43030 + Interview Questions in Mathematics

1.	A plane passing through (-1, 2, 3) and whose normal makes equal angles with the coordinate axes is
Answer» A plane passing through (-1, 2, 3) and whose normal makes equal angles with the coordinate axes is

Discussion

2.	All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
Answer» All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.

Discussion

3.	For any real number x, let [x] denote the largest integer less than or equal to x. If I=∫100[√10xx+1 ]dx, then the value of 9I is
Answer» For any real number $x$ , let $[x]$ denote the largest integer less than or equal to $x$ . If $I = \int_{0}^{10} [\sqrt{\frac{10 x}{x + 1}}] d x$ , then the value of $9 I$ is

Discussion

4.	The solution of differential equationdxdy+2xy=4y3, where y(0)=0 is
Answer» The solution of differential equation $\frac{d x}{d y} + 2 x y = 4 y^{3},$ where $y (0) = 0$ is

Discussion

5.	Tan theta = 4/3, theta lies in the third quadrant
Answer» Tan theta = 4/3, theta lies in the third quadrant

Discussion

6.	find the domain of function f(x)=1/sq.root of x^12-x^9+x^4-x+1
Answer» find the domain of function f(x)=1/sq.root of x^12-x^9+x^4-x+1

Discussion

7.	If sin(A + B) = 1 and cos(A - B) = 1 , 0 degrees < A + B = B , find A and B .
Answer» If sin(A + B) = 1 and cos(A - B) = 1 , 0 degrees < A + B <= 90 degrees , A>= B , find A and B .

Discussion

8.	If the area function ∫xaf(x)dx=x2−a2 then f(x) =
Answer» If the area function $\int_{a}^{x} f (x) d x = x^{2} - a^{2}$ then f(x) =

Discussion

9.	Write the sum of the series i+i2+i3+....upto 1000 terms.
Answer» Write the sum of the series $i + i^{2} + i^{3} + . . . .$ upto 1000 terms.

Discussion

10.	The number of solution(s) of the equation sinx=3x in [0,π2] is
Answer» The number of solution(s) of the equation $sin x = 3^{x}$ in $[0, \frac{π}{2}]$ is

Discussion

11.	A random variable X is uniformly distributed in the range [0, 5]. The variance and mean square value of X will be respectively equal to
Answer» A random variable X is uniformly distributed in the range [0, 5]. The variance and mean square value of X will be respectively equal to

Discussion

12.	If 'A' is an acute angle and tan A + cot A = 2 then find the value of tan^9 A + cot^7 A.
Answer» If 'A' is an acute angle and tan A + cot A = 2 then find the value of tan^9 A + cot^7 A.

Discussion

13.	If y = (1 – cosθ) and x = (θ + sinθ) find dy/dx at theta = pie/2
Answer» If y = (1 – cosθ) and x = (θ + sinθ) find dy/dx at theta = pie/2

Discussion

14.	if f(x)=4x^{2 }-4x+2, then the maximum value of 5-f(\vert x\vert+3) is
Answer» if f(x)=4x^{2 }-4x+2, then the maximum value of 5-f(\vert x\vert+3) is

Discussion

15.	The differential equation whose general solution is given by,y=(c1cos(x+c2))−(c3e(−x+c4))+(c5sin x) where c1,c2,c3,c4,c5 are arbitrary constants, is
Answer» The differential equation whose general solution is given by, $y = (c_{1} c o s (x + c_{2})) - (c_{3} e^{(- x + c_{4})}) + (c_{5} s i n x)$ where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants, is

Discussion

16.	∫cot−1 (ex)exdx is equal to
Answer» $\int \frac{{cot}^{- 1} (e^{x})}{e^{x}} d x$ is equal to

Discussion

17.	If the sum A+B of two vector A and B equals the diffn A-B
Answer» If the sum A+B of two vector A and B equals the diffn A-B

Discussion

18.	A tangent is drawn to the parabola y2=4x at a point P on the parabola in the first quadrant and another tangent is drawn to the vertex A of the parabola. Let both the tangent meet at a point B,if area of the triangle ABP=32 unit2, then equation of the tangent is
Answer» A tangent is drawn to the parabola $y^{2} = 4 x$ at a point $P$ on the parabola in the first quadrant and another tangent is drawn to the vertex $A$ of the parabola. Let both the tangent meet at a point $B$ ,if area of the triangle $A B P = 32 {unit}^{2}$ , then equation of the tangent is

Discussion

19.	If (x+2)√x2−2x−3≥0, then x can lie in
Answer» If $(x + 2) \sqrt{x^{2} - 2 x - 3} \geq 0,$ then $x$ can lie in

Discussion

20.	For x,y∈N, if 32x−y+1=3y−2x+1−8 and log6∣∣2x2y−xy2∣∣=1+log36(xy), then the absolute value of (x−y) is
Answer» For $x, y \in N,$ if $3^{2 x - y + 1} = 3^{y - 2 x + 1} - 8$ and ${log}_{6} ∣ ∣ 2 x^{2} y - x y^{2} ∣ ∣ = 1 + {log}_{36} (x y),$ then the absolute value of $(x - y)$ is

Discussion

21.	A mirror and a source of light are situated at the origin O and a point on OX(x-axis) respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1, – 1, 1, the DCs for the reflected ray are
Answer» A mirror and a source of light are situated at the origin O and a point on OX(x-axis) respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1, – 1, 1, the DCs for the reflected ray are

Discussion

22.	Consider ABCD is a trapezium such that AB,DC are parallel and BC is perpendicular to them. If ∠ADB=θ,BC=p and CD=q, then AB is equal to
Answer» Consider $A B C D$ is a trapezium such that $A B, D C$ are parallel and $B C$ is perpendicular to them. If $∠ A D B = θ, B C = p$ and $C D = q,$ then $A B$ is equal to

Discussion

23.	Prove that sin2π6+cos2π3−tan2π4=−12
Answer» Prove that ${sin}^{2} \frac{π}{6} + {cos}^{2} \frac{π}{3} - {tan}^{2} \frac{π}{4} = - \frac{1}{2}$

Discussion

24.	If Sn is the sum of all coefficients of (3x−y)n for n∈N, then the value of 5∑n=1Sn is
Answer» If $S_{n}$ is the sum of all coefficients of $(3 x - y)^{n}$ for $n \in N$ , then the value of $5 \sum n = 1 S_{n}$ is

Discussion

25.	While finding the roots of f(x)=x2−4=0 using Newton - Raphson method, initial value of (x, x1 = 1). If the value obtained after first iteration isx2.
Answer» While finding the roots of $f (x) = x^{2} - 4 = 0$ using Newton - Raphson method, initial value of (x, x₁ = 1). If the value obtained after first iteration is $x_{2}$ .

Discussion

26.	Mean of goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?
Answer» Mean of goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?

Discussion

27.	Find the differential equation representing the family of curves y=a ebx+5, where a and b are arbitrary constants.
Answer» Find the differential equation representing the family of curves $y = a e^{b x + 5}$ , where a and b are arbitrary constants.

Discussion

28.	24. A bag contains 5 white, 7 red, and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.
Answer» 24. A bag contains 5 white, 7 red, and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

Discussion

29.	The mean value of integral ( sin theta d theta) where the limit is pie to 0 is
Answer» The mean value of integral ( sin theta d theta) where the limit is pie to 0 is

Discussion

30.	Let z and w be two non- zero complex numbers such that \|z\|=\|w\| and arg(z)+arg(w)=π. Then the value of (z+¯¯¯¯w)10 is
Answer» Let $z$ and $w$ be two non- zero complex numbers such that $\| z \| = \| w \|$ and $arg (z) + arg (w) = π$ . Then the value of $(z + ¯ ¯¯ ¯ w)^{10}$ is

Discussion

31.	The equation of a circle which touches both axes and the line 3x - 4y + 8 =0 and whose centre lies in the third quadrant is
Answer» The equation of a circle which touches both axes and the line 3x - 4y + 8 =0 and whose centre lies in the third quadrant is

Discussion

32.	The maximum value of the function f(x)=2√x−2+√4−x is √K, then K is
Answer» The maximum value of the function $f (x) = 2 \sqrt{x - 2} + \sqrt{4 - x}$ is $\sqrt{K},$ then $K$ is

Discussion

33.	Which of the following condition is true for a monotonically increasing function f(x), which is differentiable in its domain?
Answer» Which of the following condition is true for a monotonically increasing function f(x), which is differentiable in its domain?

Discussion

34.	The width of a US letter is 5 × 10−1 mm. A pack of US letters have a width of 10m. How many US letters are there in the pack?20000
Answer» The width of a US letter is $5 \times 10^{-1}$ mm. A pack of US letters have a width of 10m. How many US letters are there in the pack? 20000

Discussion

35.	∫0π2sin x cos x1+sin4xdx=________________.
Answer» $\int_{0}^{\frac{π}{2}} \frac{\sin x \cos x}{1 + \sin^{4} x} d x =$ ________________.

Discussion

36.	Effect of annealing and hammering on elasticity? What is the meaning of annealing
Answer» Effect of annealing and hammering on elasticity? What is the meaning of annealing

Discussion

37.	The equation of the ellipse, whose length of the major axis is 20 and foci are (0,±5), is
Answer» The equation of the ellipse, whose length of the major axis is $20$ and foci are $(0, \pm 5),$ is

Discussion

38.	Sum of slopes of tangent and normal to the curve x2+y2+2x+2y=6 at (1,1) is
Answer» Sum of slopes of tangent and normal to the curve $x^{2} + y^{2} + 2 x + 2 y = 6$ at $(1, 1)$ is

Discussion

39.	If A is a square matrix then which of the following matrices will not be symmetric 1. A+A'2. AA'3. A'A4. A-A'
Answer» If A is a square matrix then which of the following matrices will not be symmetric 1. A+A' 2. AA' 3. A'A 4. A-A'

Discussion

40.	Prove that the diagonal elements of a skew symmetric matrix are all zero.
Answer» Prove that the diagonal elements of a skew symmetric matrix are all zero.

Discussion

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

Discussion

42.	The value of (7C0+7C1)+(7C1+7C2)+...+(7C6+7C7)
Answer» The value of $(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{1} +^{7} C_{2}) + . . . + (^{7} C_{6} +^{7} C_{7})$

Discussion

43.	A function of Boolean variables, X, Y and Z is expressed in terms of the min-terms asF(X,Y,Z)=∑(1,2,5,6,7)Which one of the product of sums given below is equal to the function F(X,Y,Z)?
Answer» A function of Boolean variables, X, Y and Z is expressed in terms of the min-terms as $F (X, Y, Z) = \sum (1, 2, 5, 6, 7)$ Which one of the product of sums given below is equal to the function $F (X, Y, Z) ?$

Discussion

44.	If α,β are the roots of 3x2−5x+19=0 then
Answer» If $α, β$ are the roots of $3 x^{2} - 5 x + 19 = 0$ then

Discussion

45.	Pair the multiplication equations which gives the same answers.
Answer» Pair the multiplication equations which gives the same answers.

Discussion

46.	A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation x+100x>50 satisfied, is
Answer» A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation $x + \frac{100}{x} > 50$ satisfied, is

Discussion

47.	Consider three boxes, each containing 10 balls labelled 1,2,⋯,10. Suppose one ball is randomly drawn from each of the boxes. Denoted 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. Denoted by $n_{i},$ the label of the ball drawn from the $i^{t h}$ 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

48.	∫(xxsinx+cosx)2dx is equal to (where C is a constant of integration)
Answer» $\int {(\frac{x}{x sin x + cos x})}^{2} d x$ is equal to (where $C$ is a constant of integration)

Discussion

49.	Prove that }\operatorname{tan}(θ+135^°)\operatorname{tan}(θ-315^°)=-1
Answer» Prove that }\operatorname{tan}(θ+135^°)\operatorname{tan}(θ-315^°)=-1

Discussion

50.	Transformez selon le modèle.p { margin-bottom: 0.25cm; line-height: 120%; }a:link { }(1) C'est le stylo de M. Martin?(2) C'est la maison de ton ami?(3) Ce sont les enfants de M. et Mme Vincent?(4) C'est la cousine de Pierre?(5) C'est le chien de vos voisins?
Answer» Transformez selon le modèle. (1) C'est le stylo de M. Martin? (2) C'est la maison de ton ami? (3) Ce sont les enfants de M. et Mme Vincent? (4) C'est la cousine de Pierre? (5) C'est le chien de vos voisins?

50.

Transformez selon le modèle.p { margin-bottom: 0.25cm; line-height: 120%; }a:link { }(1) C'est le stylo de M. Martin?(2) C'est la maison de ton ami?(3) Ce sont les enfants de M. et Mme Vincent?(4) C'est la cousine de Pierre?(5) C'est le chien de vos voisins?

Answer» Transformez selon le modèle.

(1) C'est le stylo de M. Martin?

(2) C'est la maison de ton ami?

(3) Ce sont les enfants de M. et Mme Vincent?

(4) C'est la cousine de Pierre?

(5) C'est le chien de vos voisins?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A plane passing through (-1, 2, 3) and whose normal makes equal angles with the coordinate axes is

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.

For any real number x, let [x] denote the largest integer less than or equal to x. If I=∫100[√10xx+1 ]dx, then the value of 9I is

The solution of differential equationdxdy+2xy=4y3, where y(0)=0 is

Tan theta = 4/3, theta lies in the third quadrant

find the domain of function f(x)=1/sq.root of x^12-x^9+x^4-x+1

If sin(A + B) = 1 and cos(A - B) = 1 , 0 degrees < A + B = B , find A and B .

If the area function ∫xaf(x)dx=x2−a2 then f(x) =

Write the sum of the series i+i2+i3+....upto 1000 terms.

The number of solution(s) of the equation sinx=3x in [0,π2] is

A random variable X is uniformly distributed in the range [0, 5]. The variance and mean square value of X will be respectively equal to

If 'A' is an acute angle and tan A + cot A = 2 then find the value of tan^9 A + cot^7 A.

If y = (1 – cosθ) and x = (θ + sinθ) find dy/dx at theta = pie/2

if f(x)=4x^{2 }-4x+2, then the maximum value of 5-f(\vert x\vert+3) is

The differential equation whose general solution is given by,y=(c1cos(x+c2))−(c3e(−x+c4))+(c5sin x) where c1,c2,c3,c4,c5 are arbitrary constants, is

∫cot−1 (ex)exdx is equal to

If the sum A+B of two vector A and B equals the diffn A-B

A tangent is drawn to the parabola y2=4x at a point P on the parabola in the first quadrant and another tangent is drawn to the vertex A of the parabola. Let both the tangent meet at a point B,if area of the triangle ABP=32 unit2, then equation of the tangent is

If (x+2)√x2−2x−3≥0, then x can lie in

For x,y∈N, if 32x−y+1=3y−2x+1−8 and log6∣∣2x2y−xy2∣∣=1+log36(xy), then the absolute value of (x−y) is

A mirror and a source of light are situated at the origin O and a point on OX(x-axis) respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1, – 1, 1, the DCs for the reflected ray are

Consider ABCD is a trapezium such that AB,DC are parallel and BC is perpendicular to them. If ∠ADB=θ,BC=p and CD=q, then AB is equal to

Prove that sin2π6+cos2π3−tan2π4=−12

If Sn is the sum of all coefficients of (3x−y)n for n∈N, then the value of 5∑n=1Sn is

While finding the roots of f(x)=x2−4=0 using Newton - Raphson method, initial value of (x, x1 = 1). If the value obtained after first iteration isx2.

Mean of goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?

Find the differential equation representing the family of curves y=a ebx+5, where a and b are arbitrary constants.

24. A bag contains 5 white, 7 red, and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

The mean value of integral ( sin theta d theta) where the limit is pie to 0 is

Let z and w be two non- zero complex numbers such that |z|=|w| and arg(z)+arg(w)=π. Then the value of (z+¯¯¯¯w)10 is

The equation of a circle which touches both axes and the line 3x - 4y + 8 =0 and whose centre lies in the third quadrant is

The maximum value of the function f(x)=2√x−2+√4−x is √K, then K is

Which of the following condition is true for a monotonically increasing function f(x), which is differentiable in its domain?

The width of a US letter is 5 × 10−1 mm. A pack of US letters have a width of 10m. How many US letters are there in the pack?20000

∫0π2sin x cos x1+sin4xdx=________________.

Effect of annealing and hammering on elasticity? What is the meaning of annealing

The equation of the ellipse, whose length of the major axis is 20 and foci are (0,±5), is

Sum of slopes of tangent and normal to the curve x2+y2+2x+2y=6 at (1,1) is

If A is a square matrix then which of the following matrices will not be symmetric 1. A+A'2. AA'3. A'A4. A-A'

Prove that the diagonal elements of a skew symmetric matrix are all zero.

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

The value of (7C0+7C1)+(7C1+7C2)+...+(7C6+7C7)

A function of Boolean variables, X, Y and Z is expressed in terms of the min-terms asF(X,Y,Z)=∑(1,2,5,6,7)Which one of the product of sums given below is equal to the function F(X,Y,Z)?

If α,β are the roots of 3x2−5x+19=0 then

Pair the multiplication equations which gives the same answers.

A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation x+100x&gt;50 satisfied, is

Consider three boxes, each containing 10 balls labelled 1,2,⋯,10. Suppose one ball is randomly drawn from each of the boxes. Denoted 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 :

∫(xxsinx+cosx)2dx is equal to (where C is a constant of integration)

Prove that }\operatorname{tan}(θ+135^°)\operatorname{tan}(θ-315^°)=-1

Transformez selon le modèle.p { margin-bottom: 0.25cm; line-height: 120%; }a:link { }(1) C'est le stylo de M. Martin?(2) C'est la maison de ton ami?(3) Ce sont les enfants de M. et Mme Vincent?(4) C'est la cousine de Pierre?(5) C'est le chien de vos voisins?

A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation x+100x>50 satisfied, is

Consider three boxes, each containing 10 balls labelled 1,2,⋯,10. Suppose one ball is randomly drawn from each of the boxes. Denoted 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 :