel to 5x+9y+12=0 is
Answer» The equation of line passing through $(3, 4)$ and parallel to $5 x + 9 y + 12 = 0$ is

Discussion

22.	A line cuts x-axis at A(7,0) and the y-axis at B(0,−5). A variable line PQ is drawn perpendicular to AB cutting the x-axis at P(a,0) and the y-axis at Q(0,b). If AQ and BP intersect at R, the locus of R is
Answer» A line cuts $x$ -axis at $A (7, 0)$ and the $y$ -axis at $B (0, - 5)$ . A variable line $P Q$ is drawn perpendicular to $A B$ cutting the $x$ -axis at $P (a, 0)$ and the $y$ -axis at $Q (0, b)$ . If $A Q$ and $B P$ intersect at $R$ , the locus of $R$ is

Discussion

23.	A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball?
Answer» A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball?

Discussion

24.	∣∣∣∣∣1+a2−b22ab−2b2ab1−a2+b22a2b−2a1−a2−b2∣∣∣∣∣=(1+a2+b2)3
Answer» $∣ ∣∣∣ ∣ \begin{matrix} 1 + a^{2} - b^{2} & 2 a b & - 2 b 2 a b & 1 - a^{2} + b^{2} & 2 a 2 b & - 2 a & 1 - a^{2} - b^{2} \end{matrix} ∣ ∣∣∣ ∣ = (1 + a^{2} + b^{2})^{3}$

Discussion

25.	Evaluate ∫10e2−3xdx as a limit of a sum.
Answer» Evaluate $\int_{0}^{1} e^{2 - 3 x} d x$ as a limit of a sum.

Discussion

26.	The locus of the point of intersection of any two perpendicular tangents to the parabola x2−6x+16y+41=0 is
Answer» The locus of the point of intersection of any two perpendicular tangents to the parabola $x^{2} - 6 x + 16 y + 41 = 0$ is

Discussion

27.	The solution of dydx=x+y+12x+2y+3 is.
Answer» $The solution of \frac{dy}{dx} = \frac{x + y + 1}{2 x + 2 y + 3} is$ .

Discussion

28.	The point(s) on the x−axis which is (are) at a distance of 5 units from the point (6,−3), is (are)
Answer» The point(s) on the $x -$ axis which is (are) at a distance of $5$ units from the point $(6, - 3),$ is (are)

Discussion

29.	If y = f(x) = tan x cot 3x, then
Answer» If y = f(x) = tan x cot 3x, then

Discussion

30.	The sum of a number of 2 digits and of the number formed by reversing the digits is 110,and the difference of the digits is 6. Find the number.
Answer» The sum of a number of 2 digits and of the number formed by reversing the digits is 110,and the difference of the digits is 6. Find the number.

Discussion

31.	If 0
Answer» If 0

Discussion

32.	If θ is the angle between the two tangents to y2=12x drawn from the point (1,4), then tanθ is equal to
Answer» If $θ$ is the angle between the two tangents to $y^{2} = 12 x$ drawn from the point $(1, 4)$ , then $tan θ$ is equal to

Discussion

33.	Water flows through a non uniform tube of area of cross section 25,15,35 cm2 ratio of velocities of water at the sections A B C is
Answer» Water flows through a non uniform tube of area of cross section 25,15,35 cm2 ratio of velocities of water at the sections A B C is

Discussion

34.	If sin x+cosec x=2, then sinn x+cosecnx is equal to
Answer» If $s i n x + c o s e c x = 2, t h e n s i n^{n} x + c o s e c^{n} x$ is equal to

Discussion

35.	If the locus of the middle point of chords of an ellipse x23+y24=1 passing through (2,0) is another ellipse A, then the length of latus rectum of the ellipse A is
Answer» If the locus of the middle point of chords of an ellipse $\frac{x^{2}}{3} + \frac{y^{2}}{4} = 1$ passing through $(2, 0)$ is another ellipse $A,$ then the length of latus rectum of the ellipse $A$ is

Discussion

36.	Write the value of limx→2\|x−2\|x−2.
Answer» Write the value of ${lim}_{x \to 2} \frac{\| x - 2 \|}{x - 2} .$

Discussion

37.	limx→0√1+x−1log(1+x)
Answer» ${lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{l o g (1 + x)}$

Discussion

38.	The values of a for which the equation 2x2−2(2a+1)x+a(a–1)=0 Has roots α and β satisfying the condition α<a<β, are
Answer» The values of a for which the equation $2 x^{2} - 2 (2 a + 1) x + a (a - 1) = 0$ Has roots $α a n d β$ satisfying the condition $α < a < β$ , are

Discussion

39.	The value of the limit limx→−∞(√4x2−x+2x) is
Answer» The value of the limit $lim x \to - \infty (\sqrt{4 x^{2} - x} + 2 x)$ is

Discussion

40.	Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same. (i)(3x2+2)2 (ii)(x+2)(x+3) (iii)(3sec x−4cosec x)(−2sin x+5cos x)
Answer» Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same. $(i) (3 x^{2} + 2)^{2}$ $(i i) (x + 2) (x + 3)$ $(i i i) (3 s e c x - 4 c o s e c x) (- 2 s i n x + 5 c o s x)$

Discussion

41.	The equation sin−1x−cos−1x=cos−1(√32) has
Answer» The equation $s i n^{- 1} x - c o s^{- 1} x = c o s^{- 1} (\frac{\sqrt{3}}{2})$ has

Discussion

42.	The minimum area of the triangle formed by the variable line 3 cosθ x+4 sinθ y=12 and the coordinate axis is
Answer» The minimum area of the triangle formed by the variable line $3 c o s θ x + 4 s i n θ y = 12$ and the coordinate axis is

Discussion

43.	How many values of x in the interval [0,2π] satisfies the equation sin6x=1+cos43x ___
Answer» How many values of $x$ in the interval $[0, 2 π]$ satisfies the equation ${sin}^{6} x = 1 + {cos}^{4} 3 x$ ___

Discussion

44.	Suppose that the foci of the ellipse x29+y25=1 are (f1,0) and (f2,0) where f1>0 and f2<0. Let P1 and P2 be two parabolas with a common vertex at (0,0) and with foci at (f1,0) and (2f2,0), respectively. Let T1 be a tangent to P1 which passes through (2f2,0) and T2 be a tangent to P2 which passes through (f1,0). If m1 is the slope of T1 and m2 is the slope of T2, then the value of (1m21+m22) is .
Answer» Suppose that the foci of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ are $(f_{1}, 0)$ and $(f_{2}, 0)$ where $f_{1} > 0$ and $f_{2} < 0$ . Let $P_{1}$ and $P_{2}$ be two parabolas with a common vertex at $(0, 0)$ and with foci at $(f_{1}, 0)$ and $(2 f_{2}, 0)$ , respectively. Let $T_{1}$ be a tangent to $P_{1}$ which passes through $(2 f_{2}, 0)$ and $T_{2}$ be a tangent to $P_{2}$ which passes through $(f_{1}, 0)$ . If $m_{1}$ is the slope of $T_{1}$ and $m_{2}$ is the slope of $T_{2}$ , then the value of $(\frac{1}{m_{1}^{2}} + m_{2}^{2})$ is .

Discussion

45.	Write the distance between the directrices of the hyperbola. x=8secθ,y=8tanθ.
Answer» Write the distance between the directrices of the hyperbola. $x = 8 s e c θ, y = 8 t a n θ .$

45.

Write the distance between the directrices of the hyperbola. x=8secθ,y=8tanθ.

Answer»

Write the distance between the directrices of the hyperbola.

$x = 8 s e c θ, y = 8 t a n θ .$

Discussion

46.	Prove that sin x+sin 3x+......+sin(2n−1)x=sin2nxsin x.
Answer» Prove that $s i n x + s i n 3 x + . . . . . . + s i n (2 n - 1) x = \frac{s i n^{2} n x}{s i n x}$ .

Discussion

47.	Two integers are selected at random from the set {1,2,…,11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :
Answer» Two integers are selected at random from the set ${1, 2, \dots, 11}$ . Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

Discussion

48.	If the equation (4a−3)x2+ay2+6x−2y+2=0 represents a circle, then its centre is
Answer» If the equation $(4 a - 3) x^{2} + a y^{2} + 6 x - 2 y + 2 = 0$ represents a circle, then its centre is

Discussion

49.	The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Answer» The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Discussion

50.	What is the probability than an ordinary year has 53 Sundays?
Answer» What is the probability than an ordinary year has 53 Sundays?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Shape of the feasible region formed by the following constraints is x + y ≤ 10, x + y ≥ 6, x ≥ 0, y ≥ 0

∫x+2(x2+3x+3)√x+1dx

For x&gt;1, the sum of the series xx+1+x2(x+1)(x2+1)+x4(x+1)(x2+1)(x4+1)+⋯∞ is

The inverse of f:R to R+ ; f(x)=x^2 is 1.not on to. 2.not one to one 3.not one to one and on to. 4.not at all a function.

In a plane, there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides no three lines pass through one point, no line passes through both points A and B, no two are parallel. Then the number of intersection points the lines have is equal to _____.

How many kids does Sakshi have? I. Roshni is the only sister of Sunder who is the only son of Sakshi. II. Sunder and Roshni have no more siblings

Find the number of solution of the equation z2 + |z|2 = 0.

If esinx−e−sinx−a=0 has no real solution, then

If the set of natural numbers is partitioned into subset S1 = {1},S2= {2,3},S3= {4,5,6} and so on.Then the sum of the terms is S50 is_______.

If x, y, z ϵ R+ [ R+ denote real positive numbers] Then, aba+b is

Let S={x∈(−π,π):x≠0,±π2}. The sum of all distinct solutions of the equation √3secx+cosec x+2(tanx−cotx)=0 in the set S is equal to:

If α and β are the roots of the equation ax2+bx+c=0 then the equation whose roots are (α2+β2),(1α2+1β2) is

∫dx(1+x2)√p2+q2(tan−1x)2=

Consider the circle c:x2+y2=1 and the line L:y=m(x+2). If line L intersect c at P and Q, then locus of middle point of PQ is

f(x)=Max{sinx,cosx}∀xϵ then Range of f(x) is.

If the sixth term of an increasing A.P. is equal to 2, then the value of the common difference of the A.P. such that the product a1 a4 a5 is greatest, is (the ith term is denoted by ai)

Two finite ets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of ma and n are respectively.

If z2+z+1=0, where z is complex number, then the value of (z+1z)+(z2+1z2)+(z3+1z3)+⋯+(z6+1z6) is

f(x)=⎧⎨⎩√1+kx−√1−kxx,if −1≤x&lt;02x+1x−1,if 0≤x≤1at x=0 What is the value of k if the function is continuous at all points?

Find the intervals in which the function f given by f(x)=4 sin x−2x−x cos x2+cos x is decreasing

The equation of line passing through (3,4) and parallel to 5x+9y+12=0 is

A line cuts x-axis at A(7,0) and the y-axis at B(0,−5). A variable line PQ is drawn perpendicular to AB cutting the x-axis at P(a,0) and the y-axis at Q(0,b). If AQ and BP intersect at R, the locus of R is

A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball?

∣∣∣∣∣1+a2−b22ab−2b2ab1−a2+b22a2b−2a1−a2−b2∣∣∣∣∣=(1+a2+b2)3

Evaluate ∫10e2−3xdx as a limit of a sum.

The locus of the point of intersection of any two perpendicular tangents to the parabola x2−6x+16y+41=0 is

The solution of dydx=x+y+12x+2y+3 is.

The point(s) on the x−axis which is (are) at a distance of 5 units from the point (6,−3), is (are)

If y = f(x) = tan x cot 3x, then

The sum of a number of 2 digits and of the number formed by reversing the digits is 110,and the difference of the digits is 6. Find the number.

If 0

If θ is the angle between the two tangents to y2=12x drawn from the point (1,4), then tanθ is equal to

Water flows through a non uniform tube of area of cross section 25,15,35 cm2 ratio of velocities of water at the sections A B C is

If sin x+cosec x=2, then sinn x+cosecnx is equal to

If the locus of the middle point of chords of an ellipse x23+y24=1 passing through (2,0) is another ellipse A, then the length of latus rectum of the ellipse A is

Write the value of limx→2|x−2|x−2.

limx→0√1+x−1log(1+x)

The values of a for which the equation 2x2−2(2a+1)x+a(a–1)=0 Has roots α and β satisfying the condition α&lt;a&lt;β, are

The value of the limit limx→−∞(√4x2−x+2x) is

Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same. (i)(3x2+2)2 (ii)(x+2)(x+3) (iii)(3sec x−4cosec x)(−2sin x+5cos x)

The equation sin−1x−cos−1x=cos−1(√32) has

The minimum area of the triangle formed by the variable line 3 cosθ x+4 sinθ y=12 and the coordinate axis is

How many values of x in the interval [0,2π] satisfies the equation sin6x=1+cos43x ___

Write the distance between the directrices of the hyperbola. x=8secθ,y=8tanθ.

Prove that sin x+sin 3x+......+sin(2n−1)x=sin2nxsin x.

Two integers are selected at random from the set {1,2,…,11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

If the equation (4a−3)x2+ay2+6x−2y+2=0 represents a circle, then its centre is

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

What is the probability than an ordinary year has 53 Sundays?

For x>1, the sum of the series xx+1+x2(x+1)(x2+1)+x4(x+1)(x2+1)(x4+1)+⋯∞ is

f(x)=⎧⎨⎩√1+kx−√1−kxx,if −1≤x<02x+1x−1,if 0≤x≤1at x=0 What is the value of k if the function is continuous at all points?

The values of a for which the equation 2x2−2(2a+1)x+a(a–1)=0 Has roots α and β satisfying the condition α<a<β, are