43030 + Interview Questions in Mathematics

1.	The graph of a function y=acosbx+c is given below Then, the function y is
Answer» The graph of a function $y = a cos b x + c$ is given below Then, the function $y$ is

Discussion

2.	The general solution of the differential equation (ey+1)cosxdx+eysinxdy=0 is(where c is constant of integration)
Answer» The general solution of the differential equation $(e^{y} + 1) cos x d x + e^{y} sin x d y = 0$ is (where $c$ is constant of integration)

Discussion

3.	For x∈R, the range of f(x)=2x−12x+1 is
Answer» For $x \in R$ , the range of $f (x) = \frac{2^{x} - 1}{2^{x} + 1}$ is

Discussion

4.	The parametric form of the circle x2+y2−4(x+y)=8 is
Answer» The parametric form of the circle $x^{2} + y^{2} - 4 (x + y) = 8$ is

Discussion

5.	Suppose OABC is a rectangle in the xy−plane where O is the origin and A,B lie on the parabola y=x2 . Then C must lie on the curve
Answer» Suppose $O A B C$ is a rectangle in the $x y -$ plane where $O$ is the origin and $A, B$ lie on the parabola $y = x^{2}$ . Then $C$ must lie on the curve

Discussion

6.	The length and bredth of a hall are in the ratio 4:3 and its height is 5.5 metres. The ost of decorating its walls (including doors and windows) at 6.60 per squaremetre is 5082. Find the length and breadth of the room.
Answer» The length and bredth of a hall are in the ratio 4:3 and its height is 5.5 metres. The ost of decorating its walls (including doors and windows) at 6.60 per squaremetre is 5082. Find the length and breadth of the room.

Discussion

7.	Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)
Answer» Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Discussion

8.	The probability of getting a "head" in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is .0.072
Answer» The probability of getting a "head" in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is . 0.072

8.

The probability of getting a "head" in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is .0.072

Answer»

The probability of getting a "head" in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is .

0.072

Discussion

9.	10. x>- 3
Answer» 10. x>- 3

Discussion

10.	Each of three identical jewellery boxes has two drawers. In each drawer of the first box, there is a gold watch. In each drawer of the second box, there is a silver watch. In one drawer of the third box, there is a gold watch while in the other, there is a silver watch. If we select a box at random, open one of the drawers and find it to contain a silver watch, then the probability that the other drawer has the gold watch in it, is
Answer» Each of three identical jewellery boxes has two drawers. In each drawer of the first box, there is a gold watch. In each drawer of the second box, there is a silver watch. In one drawer of the third box, there is a gold watch while in the other, there is a silver watch. If we select a box at random, open one of the drawers and find it to contain a silver watch, then the probability that the other drawer has the gold watch in it, is

Discussion

11.	the whole sqrt x-sqrt x^2-1 find domain
Answer» the whole sqrt x-sqrt x^2-1 find domain

Discussion

12.	A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that the locus of the centroid of triangle ABC is 1x2+1y2+1z2=1p2
Answer» A variable plane which remains at a constant distance $3 p$ from the origin cuts the coordinate axes at $A, B, C$ . Show that the locus of the centroid of triangle $A B C$ is $\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{1}{p^{2}}$

Discussion

13.	If the centre, vertex and focus of a hyperbola are (4,3),(8,3),(10,3) respectively, then the equation of the hyperbola is
Answer» If the centre, vertex and focus of a hyperbola are $(4, 3), (8, 3), (10, 3)$ respectively, then the equation of the hyperbola is

Discussion

14.	{m^2+n^2}x^2 - 2{mp+nq}x + p^2 + q^2 This quadratic equation has equal roots. Prove that mn = √pq
Answer» {m^2+n^2}x^2 - 2{mp+nq}x + p^2 + q^2 This quadratic equation has equal roots. Prove that mn = √pq

Discussion

15.	The Boolean Expression (p∧∼q)∨q∨(∼p∧q) is equivalent to:
Answer» The Boolean Expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to:

Discussion

16.	A line makes the same angle θ with each of the x and z- axis. If the angle β which it makes with y- axis, is such that sin2β=3sin2θ, then cos2θ equals
Answer» A line makes the same angle $θ$ with each of the x and z- axis. If the angle $β$ which it makes with y- axis, is such that $s i n^{2} β = 3 s i n^{2} θ$ , then $c o s^{2} θ$ equals

Discussion

17.	Four distinct integer are picked at random from {0, 1, 2, 3, 4, 5, 6}. If the probability that among those selected the second smallest is 3 is ‘P’, then ‘35P’ is equal to ___
Answer» Four distinct integer are picked at random from {0, 1, 2, 3, 4, 5, 6}. If the probability that among those selected the second smallest is 3 is ‘P’, then ‘35P’ is equal to ___

Discussion

18.	The set of points where the function f(x) = \|2x – 1\| sin x is differentiable, is(a) R(b) R-12(c) (0, ∞)(d) none of these
Answer» The set of points where the function f(x) = \|2x – 1\| sin x is differentiable, is (a) R (b) $R - \{\frac{1}{2}\}$ (c) (0, ∞) (d) none of these

Discussion

19.	Letbea function defined as.The inverse of fis map g:Range(A) (B) (C) (D)
Answer» Letbe a function defined as. The inverse of f is map g: Range (A) (B) (C) (D)

19.

Letbea function defined as.The inverse of fis map g:Range(A) (B) (C) (D)

Answer»

Letbe
a function defined as.
The inverse of f
is map g:
Range

(A) (B)

(C) (D)

Discussion

20.	Prove that: cos3 x sin 3x+sin3 x cos 3x=34 sin 4x
Answer» Prove that: $\cos^{3} x \sin 3 x + \sin^{3} x \cos 3 x = \frac{3}{4} \sin 4 x$

Discussion

21.	If the area of the quadrilateral formed by the tangents from the origin to the circle x2+y2+6x−10y+c=0 and radii corresponding to the point of contact is 15 sq. units, then value(s) of c can be
Answer» If the area of the quadrilateral formed by the tangents from the origin to the circle $x^{2} + y^{2} + 6 x - 10 y + c = 0$ and radii corresponding to the point of contact is $15$ sq. units, then value(s) of $c$ can be

Discussion

22.	The shortest distance (in units) between the lines whose equations are →r=^i+2^j+7^k+λ(^i+2^j+3^k) and →r=−^i−2^j+3^k+s(7^i+6^j+3^k) is:
Answer» The shortest distance (in units) between the lines whose equations are $\to r =^i + 2^j + 7^k + λ (^i + 2^j + 3^k)$ and $\to r = -^i - 2^j + 3^k + s (7^i + 6^j + 3^k)$ is:

Discussion

23.	Let a1,a2,............a10 be in AP and h1, h2..............h10 be in H.P. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is __
Answer» Let $a_{1}$ , $a_{2}$ ,............ $a_{10}$ be in AP and $h_{1}$ , $h_{2}$ .............. $h_{10}$ be in H.P. If $a_{1}$ = $h_{1}$ = 2 and $a_{10}$ = $h_{10}$ = 3, then $a_{4}$ $h_{7}$ is __

Discussion

24.	The number of values of k for which the linear equations4x+ky+2z=0kx+4y+z=02x+2y+z=0posses a non-zero solution is
Answer» The number of values of $k$ for which the linear equations $4 x + k y + 2 z = 0$ $k x + 4 y + z = 0$ $2 x + 2 y + z = 0$ posses a non-zero solution is

Discussion

25.	The sum of the square of all real numbers satisfying the equation x 256 - 256 32 = 0 is
Answer» The sum of the square of all real numbers satisfying the equation x ²⁵⁶ - 256 ³² = 0 is

Discussion

26.	If the solution of differential equation x lnxdydx+y=2lnx is y(lnx)=(lnx)n+C then n= ___
Answer» If the solution of differential equation $x ln x \frac{d y}{d x} + y = 2 ln x$ is $y (ln x) = (ln x)^{n} + C$ then $n =$ ___

Discussion

27.	If ∣∣∣∣∣x−12x−1x2+1−x2x−2−3x−2x24x−13x−3∣∣∣∣∣=n∑i=0aixi ∀ x∈R,n≤10, then which of the following is correct?
Answer» If $∣ ∣∣∣ ∣ \begin{matrix} x - 1 & 2 x - 1 & x^{2} + 1 - x & 2 x - 2 & - 3 x - 2 x^{2} & 4 x - 1 & 3 x - 3 \end{matrix} ∣ ∣∣∣ ∣ = n \sum i = 0 a_{i} x^{i} \forall x \in R, n \leq 10,$ then which of the following is correct?

Discussion

28.	The number of permutations by using all the letters of the word MONDAY which neither begins with M nor ends with Y, is
Answer» The number of permutations by using all the letters of the word $M O N D A Y$ which neither begins with $M$ nor ends with $Y,$ is

Discussion

29.	How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
Answer» How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

Discussion

30.	A straight line L through the point (3,–2) is inclined at an angle 60∘ to the line √3x+y=1 If L also intersects the x-axis, then the equation of L is
Answer» A straight line $L$ through the point $(3, - 2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3} x + y = 1$ If $L$ also intersects the x-axis, then the equation of $L$ is

Discussion

31.	Explain the terms ‘Over-subscription’ and ‘Under-subscription’. How are they dealt with in accounting records?
Answer» Explain the terms ‘Over-subscription’ and ‘Under-subscription’. How are they dealt with in accounting records?

Discussion

32.	Solve: cos2sin-1-x=0
Answer» Solve: $\cos \{2 \sin^{- 1} (- x)\} = 0$

Discussion

33.	Evaluate the following integrals:∫-π/4π/4sin x dx
Answer» Evaluate the following integrals: $\int_{- π / 4}^{π / 4} \|\sin x\| d x$

Discussion

34.	Consider an object function Z(x1, x2)=3x1+9x2 and the constraintsx1+x2≤8x1+2x2≤4x1≥0, x2≥0The maximum value of the objective function is .18
Answer» Consider an object function $Z (x_{1}, x_{2}) = 3 x_{1} + 9 x_{2}$ and the constraints $x_{1} + x_{2} \leq 8$ $x_{1} + 2 x_{2} \leq 4$ $x_{1} \geq 0, x_{2} \geq 0$ $The maximum value of the objective function is .$ 18

Discussion

35.	Find the distance of the point (- 1, - 5,- 10) from the point of intersection of the line r=2^i−^j+2^k+λ(3^i+4^j+2^k) and the plane r.(^i−^j+^k)=5
Answer» Find the distance of the point (- 1, - 5,- 10) from the point of intersection of the line $r = 2^i -^j + 2^k + λ (3^i + 4^j + 2^k)$ and the plane $r . (^i -^j +^k) = 5$

Discussion

36.	2.X/100-X = \sqrt{}36.5/17
Answer» 2.X/100-X = \sqrt{}36.5/17

Discussion

37.	∫∞0e−axcos bxdx=
Answer» $\int_{0}^{\infty} e^{- a x} c o s b x d x =$

Discussion

38.	19π8. tan
Answer» 19π8. tan

Discussion

39.	e(cos2x+cos4x+cos6x+⋯∞)loge2 satisfies the equation t2–9t+8=0, then the value of 2sinxsinx+√3cosx,(0<x<π2) is :
Answer» $e^{({cos}^{2} x + {cos}^{4} x + {cos}^{6} x + \dots \infty) {log}_{e} 2}$ satisfies the equation $t^{2} - 9 t + 8 = 0,$ then the value of $\frac{2 sin x}{sin x + \sqrt{3} cos x}, (0 < x < \frac{π}{2})$ is :

Discussion

40.	If kπ10 is the least positive value of θ which satisfy the equation sin3θ+cos2θ=0, then k is
Answer» If $\frac{k π}{10}$ is the least positive value of $θ$ which satisfy the equation $sin 3 θ + cos 2 θ = 0$ , then $k$ is

Discussion

41.	Examine that is a continuous function.
Answer» Examine that is a continuous function.

Discussion

42.	How many of these are correctly matched ? Coordinates of a point Name of the octant 1. (1,2,3) P.I 2. (4,−2,3) Q.IV 3. (4,−2,−5) R.VIII 4. (4,2,−5) S.V 5. (−4,2,−5) T.VI 6. (−4,2,5) U.II 7. (−3,−1,6) V.III 8. (2,−4,−7) W.VIII ___
Answer» How many of these are correctly matched ? Coordinates of a point Name of the octant 1. $(1, 2, 3) P . I$ 2. $(4, - 2, 3) Q . I V$ 3. $(4, - 2, - 5) R . V I I I$ 4. $(4, 2, - 5) S . V$ 5. $(- 4, 2, - 5) T . V I$ 6. $(- 4, 2, 5) U . I I$ 7. $(- 3, - 1, 6) V . I I I$ 8. $(2, - 4, - 7) W . V I I I$ ___

42.

How many of these are correctly matched ? Coordinates of a point Name of the octant 1. (1,2,3) P.I 2. (4,−2,3) Q.IV 3. (4,−2,−5) R.VIII 4. (4,2,−5) S.V 5. (−4,2,−5) T.VI 6. (−4,2,5) U.II 7. (−3,−1,6) V.III 8. (2,−4,−7) W.VIII ___

Answer»

How many of these are correctly matched ?

Coordinates of a point Name of the octant

1. $(1, 2, 3) P . I$

2. $(4, - 2, 3) Q . I V$

3. $(4, - 2, - 5) R . V I I I$

4. $(4, 2, - 5) S . V$

5. $(- 4, 2, - 5) T . V I$

6. $(- 4, 2, 5) U . I I$

7. $(- 3, - 1, 6) V . I I I$

8. $(2, - 4, - 7) W . V I I I$

___

Discussion

43.	cos230° cos245°+4sec260°+12cos290°-2tan260°=?(a) 818(b) 838(c) 738(d) 758
Answer» $(\cos^{2} 30 ° \cos^{2} 45 ° + 4 \sec^{2} 60 ° + \frac{1}{2} \cos^{2} 90 ° - 2 \tan^{2} 60 °) = ?$ (a) $\frac{81}{8}$ (b) $\frac{83}{8}$ (c) $\frac{73}{8}$ (d) $\frac{75}{8}$

Discussion

44.	12, x-y+z=42x+y-3z = 0"x + y + z = 2
Answer» 12, x-y+z=42x+y-3z = 0"x + y + z = 2

Discussion

45.	In a ∆ABC, if ∠C=π2, ∠A=π6, c = 20, then a = ____________.
Answer» In a ∆ABC, if $∠ C = \frac{π}{2}, ∠ A = \frac{π}{6},$ c = 20, then a = ____________.

Discussion

46.	If P (A\|B) > P (A), then which of the following is correct: (A) P (B\|A) < P (B) (B) P (A ∩ B) < P (A).P (B) (C) P (B\|A) > P (B) (D) P (B\|A) = P (B)
Answer» If P (A\|B) > P (A), then which of the following is correct: (A) P (B\|A) < P (B) (B) P (A ∩ B) < P (A).P (B) (C) P (B\|A) > P (B) (D) P (B\|A) = P (B)

Discussion

47.	If the least and the largest real values of α, for which the equation z+α\|z−1\|+2i=0(z∈C and i=√−1) has a solution, are p and q respectively; then 4(p2+q2) is equal to
Answer» If the least and the largest real values of $α$ , for which the equation $z + α \| z - 1 \| + 2 i = 0 (z \in C and i = \sqrt{- 1})$ has a solution, are $p$ and $q$ respectively; then $4 (p^{2} + q^{2})$ is equal to

Discussion

48.	If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where A=l1m1n1l2m2n2l3m3n3.
Answer» If l_i, m_i, n_i, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AA^T = I, where $A = [\begin{matrix} l_{1} & m_{1} & n_{1} \\ l_{2} & m_{2} & n_{2} \\ l_{3} & m_{3} & n_{3} \end{matrix}]$ .

Discussion

49.	For any set A, if U is the universal set, then A′=
Answer» For any set $A,$ if $U$ is the universal set, then $A^{'} =$

Discussion

50.	If ax2+bx+6=0 does not have two distinct real roots,then the least value of 3a+b is?
Answer» If ax2+bx+6=0 does not have two distinct real roots,then the least value of 3a+b is?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The graph of a function y=acosbx+c is given below Then, the function y is

The general solution of the differential equation (ey+1)cosxdx+eysinxdy=0 is(where c is constant of integration)

For x∈R, the range of f(x)=2x−12x+1 is

The parametric form of the circle x2+y2−4(x+y)=8 is

Suppose OABC is a rectangle in the xy−plane where O is the origin and A,B lie on the parabola y=x2 . Then C must lie on the curve

The length and bredth of a hall are in the ratio 4:3 and its height is 5.5 metres. The ost of decorating its walls (including doors and windows) at 6.60 per squaremetre is 5082. Find the length and breadth of the room.

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

The probability of getting a "head" in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is .0.072

10. x>- 3

the whole sqrt x-sqrt x^2-1 find domain

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that the locus of the centroid of triangle ABC is 1x2+1y2+1z2=1p2

If the centre, vertex and focus of a hyperbola are (4,3),(8,3),(10,3) respectively, then the equation of the hyperbola is

{m^2+n^2}x^2 - 2{mp+nq}x + p^2 + q^2 This quadratic equation has equal roots. Prove that mn = √pq

The Boolean Expression (p∧∼q)∨q∨(∼p∧q) is equivalent to:

A line makes the same angle θ with each of the x and z- axis. If the angle β which it makes with y- axis, is such that sin2β=3sin2θ, then cos2θ equals

Four distinct integer are picked at random from {0, 1, 2, 3, 4, 5, 6}. If the probability that among those selected the second smallest is 3 is ‘P’, then ‘35P’ is equal to ___

The set of points where the function f(x) = |2x – 1| sin x is differentiable, is(a) R(b) R-12(c) (0, ∞)(d) none of these

Letbea function defined as.The inverse of fis map g:Range(A) (B) (C) (D)

Prove that: cos3 x sin 3x+sin3 x cos 3x=34 sin 4x

If the area of the quadrilateral formed by the tangents from the origin to the circle x2+y2+6x−10y+c=0 and radii corresponding to the point of contact is 15 sq. units, then value(s) of c can be

The shortest distance (in units) between the lines whose equations are →r=^i+2^j+7^k+λ(^i+2^j+3^k) and →r=−^i−2^j+3^k+s(7^i+6^j+3^k) is:

Let a1,a2,............a10 be in AP and h1, h2..............h10 be in H.P. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is __

The number of values of k for which the linear equations4x+ky+2z=0kx+4y+z=02x+2y+z=0posses a non-zero solution is

The sum of the square of all real numbers satisfying the equation x 256 - 256 32 = 0 is

If the solution of differential equation x lnxdydx+y=2lnx is y(lnx)=(lnx)n+C then n= ___

If ∣∣∣∣∣x−12x−1x2+1−x2x−2−3x−2x24x−13x−3∣∣∣∣∣=n∑i=0aixi ∀ x∈R,n≤10, then which of the following is correct?

The number of permutations by using all the letters of the word MONDAY which neither begins with M nor ends with Y, is

How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

A straight line L through the point (3,–2) is inclined at an angle 60∘ to the line √3x+y=1 If L also intersects the x-axis, then the equation of L is

Explain the terms ‘Over-subscription’ and ‘Under-subscription’. How are they dealt with in accounting records?

Solve: cos2sin-1-x=0

Evaluate the following integrals:∫-π/4π/4sin x dx

Consider an object function Z(x1, x2)=3x1+9x2 and the constraintsx1+x2≤8x1+2x2≤4x1≥0, x2≥0The maximum value of the objective function is .18

Find the distance of the point (- 1, - 5,- 10) from the point of intersection of the line r=2^i−^j+2^k+λ(3^i+4^j+2^k) and the plane r.(^i−^j+^k)=5

2.X/100-X = \sqrt{}36.5/17

∫∞0e−axcos bxdx=

19π8. tan

e(cos2x+cos4x+cos6x+⋯∞)loge2 satisfies the equation t2–9t+8=0, then the value of 2sinxsinx+√3cosx,(0&lt;x&lt;π2) is :

If kπ10 is the least positive value of θ which satisfy the equation sin3θ+cos2θ=0, then k is

Examine that is a continuous function.

How many of these are correctly matched ? Coordinates of a point Name of the octant 1. (1,2,3) P.I 2. (4,−2,3) Q.IV 3. (4,−2,−5) R.VIII 4. (4,2,−5) S.V 5. (−4,2,−5) T.VI 6. (−4,2,5) U.II 7. (−3,−1,6) V.III 8. (2,−4,−7) W.VIII ___

cos230° cos245°+4sec260°+12cos290°-2tan260°=?(a) 818(b) 838(c) 738(d) 758

12, x-y+z=42x+y-3z = 0"x + y + z = 2

In a ∆ABC, if ∠C=π2, ∠A=π6, c = 20, then a = ____________.

If P (A|B) > P (A), then which of the following is correct: (A) P (B|A) < P (B) (B) P (A ∩ B) < P (A).P (B) (C) P (B|A) > P (B) (D) P (B|A) = P (B)

If the least and the largest real values of α, for which the equation z+α|z−1|+2i=0(z∈C and i=√−1) has a solution, are p and q respectively; then 4(p2+q2) is equal to

If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where A=l1m1n1l2m2n2l3m3n3.

For any set A, if U is the universal set, then A′=

If ax2+bx+6=0 does not have two distinct real roots,then the least value of 3a+b is?

e(cos2x+cos4x+cos6x+⋯∞)loge2 satisfies the equation t2–9t+8=0, then the value of 2sinxsinx+√3cosx,(0<x<π2) is :