43030 + Interview Questions in Mathematics

1.	20 e2re2xe2ezx
Answer» 20 e2re2xe2ezx

Discussion

2.	If 3π4<α<π, then √cosec2α+2cotα is equal to
Answer» If $\frac{3 π}{4} < α < π$ , then $\sqrt{c o s e c^{2} α + 2 c o t α}$ is equal to

Discussion

3.	Let I(n) = 2cos nx ∀n∈N, then I (1).I(n+1) - I(n) is equal to
Answer» Let I(n) = 2cos nx $\forall n \in N$ , then I (1).I(n+1) - I(n) is equal to

Discussion

4.	If z=x+iy, where x,y∈R and z,−iz and z+iz is represented on the argand plane, then the area of triangle formed (in sq.units) is
Answer» If $z = x + i y$ , where $x, y \in R$ and $z, - i z$ and $z + i z$ is represented on the argand plane, then the area of triangle formed (in sq.units) is

Discussion

5.	The Arithmetic Mean of the co-efficients in the expansion of (1+x)30 is
Answer» The Arithmetic Mean of the co-efficients in the expansion of $(1 + x)^{30}$ is

Discussion

6.	If two vertices of a triangle are (5,−1) and (−2,3) and if its orthocentre lies at the origin, then the coordinates of the third vertex are
Answer» If two vertices of a triangle are $(5, - 1)$ and $(- 2, 3)$ and if its orthocentre lies at the origin, then the coordinates of the third vertex are

Discussion

7.	22. let function f satisfies the relation f(x+y)=f(x).f(y) for all x,y R and f(1)=1. Further, if in ABC sides a,b,c are given as a=f(3), b=f(1) + f(3), c=f(2) + f(3). Find the area of ABC.
Answer» 22. let function f satisfies the relation f(x+y)=f(x).f(y) for all x,y R and f(1)=1. Further, if in ABC sides a,b,c are given as a=f(3), b=f(1) + f(3), c=f(2) + f(3). Find the area of ABC.

Discussion

8.	If y=log(sinx1+cosx), then dydx=
Answer» If $y = log (\frac{sin x}{1 + cos x}),$ then $\frac{d y}{d x} =$

Discussion

9.	If A and B are two square matrices such that B=−A−1BA, then (A+B)2 is equal to
Answer» If A and B are two square matrices such that $B = - A^{- 1} B A$ , then $(A + B)^{2}$ is equal to

Discussion

10.	Study the following information carefully and answer the questions below. (i) ′P×Q′ means 'P is the brother of Q'. (ii) ′P−Q′ means 'P is the mother of Q'. (iii) ′P+Q′ means 'P is the father of Q'. (iv) ′P÷Q′ means 'P is the sister of Q'. Which of the following means 'M is the niece of N'?
Answer» Study the following information carefully and answer the questions below. (i) $^{'} P \times Q^{'}$ means 'P is the brother of Q'. (ii) $^{'} P - Q^{'}$ means 'P is the mother of Q'. (iii) $^{'} P + Q^{'}$ means 'P is the father of Q'. (iv) $^{'} P \div Q^{'}$ means 'P is the sister of Q'. Which of the following means 'M is the niece of N'?

Discussion

11.	Find the number of all onto functions from the set {1, 2, 3, … , n ) to itself.
Answer» Find the number of all onto functions from the set {1, 2, 3, … , n ) to itself.

Discussion

12.	Evaluate the following integrals:∫-aaloga-sinθa+sinθdθ
Answer» Evaluate the following integrals: $\int_{- a}^{a} \log (\frac{a - \sin θ}{a + \sin θ}) d θ$

Discussion

13.	11. The solution of the equation dy/dx =cos(y-x) is ?
Answer» 11. The solution of the equation dy/dx =cos(y-x) is ?

Discussion

14.	The general solution of the differential equation sin−1(dydx)=x+y is (where c is a constant of integration)
Answer» The general solution of the differential equation ${sin}^{- 1} (\frac{d y}{d x}) = x + y$ is (where $c$ is a constant of integration)

Discussion

15.	The point(s) on Y-axis which is/are at a distance of 4 units from the line x3+y4=1 will be
Answer» The point(s) on Y-axis which is/are at a distance of 4 units from the line $\frac{x}{3} + \frac{y}{4} = 1$ will be

Discussion

16.	Prove that:cos 2 x1+sin 2 x=tan π4-x
Answer» Prove that: $\frac{\cos 2 x}{1 + \sin 2 x} = \tan (\frac{π}{4} - x)$

Discussion

17.	If the sum of n terms of an A.P. is 2n2+5n, then its nth term is
Answer» If the sum of n terms of an A.P. is $2 n^{2} + 5 n$ , then its nth term is

Discussion

18.	From 8 gentlemen and 5 ladies a committee of 6 is to be formed. In how many ways can this be done so that the committee contains at least 3 ladies?
Answer» From 8 gentlemen and 5 ladies a committee of 6 is to be formed. In how many ways can this be done so that the committee contains at least 3 ladies?

Discussion

19.	Let P be any moving point on the circle S1:x2+y2−2x−1=0. A chord of contact is drawn from the point P to the circle S:x2+y2−2x=0. If C is the centre and A,B are the points of contact of circle S, then the locus of the circumcentre of △CAB is
Answer» Let $P$ be any moving point on the circle $S_{1} : x^{2} + y^{2} - 2 x - 1 = 0.$ A chord of contact is drawn from the point $P$ to the circle $S : x^{2} + y^{2} - 2 x = 0.$ If $C$ is the centre and $A, B$ are the points of contact of circle $S,$ then the locus of the circumcentre of $△ C A B$ is

Discussion

20.	13. tamlx
Answer» 13. tamlx

Discussion

21.	Let f be real valued function such that f(2)=2 and f′(2)=1, then limx→2f(x)∫24t3x−2dt equals
Answer» Let $f$ be real valued function such that $f (2) = 2$ and $f^{'} (2) = 1$ , then $lim x \to 2 f (x) \int 2 \frac{4 t^{3}}{x - 2} d t$ equals

Discussion

22.	An ordered pair (α,β) for which the system of linear equations (1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2 has a unique solution, is:
Answer» An ordered pair $(α, β)$ for which the system of linear equations $(1 + α) x + β y + z = 2 α x + (1 + β) y + z = 3 α x + β y + 2 z = 2$ has a unique solution, is:

Discussion

23.	(ATBA)T =
Answer» $(A^{T} B A)^{T}$ =

Discussion

24.	Consider three boxes, each containing 10 balls labelled 1,2,…,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i=1,2,3). Then, the number of ways in which the balls can be chosen such that n1<n2<n3 is :
Answer» Consider three boxes, each containing $10$ balls labelled $1, 2, \dots, 10.$ Suppose one ball is randomly drawn from each of the boxes. Denote by $n_{i},$ the label of the ball drawn from the $i^{th}$ box, $(i = 1, 2, 3)$ . Then, the number of ways in which the balls can be chosen such that $n_{1} < n_{2} < n_{3}$ is :

Discussion

25.	The roots of the equation 2x4+x3−11x2+x+2=0 is/are
Answer» The roots of the equation $2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0$ is/are

Discussion

26.	Prove the following : 3sin−1x=sin−1(3x−4x3),x∈[−12,12]
Answer» Prove the following : $3 {sin}^{- 1} x = {sin}^{- 1} (3 x - 4 x^{3}), x \in [- \frac{1}{2}, \frac{1}{2}]$

Discussion

27.	The range of the function f(x)= sin-1 square root(mod of x – x2 is
Answer» The range of the function f(x)= sin^-1square root(mod of x – x² is

Discussion

28.	{ If }\operatorname{cos}^2A-\operatorname{sin}^2A=\operatorname{tan}^2C, then }\operatorname{cos}^2C-\operatorname{sin}^2C is }} equal to }{ (1) }\operatorname{tan}^2C}{ (2) }\operatorname{tan}^2A}{ (3) }\operatorname{cot}^2A}{ (4) }\operatorname{cot}^2C
Answer» { If }\operatorname{cos}^2A-\operatorname{sin}^2A=\operatorname{tan}^2C, then }\operatorname{cos}^2C-\operatorname{sin}^2C is }} equal to }{ (1) }\operatorname{tan}^2C}{ (2) }\operatorname{tan}^2A}{ (3) }\operatorname{cot}^2A}{ (4) }\operatorname{cot}^2C

Discussion

29.	the value of "a" for which the sum of the squares of the roots of equation x^2 - (a-2)x -a -1 =0 assumes the least value is a) 0b) 1c) 2d) 3
Answer» the value of "a" for which the sum of the squares of the roots of equation x^2 - (a-2)x -a -1 =0 assumes the least value is a) 0 b) 1 c) 2 d) 3

Discussion

30.	Show that the real function f(x)=2x^2 +3 is continuous.
Answer» Show that the real function f(x)=2x^2 +3 is continuous.

Discussion

31.	For the matrix , find the numbers a and b such that A 2 + aA + bI = O .
Answer» For the matrix , find the numbers a and b such that A 2 + aA + bI = O .

Discussion

32.	A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennants. The set of all possible 1-pennant is {(1)}, the set of all possible 2-pennants is {(2), (1,1)} and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10-pennants is 89
Answer» A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennants. The set of all possible 1-pennant is {(1)}, the set of all possible 2-pennants is {(2), (1,1)} and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10-pennants is 89

Discussion

33.	Which among the following represents the graph of curve y=2sin2x
Answer» Which among the following represents the graph of curve $y = 2 sin 2 x$

Discussion

34.	A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45° with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60° with respect to the vertical. If the girl moves further by a distanœ 2.464d (point C). Then the height h2 is (given tan30°=0.5774):
Answer» A balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_{1}$ , a girl standing at a distance $d$ (point $B$ ) from $A$ (see figure) sees it at an angle $45 °$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$ , it is seen at an angle $60 °$ with respect to the vertical. If the girl moves further by a distanœ $2.464 d$ (point $C$ ). Then the height $h_{2}$ is (given $tan 30 ° = 0.5774)$ :

Discussion

35.	Prove that (e^2x + e^-x - e^x - 1)/(e^2x - e^-x +e^x - 1) = (e^x - 1)/(e^x +1).
Answer» Prove that (e^2x + e^-x - e^x - 1)/(e^2x - e^-x +e^x - 1) = (e^x - 1)/(e^x +1).

Discussion

36.	If x+1x-1x-3x+2=4-113, then write the value of x.
Answer» If $\|\begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix}\| = \|\begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix}\|$ , then write the value of x.

Discussion

37.	If α2+α+1=0, then ∣∣∣∣∣x+1αα2αx+α21α21x+α∣∣∣∣∣=
Answer» If $α^{2} + α + 1 = 0$ , then $∣ ∣∣∣ ∣ \begin{matrix} x + 1 & α & α^{2} α & x + α^{2} & 1 α^{2} & 1 & x + α \end{matrix} ∣ ∣∣∣ ∣ =$

Discussion

38.	Let S be the circle in the xy-plane defined by the equation x2+y2=4.Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
Answer» Let $S$ be the circle in the $x y$ -plane defined by the equation $x^{2} + y^{2} = 4$ . Let $P$ be a point on the circle $S$ with both coordinates being positive. Let the tangent to $S$ at $P$ intersect the coordinate axes at the points $M$ and $N$ . Then, the mid-point of the line segment $M N$ must lie on the curve

Discussion

39.	to prove 2A²(1 + sinB) = 4A²sin²B/2
Answer» to prove 2A²(1 + sinB) = 4A²sin²B/2

Discussion

40.	The locus of middle point of the portion of the normal to y2=4ax intercepted between curve and axis of parabola is
Answer» The locus of middle point of the portion of the normal to $y^{2} = 4 a x$ intercepted between curve and axis of parabola is

Discussion

41.	The equation 2sinx2cos2x−2sinx2sin2x=cos2x−sin2x has a root for which
Answer» The equation $2 sin \frac{x}{2} {cos}^{2} x - 2 sin \frac{x}{2} {sin}^{2} x = {cos}^{2} x - {sin}^{2} x$ has a root for which

Discussion

42.	∫√x2+3x dx is equal to(where C is integration constant)
Answer» $\int \sqrt{x^{2} + 3 x} d x$ is equal to (where $C$ is integration constant)

Discussion

43.	कुँवर सिंह को बचपन में किन कामों में मज़ा आता था? क्या उन्हें उन कामों से स्वतंत्रता सेनानी बनने में कुछ मदद मिली?
Answer» कुँवर सिंह को बचपन में किन कामों में मज़ा आता था? क्या उन्हें उन कामों से स्वतंत्रता सेनानी बनने में कुछ मदद मिली?

Discussion

44.	Solve: x2+19x–150
Answer» Solve: $x^{2} + 19 x - 150$

Discussion

45.	Find the number of straight lines by the shown points in the figure
Answer» Find the number of straight lines by the shown points in the figure

45.

Find the number of straight lines by the shown points in the figure

Answer»

Find the number of straight lines by the shown points in the figure

Discussion

46.	\sqrt{2+\sqrt{2+\sqrt{\operatorname{cos}2θ}}}=?
Answer» \sqrt{2+\sqrt{2+\sqrt{\operatorname{cos}2θ}}}=?

Discussion

47.	An example of a function which is everywhere continuous but fails to be differentiable exactly at two points is ____________.
Answer» An example of a function which is everywhere continuous but fails to be differentiable exactly at two points is ____________.

Discussion

48.	Let origin and the non-real roots of 2z2+2z+λ=0 form the three vertices of an equilateral triangle in the Argand plane. Then 3λ=
Answer» Let origin and the non-real roots of $2 z^{2} + 2 z + λ = 0$ form the three vertices of an equilateral triangle in the Argand plane. Then $3 λ =$

Discussion

49.	A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(−1,1,2) and O(0,0,0). The angle between the faces OPQ and OQR is:
Answer» A tetrahedron has vertices $P (1, 2, 1), Q (2, 1, 3), R (- 1, 1, 2)$ and $O (0, 0, 0) .$ The angle between the faces $O P Q$ and $O Q R$ is:

Discussion

50.	ntDetermine the number of five digit integer 37abc in base 10 such that each of the numbers 37abc,37bca,37cab Is divisible by 37n
Answer» ntDetermine the number of five digit integer 37abc in base 10 such that each of the numbers 37abc,37bca,37cab Is divisible by 37n

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

20 e2re2xe2ezx

If 3π4&lt;α&lt;π, then √cosec2α+2cotα is equal to

Let I(n) = 2cos nx ∀n∈N, then I (1).I(n+1) - I(n) is equal to

If z=x+iy, where x,y∈R and z,−iz and z+iz is represented on the argand plane, then the area of triangle formed (in sq.units) is

The Arithmetic Mean of the co-efficients in the expansion of (1+x)30 is

If two vertices of a triangle are (5,−1) and (−2,3) and if its orthocentre lies at the origin, then the coordinates of the third vertex are

22. let function f satisfies the relation f(x+y)=f(x).f(y) for all x,y R and f(1)=1. Further, if in ABC sides a,b,c are given as a=f(3), b=f(1) + f(3), c=f(2) + f(3). Find the area of ABC.

If y=log(sinx1+cosx), then dydx=

If A and B are two square matrices such that B=−A−1BA, then (A+B)2 is equal to

Find the number of all onto functions from the set {1, 2, 3, … , n ) to itself.

Evaluate the following integrals:∫-aaloga-sinθa+sinθdθ

11. The solution of the equation dy/dx =cos(y-x) is ?

The general solution of the differential equation sin−1(dydx)=x+y is (where c is a constant of integration)

The point(s) on Y-axis which is/are at a distance of 4 units from the line x3+y4=1 will be

Prove that:cos 2 x1+sin 2 x=tan π4-x

If the sum of n terms of an A.P. is 2n2+5n, then its nth term is

From 8 gentlemen and 5 ladies a committee of 6 is to be formed. In how many ways can this be done so that the committee contains at least 3 ladies?

Let P be any moving point on the circle S1:x2+y2−2x−1=0. A chord of contact is drawn from the point P to the circle S:x2+y2−2x=0. If C is the centre and A,B are the points of contact of circle S, then the locus of the circumcentre of △CAB is

13. tamlx

Let f be real valued function such that f(2)=2 and f′(2)=1, then limx→2f(x)∫24t3x−2dt equals

An ordered pair (α,β) for which the system of linear equations (1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2 has a unique solution, is:

(ATBA)T =

Consider three boxes, each containing 10 balls labelled 1,2,…,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i=1,2,3). Then, the number of ways in which the balls can be chosen such that n1&lt;n2&lt;n3 is :

The roots of the equation 2x4+x3−11x2+x+2=0 is/are

Prove the following : 3sin−1x=sin−1(3x−4x3),x∈[−12,12]

The range of the function f(x)= sin-1 square root(mod of x – x2 is

{ If }\operatorname{cos}^2A-\operatorname{sin}^2A=\operatorname{tan}^2C, then }\operatorname{cos}^2C-\operatorname{sin}^2C is }} equal to }{ (1) }\operatorname{tan}^2C}{ (2) }\operatorname{tan}^2A}{ (3) }\operatorname{cot}^2A}{ (4) }\operatorname{cot}^2C

the value of "a" for which the sum of the squares of the roots of equation x^2 - (a-2)x -a -1 =0 assumes the least value is a) 0b) 1c) 2d) 3

Show that the real function f(x)=2x^2 +3 is continuous.

For the matrix , find the numbers a and b such that A 2 + aA + bI = O .

Which among the following represents the graph of curve y=2sin2x

Prove that (e^2x + e^-x - e^x - 1)/(e^2x - e^-x +e^x - 1) = (e^x - 1)/(e^x +1).

If x+1x-1x-3x+2=4-113, then write the value of x.

If α2+α+1=0, then ∣∣∣∣∣x+1αα2αx+α21α21x+α∣∣∣∣∣=

Let S be the circle in the xy-plane defined by the equation x2+y2=4.Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

to prove 2A²(1 + sinB) = 4A²sin²B/2

The locus of middle point of the portion of the normal to y2=4ax intercepted between curve and axis of parabola is

The equation 2sinx2cos2x−2sinx2sin2x=cos2x−sin2x has a root for which

∫√x2+3x dx is equal to(where C is integration constant)

कुँवर सिंह को बचपन में किन कामों में मज़ा आता था? क्या उन्हें उन कामों से स्वतंत्रता सेनानी बनने में कुछ मदद मिली?

Solve: x2+19x–150

Find the number of straight lines by the shown points in the figure

\sqrt{2+\sqrt{2+\sqrt{\operatorname{cos}2θ}}}=?

An example of a function which is everywhere continuous but fails to be differentiable exactly at two points is ____________.

Let origin and the non-real roots of 2z2+2z+λ=0 form the three vertices of an equilateral triangle in the Argand plane. Then 3λ=

A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(−1,1,2) and O(0,0,0). The angle between the faces OPQ and OQR is:

ntDetermine the number of five digit integer 37abc in base 10 such that each of the numbers 37abc,37bca,37cab Is divisible by 37n

If 3π4<α<π, then √cosec2α+2cotα is equal to

Consider three boxes, each containing 10 balls labelled 1,2,…,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i=1,2,3). Then, the number of ways in which the balls can be chosen such that n1<n2<n3 is :