43030 + Interview Questions in Mathematics

1.	The area of the region above the x-axis, included between the parabola y2=ax and the circle x2+y2=2axis
Answer» The area of the region above the x-axis, included between the parabola $y^{2} = ax$ and the circle $x^{2} + y^{2} = 2 ax$ is

Discussion

2.	The general solution of the differential equation dydx+yx = 1 is _____________.
Answer» The general solution of the differential equation $\frac{d y}{d x} + \frac{y}{x}$ = 1 is _____________.

Discussion

3.	10∑n=1[n∏k=1k+1k]=
Answer» $10 \sum n = 1 [n \prod k = 1 \frac{k + 1}{k}] =$

Discussion

4.	A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :
Answer» A $2 m$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate $25 c m / s e c .,$ then the rate $(in c m / s e c .)$ at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1 m$ above the ground is :

Discussion

5.	If f and g are differentiable functions in [0,1] satisfying f(0)=2=g(1),g(0)=0 and f(1)=6, then for some c ϵ ]0,1[
Answer» If f and g are differentiable functions in $[0, 1]$ satisfying $f (0) = 2 = g (1), g (0) = 0$ and $f (1) = 6$ , then for some c $ϵ$ ]0,1[

Discussion

6.	Find the point at which the tangent to the curve y =3/5x^5 - 5/3x^3 - x had its slope equal to -3
Answer» Find the point at which the tangent to the curve y =3/5x^5 - 5/3x^3 - x had its slope equal to -3

Discussion

7.	For what real value of y will matrix A be equal to matrix B, where
Answer» For what real value of y will matrix A be equal to matrix B, where

7.

For what real value of y will matrix A be equal to matrix B, where

Answer»

For what real value of y will matrix A be equal to matrix B, where

Discussion

8.	α, β are the roots of the equation x2 + 4x + 5. Find α3 + β3
Answer» α, β are the roots of the equation $x^{2}$ + 4x + 5. Find $α^{3}$ + $β^{3}$

Discussion

9.	If 4^x-4^x-1=24, then find the value of (2x)^x. How to solve this problem in a quick and easy way for better understanding.
Answer» If 4^x-4^x-1=24, then find the value of (2x)^x. How to solve this problem in a quick and easy way for better understanding.

Discussion

10.	The term independent of x in the expansion of [x+1x2/3−x1/3+1−x−1x−x1/2]10, x≠1, is equal to
Answer» The term independent of $x$ in the expansion of ${[\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}}]}^{10}, x \neq 1,$ is equal to

Discussion

11.	The maximum value of 1xx is(a) e (b) ee (c) e1/e (d) 1e1/e
Answer» The maximum value of ${(\frac{1}{x})}^{x}$ is (a) e (b) e^e (c) e^1/e (d) ${(\frac{1}{e})}^{1 / e}$

Discussion

12.	Prove that cos(π4+x)+cos(π4−x)=√2cosx
Answer» $Prove that cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x$

Discussion

13.	If t lies between real roots of the equation 2x2−2(2t+1)x+t(t+1)=0, then t cannot be
Answer» If $t$ lies between real roots of the equation $2 x^{2} - 2 (2 t + 1) x + t (t + 1) = 0,$ then $t$ cannot be

Discussion

14.	Let S be a circle whose centre is C(2,3) and touching the y-axis. Tangents OA and OB are drawn from the origin O to the circle which touches the circle at A and B.List IList II (A)The finite slope of the tangent OA is(P)1213(B)If α is the acute angle between the(Q)5413tangents, then the value of sinα is(C)If P(x1,y1) is any point on the circle,(R)512 then the product of the minimum and the maximum values of OP, is(D)A line is drawn from S(4,5), intersecting (S)9the circle at M and N. Then the value of SM⋅SN is(T)4Which of the following is the only CORRECT combination?
Answer» Let $S$ be a circle whose centre is $C (2, 3)$ and touching the $y$ -axis. Tangents $O A$ and $O B$ are drawn from the origin $O$ to the circle which touches the circle at $A$ and $B .$ $\begin{matrix} List I & List II (A) & The finite slope of the tangent OA is & (P) & \frac{12}{13} (B) & If α is the acute angle between the & (Q) & \frac{54}{13} tangents, then the value of sin α is (C) & If P (x_{1}, y_{1}) is any point on the circle, & (R) & \frac{5}{12} then the product of the minimum and the maximum values of O P, is (D) & A line is drawn from S (4, 5), intersecting & (S) & 9 the circle at M and N . Then the value of S M \cdot S N is (T) & 4 \end{matrix}$ Which of the following is the only CORRECT combination?

Discussion

15.	If period of function f(x)=cos(nx)sin5xn is 3π, then number of integral values of n must be
Answer» If period of function $f (x) = cos (n x) sin \frac{5 x}{n}$ is $3 π$ , then number of integral values of $n$ must be

Discussion

16.	Determine if f defined by is a continuous function?
Answer» Determine if f defined by is a continuous function?

Discussion

17.	The area of the quadrilateral formed by the lines 4x−3y−a=0,3x−4y+a=0, 4x−3y−3a=0 and 3x−4y+2a=0 is
Answer» The area of the quadrilateral formed by the lines $4 x - 3 y - a = 0, 3 x - 4 y + a = 0$ , $4 x - 3 y - 3 a = 0$ and $3 x - 4 y + 2 a = 0$ is

Discussion

18.	∫ba\|sinx\|dx=8 and ∫a+b0\|cosx\|dx=9, then value of 1√2π∣∣∫baxsinxdx∣∣ is
Answer» $\int_{a}^{b} \| sin x \| d x = 8$ and $\int_{0}^{a + b} \| cos x \| d x = 9,$ then value of $\frac{1}{\sqrt{2} π} ∣ ∣ \int_{a}^{b} x sin x d x ∣ ∣$ is

Discussion

19.	the number of points where f(x) = \|x^2 - 3x + 2\| is non differentiable is
Answer» the number of points where f(x) = \|x^2 - 3x + 2\| is non differentiable is

Discussion

20.	Tangents drawn at A(at21,2at1) and B (at22,2at2) intersect at (p,q).Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively (given t1≠t2)
Answer» Tangents drawn at A $(a t_{1}^{2}, 2 a t_{1})$ and B $(a t_{2}^{2}, 2 a t_{2})$ intersect at (p,q). Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively $(g i v e n t_{1} \neq t_{2})$

20.

Tangents drawn at A(at21,2at1) and B (at22,2at2) intersect at (p,q).Then p and q are and of corresponding x and y coordinates of A and B respectively (given t1≠t2)

Answer»

Tangents drawn at A $(a t_{1}^{2}, 2 a t_{1})$ and B $(a t_{2}^{2}, 2 a t_{2})$ intersect at (p,q).

Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively $(g i v e n t_{1} \neq t_{2})$

Discussion

21.	Let dydx+y=f(x) where y is a continuous function of x with y(0)=1 and f(x)={e−x,if 0≤x≤2e−2,if x>2Which of the following hold(s) good ?
Answer» Let $\frac{d y}{d x} + y = f (x)$ where $y$ is a continuous function of $x$ with $y (0) = 1$ and $f (x) = {\begin{matrix} e^{- x}, & if 0 \leq x \leq 2 e^{- 2}, & if x > 2 \end{matrix}$ Which of the following hold(s) good ?

Discussion

22.	The equation of the parabola having focus at (−1,−2) and the directrix x−2y+3=0 is ax2+bxy+cy2+gx+fy+16=0. If α and β are the roots of the equation gx2−fx+60=0, then the value of α3+β3 is
Answer» The equation of the parabola having focus at $(- 1, - 2)$ and the directrix $x - 2 y + 3 = 0$ is $a x^{2} + b x y + c y^{2} + g x + f y + 16 = 0$ . If $α$ and $β$ are the roots of the equation $g x^{2} - f x + 60 = 0$ , then the value of $α^{3} + β^{3}$ is

Discussion

23.	Let f(x)=a∫1/atan−1ttexdt, a∈R+. If f(0)−f′(0)=πln5, then the sum of all possible values of a is
Answer» Let $f (x) = a \int 1 / a \frac{{tan}^{- 1} t}{t e^{x}} d t,$ $a \in R^{+} .$ If $f (0) - f^{'} (0) = π ln 5,$ then the sum of all possible values of $a$ is

Discussion

24.	6.02/
Answer» 6.02/

Discussion

25.	If a tangent of slope ‘m’ at a point of the ellipse x2a2+y2b2=1 passes through (2a, 0) and if ‘e’ denotes its eccentricity, then
Answer» If a tangent of slope ‘m’ at a point of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ passes through (2a, 0) and if ‘e’ denotes its eccentricity, then

Discussion

26.	Volume of a cone is 900 cu. cm. Its height is 90 cm. Find the area of its base.
Answer» Volume of a cone is 900 cu. cm. Its height is 90 cm. Find the area of its base.

Discussion

27.	Find the effective resistance between A & B.
Answer» Find the effective resistance between $A$ & $B$ .

Discussion

28.	limx→∞(√x2+2x−1−x)=
Answer» $lim x \to \infty (\sqrt{x^{2} + 2 x - 1} - x) =$

Discussion

29.	Solve the following system of linear equations, using matrix method x−y+2z=7,3x+4y−5z=−5,2x−y+3z=12
Answer» Solve the following system of linear equations, using matrix method $x - y + 2 z = 7, 3 x + 4 y - 5 z = - 5, 2 x - y + 3 z = 12$

29.

Solve the following system of linear equations, using matrix method x−y+2z=7,3x+4y−5z=−5,2x−y+3z=12

Answer»

Solve the following system of linear equations, using matrix method

$x - y + 2 z = 7, 3 x + 4 y - 5 z = - 5, 2 x - y + 3 z = 12$

Discussion

30.	The integral of tan−1(x) is -
Answer» The integral of ${tan}^{- 1} (x)$ is -

Discussion

31.	If alpha and beta are zeroes of the polynomial x^2 + x + 1 , then the polynomial whose zeroes are [ alpha+beta ] and [alpha x beta] is ___
Answer» If alpha and beta are zeroes of the polynomial x^2 + x + 1 , then the polynomial whose zeroes are [ alpha+beta ] and [alpha x beta] is ___

Discussion

32.	The length of two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60∘. If length of the third side is 3, then length of the fourth side is
Answer» The length of two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^{\circ} .$ If length of the third side is $3,$ then length of the fourth side is

Discussion

33.	If nC4= nC5, then the value of nC2 is
Answer» If $^{n} C_{4} =^{n} C_{5}$ , then the value of $^{n} C_{2}$ is

Discussion

34.	The angle of intersection of curves y=[\|sinx\|+\|cosx\|]andx2+y2=5, where [∙] denotes the greatest integer function, is
Answer» The angle of intersection of curves $y = [\| s i n x \| + \| c o s x \|] a n d x^{2} + y^{2} = 5$ , where [∙] denotes the greatest integer function, is

Discussion

35.	Let {an} be a sequence such that a0=1, a1=0, an=3an−1−2an−2.Then, which of the following is a correct statement?
Answer» $Let {a_{n}} be a sequence such that a_{0} = 1, a_{1} = 0, a_{n} = 3 a_{n - 1} - 2 a_{n - 2} . Then, which of the following is a correct statement?$

Discussion

36.	Prove the following by using the principle of mathematical induction for all n ∈ N:
Answer» Prove the following by using the principle of mathematical induction for all n ∈ N:

Discussion

37.	If A and B are two matrices such that AB=B and BA=A, then A2+B2=
Answer» If A and B are two matrices such that AB=B and BA=A, then $A^{2} + B^{2}$ =

Discussion

38.	Let aand b be two unit vectors. If the vectors c= a + 2b and d : 5a-4b are perpendicular toeach other, then the angle between a and b is
Answer» Let aand b be two unit vectors. If the vectors c= a + 2b and d : 5a-4b are perpendicular toeach other, then the angle between a and b is

Discussion

39.	If,then find the least positive integral value of m.
Answer» If, then find the least positive integral value of m.

Discussion

40.	Let z be a complex such that −π4≤arg(z)≤π4 and \|z\|≤4. Then the area enclosed between them is
Answer» Let $z$ be a complex such that $- \frac{π}{4} \leq arg (z) \leq \frac{π}{4}$ and $\| z \| \leq 4$ . Then the area enclosed between them is

Discussion

41.	If X={x:x=8n−7n−1\|n∈N} and Y={y:y=49n−49\|n∈N}
Answer» If $X = {x : x = 8^{n} - 7 n - 1 \| n \in N}$ and $Y = {y : y = 49 n - 49 \| n \in N}$

Discussion

42.	When two projectiles are fired from complementary angles having times of flight T1,T2 and maximum heights H1,H2 respectively, which of the following is correct1.R=gT1T2/2 2.R=4√H1,H23. angle=tan^T1/T24.angle=tan^H1/H2
Answer» When two projectiles are fired from complementary angles having times of flight T1,T2 and maximum heights H1,H2 respectively, which of the following is correct 1.R=gT1T2/2 2.R=4√H1,H2 3. angle=tan^T1/T2 4.angle=tan^H1/H2

Discussion

43.	State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N , a * a = a a * N . (ii) If * is a commutative binary operation on N , then a * ( b * c ) = ( c * b ) * a
Answer» State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N , a * a = a a * N . (ii) If * is a commutative binary operation on N , then a * ( b * c ) = ( c * b ) * a

Discussion

44.	n(n+1)(n+5) is a multiple of 3 for all nϵN.
Answer» $n (n + 1) (n + 5)$ is a multiple of 3 for all $n ϵ N$ .

Discussion

45.	Find the equation of the normal at the point ( am 2 , am 3 ) for the curve ay 2 = x 3 .
Answer» Find the equation of the normal at the point ( am 2 , am 3 ) for the curve ay 2 = x 3 .

Discussion

46.	If α,β are the roots of the equation ax2+bx+c=0 and α+h,β+h are the roots of the equation Ax2+Bx+C=0, then find the value of b2−acB2−AC.
Answer» If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ and $α + h, β + h$ are the roots of the equation $A x^{2} + B x + C = 0,$ then find the value of $\frac{b^{2} - a c}{B^{2} - A C} .$

Discussion

47.	Find the values of x,y, zif the matrix satisfythe equation
Answer» Find the values of x, y, z if the matrix satisfy the equation

Discussion

48.	Find the value of d/ dx(√x+1/√x)^2
Answer» Find the value of d/ dx(√x+1/√x)^2

Discussion

49.	if alpha and beta are the zeros of the polynomial x square minus a X + a then find the value of (1)alpha^4-beta^4(2)-1/alpha^3+1/beta^3 (3)alpha/beta^2 + beta/ alpha^2(4)1/alpha+1/beta-2
Answer» if alpha and beta are the zeros of the polynomial x square minus a X + a then find the value of (1)alpha^4-beta^4 (2)-1/alpha^3+1/beta^3 (3)alpha/beta^2 + beta/ alpha^2 (4)1/alpha+1/beta-2

Discussion

50.	Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis
Answer» Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The area of the region above the x-axis, included between the parabola y2=ax and the circle x2+y2=2axis

The general solution of the differential equation dydx+yx = 1 is _____________.

10∑n=1[n∏k=1k+1k]=

A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :

If f and g are differentiable functions in [0,1] satisfying f(0)=2=g(1),g(0)=0 and f(1)=6, then for some c ϵ ]0,1[

Find the point at which the tangent to the curve y =3/5x^5 - 5/3x^3 - x had its slope equal to -3

For what real value of y will matrix A be equal to matrix B, where

α, β are the roots of the equation x2 + 4x + 5. Find α3 + β3

If 4^x-4^x-1=24, then find the value of (2x)^x. How to solve this problem in a quick and easy way for better understanding.

The term independent of x in the expansion of [x+1x2/3−x1/3+1−x−1x−x1/2]10, x≠1, is equal to

The maximum value of 1xx is(a) e (b) ee (c) e1/e (d) 1e1/e

Prove that cos(π4+x)+cos(π4−x)=√2cosx

If t lies between real roots of the equation 2x2−2(2t+1)x+t(t+1)=0, then t cannot be

If period of function f(x)=cos(nx)sin5xn is 3π, then number of integral values of n must be

Determine if f defined by is a continuous function?

The area of the quadrilateral formed by the lines 4x−3y−a=0,3x−4y+a=0, 4x−3y−3a=0 and 3x−4y+2a=0 is

∫ba|sinx|dx=8 and ∫a+b0|cosx|dx=9, then value of 1√2π∣∣∫baxsinxdx∣∣ is

the number of points where f(x) = |x^2 - 3x + 2| is non differentiable is

Tangents drawn at A(at21,2at1) and B (at22,2at2) intersect at (p,q).Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively (given t1≠t2)

Let dydx+y=f(x) where y is a continuous function of x with y(0)=1 and f(x)={e−x,if 0≤x≤2e−2,if x&gt;2Which of the following hold(s) good ?

The equation of the parabola having focus at (−1,−2) and the directrix x−2y+3=0 is ax2+bxy+cy2+gx+fy+16=0. If α and β are the roots of the equation gx2−fx+60=0, then the value of α3+β3 is

Let f(x)=a∫1/atan−1ttexdt, a∈R+. If f(0)−f′(0)=πln5, then the sum of all possible values of a is

6.02/

If a tangent of slope ‘m’ at a point of the ellipse x2a2+y2b2=1 passes through (2a, 0) and if ‘e’ denotes its eccentricity, then

Volume of a cone is 900 cu. cm. Its height is 90 cm. Find the area of its base.

Find the effective resistance between A &amp; B.

limx→∞(√x2+2x−1−x)=

Solve the following system of linear equations, using matrix method x−y+2z=7,3x+4y−5z=−5,2x−y+3z=12

The integral of tan−1(x) is -

If alpha and beta are zeroes of the polynomial x^2 + x + 1 , then the polynomial whose zeroes are [ alpha+beta ] and [alpha x beta] is ___

The length of two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60∘. If length of the third side is 3, then length of the fourth side is

If nC4= nC5, then the value of nC2 is

The angle of intersection of curves y=[|sinx|+|cosx|]andx2+y2=5, where [∙] denotes the greatest integer function, is

Let {an} be a sequence such that a0=1, a1=0, an=3an−1−2an−2.Then, which of the following is a correct statement?

Prove the following by using the principle of mathematical induction for all n ∈ N:

If A and B are two matrices such that AB=B and BA=A, then A2+B2=

Let aand b be two unit vectors. If the vectors c= a + 2b and d : 5a-4b are perpendicular toeach other, then the angle between a and b is

If,then find the least positive integral value of m.

Let z be a complex such that −π4≤arg(z)≤π4 and |z|≤4. Then the area enclosed between them is

If X={x:x=8n−7n−1|n∈N} and Y={y:y=49n−49|n∈N}

When two projectiles are fired from complementary angles having times of flight T1,T2 and maximum heights H1,H2 respectively, which of the following is correct1.R=gT1T2/2 2.R=4√H1,H23. angle=tan^T1/T24.angle=tan^H1/H2

State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N , a * a = a a * N . (ii) If * is a commutative binary operation on N , then a * ( b * c ) = ( c * b ) * a

n(n+1)(n+5) is a multiple of 3 for all nϵN.

Find the equation of the normal at the point ( am 2 , am 3 ) for the curve ay 2 = x 3 .

If α,β are the roots of the equation ax2+bx+c=0 and α+h,β+h are the roots of the equation Ax2+Bx+C=0, then find the value of b2−acB2−AC.

Find the values of x,y, zif the matrix satisfythe equation

Find the value of d/ dx(√x+1/√x)^2

if alpha and beta are the zeros of the polynomial x square minus a X + a then find the value of (1)alpha^4-beta^4(2)-1/alpha^3+1/beta^3 (3)alpha/beta^2 + beta/ alpha^2(4)1/alpha+1/beta-2

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Tangents drawn at A(at21,2at1) and B (at22,2at2) intersect at (p,q).Then p and q are and of corresponding x and y coordinates of A and B respectively (given t1≠t2)

Let dydx+y=f(x) where y is a continuous function of x with y(0)=1 and f(x)={e−x,if 0≤x≤2e−2,if x>2Which of the following hold(s) good ?

Find the effective resistance between A & B.