43030 + Interview Questions in Mathematics

1.	If the ratio of sum of n terms of two APs is (7n+1):(4n+27), then find the ratio of the n th term of the APs.
Answer» If the ratio of sum of n terms of two APs is (7n+1):(4n+27), then find the ratio of the n th term of the APs.

Discussion

2.	Let the vectors and be such that and , then is a unit vector, if the angle between and is (A) (B) (C) (D)
Answer» Let the vectors and be such that and , then is a unit vector, if the angle between and is (A) (B) (C) (D)

Discussion

3.	Let the coefficients of powers of x in the second, third and fourth terms in the binomial expansion of (1+x)n, where n is a positive integer, be in arithmetic progression. The sum of the coefficients of odd powers of x in the expansion is
Answer» Let the coefficients of powers of $x$ in the second, third and fourth terms in the binomial expansion of $(1 + x)^{n},$ where $n$ is a positive integer, be in arithmetic progression. The sum of the coefficients of odd powers of $x$ in the expansion is

Discussion

4.	An event has odds in favour 4 : 5, then the probability that event occurs, is
Answer» An event has odds in favour 4 : 5, then the probability that event occurs, is

Discussion

5.	Raj has a boat with a maximum weight capacity of 2700 kg. He wants to take as many of his friends as possible. The average weight of each friend is considered to be 70 kg. Then the maximum number of persons that can travel in the boat if 2 VIP persons weighing 98 kg and 86 kg have to travel compulsorily is
Answer» Raj has a boat with a maximum weight capacity of $2700$ kg. He wants to take as many of his friends as possible. The average weight of each friend is considered to be $70$ kg. Then the maximum number of persons that can travel in the boat if $2$ VIP persons weighing $98$ kg and $86$ kg have to travel compulsorily is

Discussion

6.	In triangle ABC cosa/a=cosb/b=cosc/c the value of r1+r2+r3/r is equal to
Answer» In triangle ABC cosa/a=cosb/b=cosc/c the value of r1+r2+r3/r is equal to

Discussion

7.	If α≤2 sin-1 x+cos-1 x≤β, then(a) α=-π2, β=π2 (b) α=0, β=π (c) α=-π2, β=3π2 (d) α=0, β=2π
Answer» $If α \leq 2 \sin^{- 1} x + \cos^{- 1} x \leq β, then (a) α = - \frac{π}{2}, β = \frac{π}{2} (b) α = 0, β = π (c) α = - \frac{π}{2}, β = \frac{3 π}{2} (d) α = 0, β = 2 π$

Discussion

8.	3. cot x--V3
Answer» 3. cot x--V3

Discussion

9.	If the length of the chord of the parabola y2=4x whose slope is 1, is 10√2 units, then equation of the chord is
Answer» If the length of the chord of the parabola $y^{2} = 4 x$ whose slope is $1$ , is $10 \sqrt{2}$ units, then equation of the chord is

Discussion

10.	a(cos B cos C+cos A)=b(cos C cos A+cos B)=c(cos A cos B+cos C).
Answer» $a (c o s B c o s C + c o s A) = b (c o s C c o s A + c o s B) = c (c o s A c o s B + c o s C) .$

Discussion

11.	Find the 7th term in the expansion of (4x5+52x)8
Answer» Find the 7th term in the expansion of ${(\frac{4 x}{5} + \frac{5}{2 x})}^{8}$

Discussion

12.	If the points (0,7,10),(−1,6,6)and(−4,9,6) are the vertices of a triangle, then the triangle is _____
Answer» If the points $(0, 7, 10), (- 1, 6, 6) a n d (- 4, 9, 6)$ are the vertices of a triangle, then the triangle is _____

Discussion

13.	The value of ∫3x2+73x3+6x2+7x+14dx is(where C is constant of integration)
Answer» The value of $\int \frac{3 x^{2} + 7}{3 x^{3} + 6 x^{2} + 7 x + 14} d x$ is (where $C$ is constant of integration)

Discussion

14.	In how many ways a garland can be made from exactly 10 flowers
Answer» In how many ways a garland can be made from exactly 10 flowers

Discussion

15.	Find the total number of ways in which six '+' and four '–' signs can be arranged in a line such that no two '–' signs occur together.
Answer» Find the total number of ways in which six '+' and four '–' signs can be arranged in a line such that no two '–' signs occur together.

Discussion

16.	The quadratic equation 11/4x^2 - 11(p+q)x+(10p^2 +24pq+10q^2) =0, where pis not equal to +or-q has what type of rootsReal and equal Real and distinct No real roots
Answer» The quadratic equation 11/4x^2 - 11(p+q)x+(10p^2 +24pq+10q^2) =0, where pis not equal to +or-q has what type of roots Real and equal Real and distinct No real roots

Discussion

17.	Solve the equation x2 + 3 = 0
Answer» Solve the equation x² + 3 = 0

Discussion

18.	If roots of 10x^3-cx^2-54x-27=0 are in H.P.,find
Answer» If roots of 10x^3-cx^2-54x-27=0 are in H.P.,find

Discussion

19.	Let ∣∣∣∣x2xx2x6xx6∣∣∣∣=Ax4+Bx3+Cx2+Dx+E
Answer» Let $∣ ∣∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣∣ ∣ = A x^{4} + B x^{3} + C x^{2} + D x + E$

Discussion

20.	If the incircle of the triangle ABC (AB≠BC≠CA), passes through it's circumcentre, then the (cosA+cosB+cosC)2 is
Answer» If the incircle of the triangle $A B C (A B \neq B C \neq C A)$ , passes through it's circumcentre, then the $(cos A + cos B + cos C)^{2}$ is

Discussion

21.	If ycosx=2, then dydx=
Answer» If $y^{cos x} = 2,$ then $\frac{d y}{d x} =$

Discussion

22.	The line through (h, 3) and (4, 1) intersects the line 7x−9y−19=0 at right angle. Find the value of h.
Answer» The line through $(h, 3)$ and $(4, 1)$ intersects the line $7 x - 9 y - 19 = 0$ at right angle. Find the value of h.

Discussion

23.	If nCr=84, nCr−1=36 and nCr+1=126, then the value of n is
Answer» If $^{n} C_{r} = 84,^{n} C_{r - 1} = 36$ and $^{n} C_{r + 1} = 126$ , then the value of $n$ is

Discussion

24.	If the probability that a student is not a swimmer is 1/5, then the probability that out of 5 students one is swimmer is
Answer» If the probability that a student is not a swimmer is 1/5, then the probability that out of 5 students one is swimmer is

Discussion

25.	The equation of the circle which orthogonally intersects the circles x2+y2−2x+3y−7=0, x2+y2+5x−5y+9=0 and x2+y2+7x−9y+29=0, is
Answer» The equation of the circle which orthogonally intersects the circles $x^{2} + y^{2} - 2 x + 3 y - 7 = 0$ , $x^{2} + y^{2} + 5 x - 5 y + 9 = 0$ and $x^{2} + y^{2} + 7 x - 9 y + 29 = 0$ , is

Discussion

26.	The number of committees of five persons with a chairperson that can be formed from 12 persons, is(a) 12C5(b) 12C4(c) 12 × 11C4(d) 11C4
Answer» The number of committees of five persons with a chairperson that can be formed from 12 persons, is (a) ¹²C₅ (b) ¹²C₄ (c) 12 × ¹¹C₄ (d) ¹¹C₄

Discussion

27.	Find the equation of the plane passing through the line of intersection of the planes and and parallel to x -axis.
Answer» Find the equation of the plane passing through the line of intersection of the planes and and parallel to x -axis.

Discussion

28.	19. If the equation (l+M2)X2+2mcx+(c2-a2)=0 has equal roots,prove that C2=A2(l+M2).
Answer» 19. If the equation (l+M2)X2+2mcx+(c2-a2)=0 has equal roots,prove that C2=A2(l+M2).

Discussion

29.	If 1+iz=1-iz¯, then show that z=-iz¯.
Answer» If $(1 + i) z = (1 - i) \bar{z}$ , then show that $z = - i \bar{z}$ .

Discussion

30.	The length of a rectangular field is 5 metres less than twice the breadth. If its area is 700 square metres, then the perimeter (in metres) of the field is
Answer» The length of a rectangular field is $5$ metres less than twice the breadth. If its area is $700$ square metres, then the perimeter (in metres) of the field is

Discussion

31.	11. cos4 2x
Answer» 11. cos4 2x

Discussion

32.	If ϕ denotes the empty set, then which of the folowing is correct
Answer» If $ϕ$ denotes the empty set, then which of the folowing is correct

Discussion

33.	The quadratic equations x2−6x+a=0, x2−cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3 . Then common root is :
Answer» The quadratic equations $x^{2} - 6 x + a = 0,$ $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4 : 3$ . Then common root is :

Discussion

34.	Show that the given differential equation is homogeneous and then solve it. ydx+xlog(yx)dy−2xdy=0
Answer» Show that the given differential equation is homogeneous and then solve it. $y d x + x l o g (\frac{y}{x}) d y - 2 x d y = 0$

Discussion

35.	If ⎛⎜⎝x2x1021314∣∣∣∣∣ =28, then the value of x is
Answer» $If ⎛ ⎜ ⎝ \begin{matrix} x^{2} & x & 1 0 & 2 & 1 3 & 1 & 4 \end{matrix} ∣ ∣∣∣ ∣ = 28, then the value of x is$

Discussion

36.	The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x2−y2−2x+4y−3=0, is
Answer» The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines $x^{2} - y^{2} - 2 x + 4 y - 3 = 0,$ is

Discussion

37.	If matrix P=⎛⎜⎝01−14−343−34⎤⎥⎦= Q + R, where Q is symmetric matrix and R is skew symmetric matrix. Then find matrix Q and R.
Answer» If matrix $P = ⎛ ⎜ ⎝ \begin{matrix} 0 & 1 & - 1 4 & - 3 & 4 3 & - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ = Q + R$ , where Q is symmetric matrix and R is skew symmetric matrix. Then find matrix Q and R.

Discussion

38.	Differentiate the following equation, x−3(5+3x)
Answer» Differentiate the following equation, $x^{- 3} (5 + 3 x)$

Discussion

39.	Let f(x)=x2+px+3 and g(x)=x+q, where p,q∈R. If F(x)=limn→∞f(x)+xng(x)1+xn is derivable at x=1, then the value of p2+q2 is
Answer» Let $f (x) = x^{2} + p x + 3$ and $g (x) = x + q,$ where $p, q \in R .$ If $F (x) = lim n \to \infty \frac{f (x) + x^{n} g (x)}{1 + x^{n}}$ is derivable at $x = 1$ , then the value of $p^{2} + q^{2}$ is

Discussion

40.	6.The points A(0,3),B(-2, y) and C(-1,4) are the vertices of Δ ABC, right angled at A. Find the value of y ??
Answer» 6.The points A(0,3),B(-2, y) and C(-1,4) are the vertices of Δ ABC, right angled at A. Find the value of y ??

Discussion

41.	If x +2y +3z= 0, then the value of x^3+8y^3+27z^3 s
Answer» If x +2y +3z= 0, then the value of x^3+8y^3+27z^3 s

Discussion

42.	The value of the integral ∫2x(x2+1)(x2+3)dx is(where C is an arbitrary constant)
Answer» The value of the integral $\int \frac{2 x}{(x^{2} + 1) (x^{2} + 3)} d x$ is (where $C$ is an arbitrary constant)

Discussion

43.	The number of 4×4 skew symmetric matrices that can be formed using exactly four 0's, six 3's and six −3's is
Answer» The number of $4 \times 4$ skew symmetric matrices that can be formed using exactly four $0$ 's, six $3$ 's and six $- 3$ 's is

Discussion

44.	The maximum value of 2cos4x+2cos4(90∘−x) is
Answer» The maximum value of $2 {cos}^{4} x + 2 {cos}^{4} (90^{\circ} - x)$ is

Discussion

45.	Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
Answer» Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Discussion

46.	11.(X3 + X2 +X+Day-2x2 + x; y = 1 when x = 0dx
Answer» 11.(X3 + X2 +X+Day-2x2 + x; y = 1 when x = 0dx

Discussion

47.	Solve the following system of equations in R. 2x+17x−1>5,x+7x−8>2
Answer» Solve the following system of equations in R. $\frac{2 x + 1}{7 x - 1} > 5, \frac{x + 7}{x - 8} > 2$

47.

Solve the following system of equations in R. 2x+17x−1>5,x+7x−8>2

Answer»

Solve the following system of equations in R.

$\frac{2 x + 1}{7 x - 1} > 5, \frac{x + 7}{x - 8} > 2$

Discussion

48.	If A and B are two events such that P(A)=12,P(B)=13 and P(A∩B)=14, then find P(A′B′)
Answer» If A and B are two events such that $P (A) = \frac{1}{2}, P (B) = \frac{1}{3}$ and $P (A \cap B) = \frac{1}{4},$ then find $P (\frac{A^{'}}{B^{'}})$

48.

If A and B are two events such that P(A)=12,P(B)=13 and P(A∩B)=14, then find P(A′B′)

Answer»

If A and B are two events such that

$P (A) = \frac{1}{2}, P (B) = \frac{1}{3}$ and $P (A \cap B) = \frac{1}{4},$ then find

$P (\frac{A^{'}}{B^{'}})$

Discussion

49.	If the tangents are drawn at (at21,2at1) and (at22,2at2) on the parabola y2=4ax intersect on axis of the parabola, then
Answer» If the tangents are drawn at $(a t_{1}^{2}, 2 a t_{1})$ and $(a t_{2}^{2}, 2 a t_{2})$ on the parabola $y^{2} = 4 a x$ intersect on axis of the parabola, then

Discussion

50.	limx→π2tan2xx=π2
Answer» ${lim}_{x \to \frac{π}{2}} \frac{t a n 2 x}{x = \frac{π}{2}}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the ratio of sum of n terms of two APs is (7n+1):(4n+27), then find the ratio of the n th term of the APs.

Let the vectors and be such that and , then is a unit vector, if the angle between and is (A) (B) (C) (D)

Let the coefficients of powers of x in the second, third and fourth terms in the binomial expansion of (1+x)n, where n is a positive integer, be in arithmetic progression. The sum of the coefficients of odd powers of x in the expansion is

An event has odds in favour 4 : 5, then the probability that event occurs, is

In triangle ABC cosa/a=cosb/b=cosc/c the value of r1+r2+r3/r is equal to

If α≤2 sin-1 x+cos-1 x≤β, then(a) α=-π2, β=π2 (b) α=0, β=π (c) α=-π2, β=3π2 (d) α=0, β=2π

3. cot x--V3

If the length of the chord of the parabola y2=4x whose slope is 1, is 10√2 units, then equation of the chord is

a(cos B cos C+cos A)=b(cos C cos A+cos B)=c(cos A cos B+cos C).

Find the 7th term in the expansion of (4x5+52x)8

If the points (0,7,10),(−1,6,6)and(−4,9,6) are the vertices of a triangle, then the triangle is _____

The value of ∫3x2+73x3+6x2+7x+14dx is(where C is constant of integration)

In how many ways a garland can be made from exactly 10 flowers

Find the total number of ways in which six '+' and four '–' signs can be arranged in a line such that no two '–' signs occur together.

The quadratic equation 11/4x^2 - 11(p+q)x+(10p^2 +24pq+10q^2) =0, where pis not equal to +or-q has what type of rootsReal and equal Real and distinct No real roots

Solve the equation x2 + 3 = 0

If roots of 10x^3-cx^2-54x-27=0 are in H.P.,find

Let ∣∣∣∣x2xx2x6xx6∣∣∣∣=Ax4+Bx3+Cx2+Dx+E

If the incircle of the triangle ABC (AB≠BC≠CA), passes through it's circumcentre, then the (cosA+cosB+cosC)2 is

If ycosx=2, then dydx=

The line through (h, 3) and (4, 1) intersects the line 7x−9y−19=0 at right angle. Find the value of h.

If nCr=84, nCr−1=36 and nCr+1=126, then the value of n is

If the probability that a student is not a swimmer is 1/5, then the probability that out of 5 students one is swimmer is

The equation of the circle which orthogonally intersects the circles x2+y2−2x+3y−7=0, x2+y2+5x−5y+9=0 and x2+y2+7x−9y+29=0, is

The number of committees of five persons with a chairperson that can be formed from 12 persons, is(a) 12C5(b) 12C4(c) 12 × 11C4(d) 11C4

Find the equation of the plane passing through the line of intersection of the planes and and parallel to x -axis.

19. If the equation (l+M2)X2+2mcx+(c2-a2)=0 has equal roots,prove that C2=A2(l+M2).

If 1+iz=1-iz¯, then show that z=-iz¯.

The length of a rectangular field is 5 metres less than twice the breadth. If its area is 700 square metres, then the perimeter (in metres) of the field is

11. cos4 2x

If ϕ denotes the empty set, then which of the folowing is correct

The quadratic equations x2−6x+a=0, x2−cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3 . Then common root is :

Show that the given differential equation is homogeneous and then solve it. ydx+xlog(yx)dy−2xdy=0

If ⎛⎜⎝x2x1021314∣∣∣∣∣ =28, then the value of x is

The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x2−y2−2x+4y−3=0, is

If matrix P=⎛⎜⎝01−14−343−34⎤⎥⎦= Q + R, where Q is symmetric matrix and R is skew symmetric matrix. Then find matrix Q and R.

Differentiate the following equation, x−3(5+3x)

Let f(x)=x2+px+3 and g(x)=x+q, where p,q∈R. If F(x)=limn→∞f(x)+xng(x)1+xn is derivable at x=1, then the value of p2+q2 is

6.The points A(0,3),B(-2, y) and C(-1,4) are the vertices of Δ ABC, right angled at A. Find the value of y ??

If x +2y +3z= 0, then the value of x^3+8y^3+27z^3 s

The value of the integral ∫2x(x2+1)(x2+3)dx is(where C is an arbitrary constant)

The number of 4×4 skew symmetric matrices that can be formed using exactly four 0's, six 3's and six −3's is

The maximum value of 2cos4x+2cos4(90∘−x) is

Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

11.(X3 + X2 +X+Day-2x2 + x; y = 1 when x = 0dx

Solve the following system of equations in R. 2x+17x−1&gt;5,x+7x−8&gt;2

If A and B are two events such that P(A)=12,P(B)=13 and P(A∩B)=14, then find P(A′B′)

If the tangents are drawn at (at21,2at1) and (at22,2at2) on the parabola y2=4ax intersect on axis of the parabola, then

limx→π2tan2xx=π2

Solve the following system of equations in R. 2x+17x−1>5,x+7x−8>2