43030 + Interview Questions in Mathematics

1.	Evaluate the product (3a - 5b).(2a + 7b)
Answer» Evaluate the product (3a - 5b).(2a + 7b)

Discussion

2.	Let a>0 be a real number. Then the limit limx→2ax+a3−x−(a2+a)a3−x−ax2 is
Answer» Let $a > 0$ be a real number. Then the limit $lim x \to 2 \frac{a^{x} + a^{3 - x} - (a^{2} + a)}{a^{3 - x} - a^{\frac{x}{2}}}$ is

Discussion

3.	James earn $82 weekly and gets $4.5 extra for every extra hour of baby sitting.The correct equation is .where,Total earnings : wTime(hour) : t
Answer» James earn $$ 82$ weekly and gets $$ 4.5$ extra for every extra hour of baby sitting.The correct equation is . where, Total earnings : w Time(hour) : t

Discussion

4.	Divide x2+5x+6 by x+3 by division method and find the quotient.
Answer» $Divide x^{2} + 5 x + 6 by x + 3 by division method and find the quotient.$

Discussion

5.	Let A,B,C be three square matrices of order 3 such that A2+2I=O, det(2C−A2)=32 and A5−2A3C+BA2−2BC=O. Then the absolute value of (det(B−A))2 is
Answer» Let $A, B, C$ be three square matrices of order $3$ such that $A^{2} + 2 I = O,$ $det (2 C - A^{2}) = 32$ and $A^{5} - 2 A^{3} C + B A^{2} - 2 B C = O .$ Then the absolute value of $(det (B - A))^{2}$ is

Discussion

6.	Mark the correct alternative in the following question:If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is(a) 10C7 (b) 10C7 × 7! (c) 710 (d)107
Answer» Mark the correct alternative in the following question: If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is (a) ¹⁰C₇ (b) ¹⁰C₇ $\times$ 7! (c) 7¹⁰ (d)10⁷

Discussion

7.

Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let X1,X2,X3,X4,X5 and X6 be the place holders for the non-terminals D, T, L or L1 in the following table: Production ruleSemantic actionD→TLX1.type=X2.typeT→intT.type = intT→FloatT.type = floatL→L1.idX3.type=X4.type add Type (id.entry, X5. type)L→idadd Type (id. entry, X6. type)Which one of the following are the appropriate choices for X1,X2,X3 and X4?

Answer»

Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let $X_{1}, X_{2}, X_{3}, X_{4}, X_{5} and X_{6}$ be the place holders for the non-terminals D, T, L or $L_{1}$ in the following table:

Production rule	Semantic action
$D \to T L$	$X_{1} . t y p e = X_{2} . t y p e$
$T \to i n t$	T.type = int
$T \to F l o a t$	T.type = float
$L \to L_{1} . i d$	$X_{3} . t y p e = X_{4} . t y p e add Type (id.entry, X_{5} . t y p e)$
$L \to i d$	add Type (id. entry, $X_{6}$ . type)

Which one of the following are the appropriate choices for

X_{1}, X_{2}, X_{3} and X_{4} ?

Discussion

8.	If α,β are the roots of x2−p(x+1)−c=0, then the value of α2+2α+1α2+2α+c+β2+2β+1β2+2β+c is
Answer» If $α, β$ are the roots of $x^{2} - p (x + 1) - c = 0$ , then the value of $\frac{α^{2} + 2 α + 1}{α^{2} + 2 α + c} + \frac{β^{2} + 2 β + 1}{β^{2} + 2 β + c}$ is

Discussion

9.	For any two sets A & B;n(A)=4,n(B)=7,n(AΔB)=3, then, n(A∩B)=
Answer» For any two sets $A & B; n (A) = 4, n (B) = 7, n (A Δ B) = 3$ , then, $n (A \cap B) =$

Discussion

10.	If E and F are two independent events such that P(¯E∪F)=215 and P(E∪¯F)=16 then P(F) is
Answer» If E and F are two independent events such that $P (¯ E \cup F) = \frac{2}{15}$ and $P (E \cup ¯ F) = \frac{1}{6}$ then P(F) is

Discussion

11.	19. Given is E^° Fe+2/Fe=0.44V E^° Fe+3/Fe+2=0.77V if Fe+2 &Fe+3 put with the solid Fe so 1)Fe+3is increasing 2)Fe+3 is decreasing 3)Fe+2&Fe+3 are not change 4)Fe+2 is decreasing
Answer» 19. Given is E^° Fe+2/Fe=0.44V E^° Fe+3/Fe+2=0.77V if Fe+2 &Fe+3 put with the solid Fe so 1)Fe+3is increasing 2)Fe+3 is decreasing 3)Fe+2&Fe+3 are not change 4)Fe+2 is decreasing

Discussion

12.	How many two-digit numbers are divisible by 3?
Answer» How many two-digit numbers are divisible by 3?

Discussion

13.	Real part of eeiθ is
Answer» Real part of $e^{e^{i θ}}$ is

Discussion

14.	If f(x)=sinx⋅sin2x⋅sin3x, then which of the following is/are true
Answer» If $f (x) = sin x \cdot sin 2 x \cdot sin 3 x$ , then which of the following is/are true

Discussion

15.	If y=1√x, then dydx=?
Answer» If $y = \frac{1}{\sqrt{x}}, t h e n \frac{d y}{d x}$ =?

Discussion

16.	What is the inverse of the matrix [−325−1]
Answer» What is the inverse of the matrix $[\begin{matrix} - 3 & 2 5 & - 1 \end{matrix}]$

Discussion

17.	The shortest distance between the parabola y2=4x and the circle x2+y2+6x−12y+20=0 is
Answer» The shortest distance between the parabola $y^{2} = 4 x$ and the circle $x^{2} + y^{2} + 6 x - 12 y + 20 = 0$ is

Discussion

18.	Sin(-420^°)cos(390^°)+cos(-660^°)sin(330^°)
Answer» Sin(-420^°)cos(390^°)+cos(-660^°)sin(330^°)

Discussion

19.	If →a,→b,→c are three unit vectors, then \|→a−→b\|2+\|→b−→c\|2+\|→c−→a\|2 does not exceed
Answer» If $\to a, \to b, \to c$ are three unit vectors, then $\| \to a - \to b \|^{2} + \| \to b - \to c \|^{2} + \| \to c - \to a \|^{2}$ does not exceed

Discussion

20.	If 4x+22x−1=3x+12+3x−12, then x=
Answer» If $4^{x} + 2^{2 x - 1} = 3^{x + \frac{1}{2}} + 3^{x - \frac{1}{2}}$ , then $x =$

Discussion

21.	If A={x,x∈Z and \|x2+5x−6\|=6−5x−x2}, then cardinality of set A is
Answer» If $A = {x, x \in Z and \| x^{2} + 5 x - 6 \| = 6 - 5 x - x^{2}}$ , then cardinality of set $A$ is

Discussion

22.	In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Answer» In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

Discussion

23.	Find the integral: ∫(ax2+bx+c)dx
Answer» Find the integral: $\int (a x^{2} + b x + c) d x$

Discussion

24.	There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that: • The fastest computer gets the toughest job and the slowest computer gets the easiest job. • Every computer gets at least one job. The number of ways in which this can be done is 65
Answer» There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that: • The fastest computer gets the toughest job and the slowest computer gets the easiest job. • Every computer gets at least one job. The number of ways in which this can be done is 65

Discussion

25.	While watching a game of champions league football in a cafe, Andrew observe someone who is clearly supporting Manchester United in the game. The probability that they were actually born within 25 miles of Manchester. Assume that:⋅ The probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is 120.⋅ The chance that a person born within 25 miles of manchester actually supports united is 710.⋅ The probability that a person not born within 25 miles of Manchester supports United with probability 110.
Answer» While watching a game of champions league football in a cafe, $Andrew$ observe someone who is clearly supporting Manchester United in the game. The probability that they were actually born within $25$ miles of Manchester. Assume that: $\cdot$ The probability that a randomly selected person in a typical local bar environment is born within $25$ miles of Manchester is $\frac{1}{20} .$ $\cdot$ The chance that a person born within $25$ miles of manchester actually supports united is $\frac{7}{10} .$ $\cdot$ The probability that a person not born within $25$ miles of Manchester supports United with probability $\frac{1}{10} .$

Discussion

26.	If I is a unit matrix, then 3I will be
Answer» If I is a unit matrix, then 3I will be

Discussion

27.	The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is (A) 1 (B) 2 (C) 5 (D)
Answer» The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is (A) 1 (B) 2 (C) 5 (D)

Discussion

28.	(a+b+c+d+e)³=?
Answer» (a+b+c+d+e)³=?

Discussion

29.	54. If f(x) be defined on [-2,2 ] and is given by f(x)={-1 ,-2≤x≤0 and x-1 when 0
Answer» 54. If f(x) be defined on [-2,2 ] and is given by f(x)={-1 ,-2≤x≤0 and x-1 when 0

Discussion

30.	if tan^2 theta=sin^2 pi/2 then theta =
Answer» if tan^2 theta=sin^2 pi/2 then theta =

Discussion

31.	For the function f(x) = logex, x ∈ [1, 2], the value of c for the lagrange's mean value theorem is _______________.
Answer» For the function f(x) = log_ex, x ∈ [1, 2], the value of c for the lagrange's mean value theorem is _______________.

Discussion

32.	The interval in which θ belongs, such that the inequality 2sin2(θ−π3)−sin(θ−π3)−1≤0 is satisfied and θ∈[−π,π] is
Answer» The interval in which $θ$ belongs, such that the inequality $2 {sin}^{2} (θ - \frac{π}{3}) - sin (θ - \frac{π}{3}) - 1 \leq 0$ is satisfied and $θ \in [- π, π]$ is

Discussion

33.	The solution of the differential equation d2ydx2−dydx−2y=3e2x, where, y(0)=0 and y(0)=−2
Answer» The solution of the differential equation $\frac{d^{2} y}{d x^{2}} - \frac{d y}{d x} - 2 y = 3 e^{2 x}$ , where, $y (0) = 0$ and $y (0) = - 2$

Discussion

34.	The degree of the differential equation [1+(dydx)3]7/3=7(d2ydx2) is
Answer» The degree of the differential equation ${[1 + {(\frac{d y}{d x})}^{3}]}^{7 / 3} = 7 (\frac{d^{2} y}{d x^{2}})$ is

Discussion

35.	The inverse of the proposition (p ∧∼q)→r is
Answer» The inverse of the proposition $(p \land \sim q) \to r$ is

Discussion

36.	Check whether the following are quadratic equations:(x−2)(x+1)=(x−1)(x+3)
Answer» Check whether the following are quadratic equations: $(x - 2) (x + 1) = (x - 1) (x + 3)$

Discussion

37.	The value of the integral ∫12ex1x-1x2dx is _______________.
Answer» The value of the integral $\int_{1}^{2} e^{x} (\frac{1}{x} - \frac{1}{x^{2}}) d x$ is _______________.

Discussion

38.	Find the length of the perpendicular from the point (4, -7) to the line joining the origin and the point of intersection of the lines 2x−3y+14=0 and 5x+4y−7=0
Answer» Find the length of the perpendicular from the point (4, -7) to the line joining the origin and the point of intersection of the lines $2 x - 3 y + 14 = 0$ and $5 x + 4 y - 7 = 0$

Discussion

39.	If Δ=∣∣∣∣xax+ayby+bzcz+c∣∣∣∣, then which of the following is not correct?
Answer» If $Δ = ∣ ∣∣ ∣ \begin{matrix} x & a & x + a y & b & y + b z & c & z + c \end{matrix} ∣ ∣∣ ∣,$ then which of the following is not correct?

Discussion

40.	If logx(log4(logx(5x2+4x3)))=0, then the value of x is
Answer» If ${log}_{x} ({log}_{4} ({log}_{x} (5 x^{2} + 4 x^{3}))) = 0$ , then the value of $x$ is

Discussion

41.	Let a matrix A=[2sin2x2cos2x1] is such that Adj(A)=[1−202] for x∈[0,10π]. Then the number of values of x is
Answer» Let a matrix $A = [\begin{matrix} 2 {sin}^{2} x & 2 {cos}^{2} x & 1 \end{matrix}]$ is such that $Adj (A) = [\begin{matrix} 1 & - 2 0 & 2 \end{matrix}]$ for $x \in [0, 10 π] .$ Then the number of values of $x$ is

Discussion

42.	I. (x2 +xy) dy(x2 + y2) dr
Answer» I. (x2 +xy) dy(x2 + y2) dr

Discussion

43.	The number of ways in which 100 people can be divided in 50 pairs is
Answer» The number of ways in which $100$ people can be divided in $50$ pairs is

Discussion

44.	There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a testMarksFrequency0x−21x2x23(x+1)242x5x+1Where x is positive integer. Then the variance of the marks is
Answer» There are $60$ students in a class. The following is the frequency distribution of the marks obtained by the students in a test $\begin{matrix} Marks & Frequency 0 & x - 2 1 & x 2 & x^{2} 3 & (x + 1)^{2} 4 & 2 x 5 & x + 1 \end{matrix}$ Where $x$ is positive integer. Then the variance of the marks is

Discussion

45.	Find the number of solutions (x,y,z) to the system of equations X+2y+4z=9,4yz+2xz+xy=13, xyz=13, such that at least two of X,y,z are integers.
Answer» Find the number of solutions (x,y,z) to the system of equations X+2y+4z=9,4yz+2xz+xy=13, xyz=13, such that at least two of X,y,z are integers.

Discussion

46.	If sgn(y) denotes the signum function of y, then the number of solution(s) of the equation \|\|x+2\|−3\|=sgn(1−∣∣∣∣(x−2)(x2+10x+24)(x2+1)(x+4)(x2+4x−12)∣∣∣∣) is
Answer» If $sgn (y)$ denotes the signum function of $y,$ then the number of solution(s) of the equation $\| \| x + 2 \| - 3 \| = sgn (1 - ∣ ∣∣ ∣ \frac{(x - 2) (x^{2} + 10 x + 24)}{(x^{2} + 1) (x + 4) (x^{2} + 4 x - 12)} ∣ ∣∣ ∣)$ is

Discussion

47.	∫(2-3x)/(\sqrt{1+3x })dx
Answer» ∫(2-3x)/(\sqrt{1+3x })dx

Discussion

48.	Prove that: sin8xcosx - sin6xcos3x / cos2xcosx - sin3xsin4x = tan2x
Answer» Prove that: sin8xcosx - sin6xcos3x / cos2xcosx - sin3xsin4x = tan2x

Discussion

49.	I want all the derivations of this chapter
Answer» I want all the derivations of this chapter

Discussion

50.	For the following equation form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. y=ae3x+be−2x.
Answer» For the following equation form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y = a e^{3 x} + b e^{- 2 x} .$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate the product (3a - 5b).(2a + 7b)

Let a&gt;0 be a real number. Then the limit limx→2ax+a3−x−(a2+a)a3−x−ax2 is

James earn $82 weekly and gets $4.5 extra for every extra hour of baby sitting.The correct equation is .where,Total earnings : wTime(hour) : t

Divide x2+5x+6 by x+3 by division method and find the quotient.

Let A,B,C be three square matrices of order 3 such that A2+2I=O, det(2C−A2)=32 and A5−2A3C+BA2−2BC=O. Then the absolute value of (det(B−A))2 is

Mark the correct alternative in the following question:If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is(a) 10C7 (b) 10C7 × 7! (c) 710 (d)107

If α,β are the roots of x2−p(x+1)−c=0, then the value of α2+2α+1α2+2α+c+β2+2β+1β2+2β+c is

For any two sets A &amp; B;n(A)=4,n(B)=7,n(AΔB)=3, then, n(A∩B)=

If E and F are two independent events such that P(¯E∪F)=215 and P(E∪¯F)=16 then P(F) is

19. Given is E^° Fe+2/Fe=0.44V E^° Fe+3/Fe+2=0.77V if Fe+2 &Fe+3 put with the solid Fe so 1)Fe+3is increasing 2)Fe+3 is decreasing 3)Fe+2&Fe+3 are not change 4)Fe+2 is decreasing

How many two-digit numbers are divisible by 3?

Real part of eeiθ is

If f(x)=sinx⋅sin2x⋅sin3x, then which of the following is/are true

If y=1√x, then dydx=?

What is the inverse of the matrix [−325−1]

The shortest distance between the parabola y2=4x and the circle x2+y2+6x−12y+20=0 is

Sin(-420^°)cos(390^°)+cos(-660^°)sin(330^°)

If →a,→b,→c are three unit vectors, then |→a−→b|2+|→b−→c|2+|→c−→a|2 does not exceed

If 4x+22x−1=3x+12+3x−12, then x=

If A={x,x∈Z and |x2+5x−6|=6−5x−x2}, then cardinality of set A is

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

Find the integral: ∫(ax2+bx+c)dx

If I is a unit matrix, then 3I will be

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is (A) 1 (B) 2 (C) 5 (D)

(a+b+c+d+e)³=?

54. If f(x) be defined on [-2,2 ] and is given by f(x)={-1 ,-2≤x≤0 and x-1 when 0

if tan^2 theta=sin^2 pi/2 then theta =

For the function f(x) = logex, x ∈ [1, 2], the value of c for the lagrange's mean value theorem is _______________.

The interval in which θ belongs, such that the inequality 2sin2(θ−π3)−sin(θ−π3)−1≤0 is satisfied and θ∈[−π,π] is

The solution of the differential equation d2ydx2−dydx−2y=3e2x, where, y(0)=0 and y(0)=−2

The degree of the differential equation [1+(dydx)3]7/3=7(d2ydx2) is

The inverse of the proposition (p ∧∼q)→r is

Check whether the following are quadratic equations:(x−2)(x+1)=(x−1)(x+3)

The value of the integral ∫12ex1x-1x2dx is _______________.

Find the length of the perpendicular from the point (4, -7) to the line joining the origin and the point of intersection of the lines 2x−3y+14=0 and 5x+4y−7=0

If Δ=∣∣∣∣xax+ayby+bzcz+c∣∣∣∣, then which of the following is not correct?

If logx(log4(logx(5x2+4x3)))=0, then the value of x is

Let a matrix A=[2sin2x2cos2x1] is such that Adj(A)=[1−202] for x∈[0,10π]. Then the number of values of x is

I. (x2 +xy) dy(x2 + y2) dr

The number of ways in which 100 people can be divided in 50 pairs is

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a testMarksFrequency0x−21x2x23(x+1)242x5x+1Where x is positive integer. Then the variance of the marks is

Find the number of solutions (x,y,z) to the system of equations X+2y+4z=9,4yz+2xz+xy=13, xyz=13, such that at least two of X,y,z are integers.

If sgn(y) denotes the signum function of y, then the number of solution(s) of the equation ||x+2|−3|=sgn(1−∣∣∣∣(x−2)(x2+10x+24)(x2+1)(x+4)(x2+4x−12)∣∣∣∣) is

∫(2-3x)/(\sqrt{1+3x })dx

Prove that: sin8xcosx - sin6xcos3x / cos2xcosx - sin3xsin4x = tan2x

I want all the derivations of this chapter

For the following equation form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.​ y=ae3x+be−2x.

Let a>0 be a real number. Then the limit limx→2ax+a3−x−(a2+a)a3−x−ax2 is

For any two sets A & B;n(A)=4,n(B)=7,n(AΔB)=3, then, n(A∩B)=

For the following equation form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. y=ae3x+be−2x.