43030 + Interview Questions in Mathematics

1.	For two 3×3 matrices A and B, let A+B=2B′ and 3A+2B=I3, where B′ is the transpose of B and I3 is 3×3 identity matrix, then
Answer» For two $3 \times 3$ matrices $A$ and $B$ , let $A + B = 2 B^{'}$ and $3 A + 2 B = I_{3}$ , where $B^{'}$ is the transpose of $B$ and $I_{3}$ is $3 \times 3$ identity matrix, then

Discussion

2.	the position of a particle moving in a straight line along x axis varies with time t as x =12t-3t^2m, where t is in seconds .the distance covered by particle in irst 5 seconds is
Answer» the position of a particle moving in a straight line along x axis varies with time t as x =12t-3t^2m, where t is in seconds .the distance covered by particle in irst 5 seconds is

Discussion

3.	Consider a triangle Δ whose two sides lie on the x−axis and the line x+y+1=0. If the orthocenter of Δ is (1,1), then the equation of the circle passing through the vertices of the triangle Δ is
Answer» Consider a triangle $Δ$ whose two sides lie on the $x -$ axis and the line $x + y + 1 = 0.$ If the orthocenter of $Δ$ is $(1, 1),$ then the equation of the circle passing through the vertices of the triangle $Δ$ is

Discussion

4.	If α,β,γ are the roots of equation x3−6x2+11x−6=0, then find the equation whose roots are α2+β2,β2+γ2,γ2+α2 is
Answer» If $α, β, γ$ are the roots of equation $x^{3} - 6 x^{2} + 11 x - 6 = 0$ , then find the equation whose roots are $α^{2} + β^{2}, β^{2} + γ^{2}, γ^{2} + α^{2}$ is

Discussion

5.	49.Solve for x: yAl +xH^+=yAl^{3+} + zH_2
Answer» 49.Solve for x: yAl +xH^+=yAl^{3+} + zH_2

Discussion

6.	A school awarded 42 medals in hockey , 18 in basketball and 23 in cricket. if these medals are bagged by a total of 65 students and only 4 students got medals in all the three sports; find 1) How many students received medals in exactly two of the three sports? 2) How many students received medals in exactly one of the three sports?
Answer» A school awarded 42 medals in hockey , 18 in basketball and 23 in cricket. if these medals are bagged by a total of 65 students and only 4 students got medals in all the three sports; find 1) How many students received medals in exactly two of the three sports? 2) How many students received medals in exactly one of the three sports?

6.

A school awarded 42 medals in hockey , 18 in basketball and 23 in cricket. if these medals are bagged by a total of 65 students and only 4 students got medals in all the three sports; find 1) How many students received medals in exactly two of the three sports? 2) How many students received medals in exactly one of the three sports?

Answer»

A school awarded 42 medals in hockey , 18 in basketball and 23 in cricket. if these medals are bagged by a total of 65 students and only 4 students got medals in all the three sports; find

1) How many students received medals in exactly two of the three sports?

2) How many students received medals in exactly one of the three sports?

Discussion

7.	There are three distinct positive integers whose sum is equal to the product of the largest two of them. Find the product of these three integers.
Answer» There are three distinct positive integers whose sum is equal to the product of the largest two of them. Find the product of these three integers.

Discussion

8.	Let f:R→R given by f(x)=(3−x3)1/3. Then fof(x) is
Answer» Let $f : R \to R$ given by $f (x) = {(3 - x^{3})}^{1 / 3}$ . Then $f o f (x)$ is

Discussion

9.	If system of equations ax + y + z = a, x + by + z = b and x + y + cz = c is inconsistent, then which of the following is correct?
Answer» If system of equations ax + y + z = a, x + by + z = b and x + y + cz = c is inconsistent, then which of the following is correct?

Discussion

10.	The value of 108 sinπ9-144 sin3π9 is ____________.
Answer» The value of 108 $\sin \frac{π}{9} - 144 \sin^{3} \frac{π}{9}$ is ____________.

Discussion

11.	The arithmetic mean of a and b is an+bnan−1+bn−1. The value of n is
Answer» The arithmetic mean of a and b is $\frac{a^{n} + b^{n}}{a^{n - 1} + b^{n - 1}}$ . The value of n is

Discussion

12.	34. In Triangle ABC, ANGLE BISECTS ANGLE A AND ANGLE C >ANGLE B. PROVE THAT ANGLE ADB>ANGLE ADC
Answer» 34. In Triangle ABC, ANGLE BISECTS ANGLE A AND ANGLE C >ANGLE B. PROVE THAT ANGLE ADB>ANGLE ADC

Discussion

13.	If ∫xexcosx dx=aex(b(1−x)sinx+cxcosx)+d, (where d is constant of integration), then
Answer» If $\int x e^{x} cos x d x = a e^{x} (b (1 - x) sin x + c x cos x) + d,$ (where $d$ is constant of integration), then

Discussion

14.	what are coordination number
Answer» what are coordination number

Discussion

15.	There are 12 points (A1,A2,...,A12) in a plane, where (A1,A2,A3,A4) are collinear to each other and (A5,A6,A7,A8) are collinear to each other. If no points other than these two set of points are collinear, then the total number of straight lines that can be formed using these 12 points is
Answer» There are $12$ points $(A_{1}, A_{2}, . . ., A_{12})$ in a plane, where $(A_{1}, A_{2}, A_{3}, A_{4})$ are collinear to each other and $(A_{5}, A_{6}, A_{7}, A_{8})$ are collinear to each other. If no points other than these two set of points are collinear, then the total number of straight lines that can be formed using these $12$ points is

Discussion

16.	The number of words not starting and ending with vowels formed using all the letters of the word 'UNIVERSITY' such that all the vowels are in alphabetical order is
Answer» The number of words not starting and ending with vowels formed using all the letters of the word 'UNIVERSITY' such that all the vowels are in alphabetical order is

Discussion

17.	A flood having a return period of 50 years . The risk that this flood may occur in next 20 years will be ___________0.33
Answer» A flood having a return period of 50 years . The risk that this flood may occur in next 20 years will be ___________ 0.33

Discussion

18.	1x dx
Answer» 1x dx

Discussion

19.	Inverse of x+1/x+2
Answer» Inverse of x+1/x+2

Discussion

20.	A perpendicular is drawn from the point A(1,8,4) to the line joining the points B(0,−1,3) and C(2,−3,−1). The co-ordinates of the foot of the perpendicular is:
Answer» A perpendicular is drawn from the point $A (1, 8, 4)$ to the line joining the points $B (0, - 1, 3)$ and $C (2, - 3, - 1)$ . The co-ordinates of the foot of the perpendicular is:

Discussion

21.	Which of the following is/are true, if z, z1, z2 are complex numbers?
Answer» Which of the following is/are true, if z, z₁, z₂ are complex numbers?

Discussion

22.	Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:Omar helps his mother 1 hour more than his sister does.
Answer» Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement: Omar helps his mother 1 hour more than his sister does.

22.

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:Omar helps his mother 1 hour more than his sister does.

Answer»

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

Omar helps his mother 1 hour more than his sister does.

Discussion

23.	If n≠3k and 1,ω,ω2 are the cube roots of unity, then Δ=∣∣∣∣∣1ωnω2nω2n1ωnωnω2n1∣∣∣∣∣ has the value
Answer» If $n \neq 3 k$ and $1, ω, ω^{2}$ are the cube roots of unity, then $Δ = ∣ ∣∣∣ ∣ \begin{matrix} 1 & ω^{n} & ω^{2 n} ω^{2 n} & 1 & ω^{n} ω^{n} & ω^{2 n} & 1 \end{matrix} ∣ ∣∣∣ ∣$ has the value

Discussion

24.	Prove that sin2x+2sin4x+sin6x=4cos2xsin4x
Answer» Prove that $sin 2 x + 2 sin 4 x + sin 6 x = 4 {cos}^{2} x sin 4 x$

Discussion

25.	How many 6-letter words can be formed from the letters of the word WEDNESDAY such that vowel A is always included in each arrangement?Also, find out the combinations of such words.
Answer» How many 6-letter words can be formed from the letters of the word WEDNESDAY such that vowel A is always included in each arrangement?Also, find out the combinations of such words.

Discussion

26.	A basket has 5 yellow and 12 black balls. Find probability that second ball drawn is black in the first ball is yellow.
Answer» A basket has 5 yellow and 12 black balls. Find probability that second ball drawn is black in the first ball is yellow.

Discussion

27.	The value of π/2∫0dx1+tan4x is
Answer» The value of $π / 2 \int 0 \frac{d x}{1 + {tan}^{4} x}$ is

Discussion

28.	Prove that x2n−1+y2n−1 is divisible by x+y for all n∈N.
Answer» Prove that $x^{2 n - 1} + y^{2 n - 1}$ is divisible by $x + y$ for all $n \in N$ .

Discussion

29.	Question 11 (iv)State whether the following are true or false. Justify your answer. (iv) cot A is the product of cot and A.
Answer» Question 11 (iv) State whether the following are true or false. Justify your answer. (iv) cot A is the product of cot and A.

Discussion

30.	Evaluate ∫1−cot2x1+cot2xdx(where C is constant of integration)
Answer» Evaluate $\int \frac{1 - {cot}^{2} x}{1 + {cot}^{2} x} d x$ (where $C$ is constant of integration)

Discussion

31.	limn→∞1⋅n2+2(n−1)2+3(n−2)2 +⋯+ n⋅1213+23 +⋯+ n3 is equal to
Answer» $lim n \to \infty \frac{1 \cdot n^{2} + 2 {(n - 1)}^{2} + 3 {(n - 2)}^{2} + \dots + n \cdot 1^{2}}{1^{3} + 2^{3} + \dots + n^{3}}$ is equal to

Discussion

32.	If area of a triangle whose vertices in argand plane are z, iz, z+iz is 16 square units, find \|z\|
Answer» If area of a triangle whose vertices in argand plane are z, iz, z+iz is 16 square units, find \|z\|

Discussion

33.	If the system of linear equations 2x+py+6z=8 x+2y+qz=5 x+y+3z=4 has infinitely many solutions, then a possible pair of p and q is
Answer» If the system of linear equations $2 x + p y + 6 z = 8$ $x + 2 y + q z = 5$ $x + y + 3 z = 4$ has infinitely many solutions, then a possible pair of $p$ and $q$ is

Discussion

34.	Slope of the normal at (1,1) to the curve x3+3xy+y3=5 is
Answer» Slope of the normal at $(1, 1)$ to the curve $x^{3} + 3 x y + y^{3} = 5$ is

Discussion

35.	The number of points having position vector a^i+b^j+c^k where a,b,c∈{1,2,3,4,5} such that 2a+3b+5c is divisible by 4, is
Answer» The number of points having position vector $a^i + b^j + c^k$ where $a, b, c \in {1, 2, 3, 4, 5}$ such that $2^{a} + 3^{b} + 5^{c}$ is divisible by $4,$ is

Discussion

36.	If the equations x2+2x+3=0 and ax2+bx+c=0,a,b,c∈R, have a common root, then a:b:c is
Answer» If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R$ , have a common root, then $a : b : c$ is

Discussion

37.	Represent to solution set of each of the following in equations graphically in two dimensional plane : −3x+2y≤6
Answer» Represent to solution set of each of the following in equations graphically in two dimensional plane : $- 3 x + 2 y \leq 6$

37.

Represent to solution set of each of the following in equations graphically in two dimensional plane : −3x+2y≤6

Answer»

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$- 3 x + 2 y \leq 6$

Discussion

38.	f(x)=1+[cos x]x,in 0<x⩽π2
Answer» $f (x) = 1 + [c o s x] x, i n 0 < x ⩽ \frac{π}{2}$

Discussion

39.	The sum of 10 terms of the series 2⋅5+5⋅8+8⋅11+… is
Answer» The sum of $10$ terms of the series $2 \cdot 5 + 5 \cdot 8 + 8 \cdot 11 + \dots$ is

Discussion

40.	In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. The probability that a student chosen randomly studies in class XII, given that the chosen student is a girl, is given by a) 43/100 b) 1/43 c) 1/10 d) 10/43
Answer» In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. The probability that a student chosen randomly studies in class XII, given that the chosen student is a girl, is given by a) 43/100 b) 1/43 c) 1/10 d) 10/43

Discussion

41.	Let L be the line obtained by rotating the tangent line, drawn to the parabola y=x2 at the point A(1,1) about the point A by an angle of 45∘ in the clockwise direction. Let B bet the intersection of the line L with y=x2 other than A. If the area enclosed by the line L and the parabola is K sq.unit, then [K] is equal to, ( where [⋅] denotes greatest integer function ):
Answer» Let $L$ be the line obtained by rotating the tangent line, drawn to the parabola $y = x^{2}$ at the point $A (1, 1)$ about the point $A$ by an angle of $45^{\circ}$ in the clockwise direction. Let $B$ bet the intersection of the line $L$ with $y = x^{2}$ other than $A$ . If the area enclosed by the line $L$ and the parabola is $K$ sq.unit, then $[K]$ is equal to, $($ where $[\cdot]$ denotes greatest integer function $)$ :

Discussion

42.	Some students went for the picnic. The bugdet for the food is Rs 240. Because 4students failed to go the cost of food to each student will increase Rs 5 . So how many students went for the picnic?
Answer» Some students went for the picnic. The bugdet for the food is Rs 240. Because 4students failed to go the cost of food to each student will increase Rs 5 . So how many students went for the picnic?

Discussion

43.	x+5>4x-10
Answer» x+5>4x-10

Discussion

44.	Minimize Z = 3x + 5y, subject to constraints are x + 3y ≥ 3, x+y≥2 and x, y ≥0.
Answer» Minimize Z = 3x + 5y, subject to constraints are x + 3y $\geq$ 3, $x + y \geq 2 a n d x, y \geq 0$ .

Discussion

45.	Maximum number of real roots does the equation ax¹⁰-bx⁸+cx²+e=0 ,a,b,c,e>0 can have.
Answer» Maximum number of real roots does the equation ax¹⁰-bx⁸+cx²+e=0 ,a,b,c,e>0 can have.

Discussion

46.	Express each of the following as the product of sinces and cosines (i) sin12θ+sin4θ (ii) sin5θ−sinθ (iii) cos12θ−cos4θ (iv) sin2θ+cos4θ
Answer» Express each of the following as the product of sinces and cosines (i) $s i n 12 θ + s i n 4 θ$ (ii) $s i n 5 θ - s i n θ$ (iii) $c o s 12 θ - c o s 4 θ$ (iv) $s i n 2 θ + c o s 4 θ$

Discussion

47.	find the range of f(x) = 1 + x
Answer» find the range of f(x) = 1 + x

Discussion

48.	a group consist of 4 girls and 7 boys in how many ways can a team of 5 members be selected if the team has 1) no girl 2)atlest one boy and one girl 3)at least 3 girls
Answer» a group consist of 4 girls and 7 boys in how many ways can a team of 5 members be selected if the team has 1) no girl 2)atlest one boy and one girl 3)at least 3 girls

Discussion

49.	An urn contains 9 red balls and x green balls. If the probability of picking a red ball is thrice that of picking a green ball, then x = ________.
Answer» An urn contains 9 red balls and x green balls. If the probability of picking a red ball is thrice that of picking a green ball, then x = ________.

Discussion

50.	If the equation of a circle is λx2+(2λ−3) y2−4x+6y−1=0 then the coordinates of centre are
Answer» If the equation of a circle is $λ x^{2} + (2 λ - 3) y^{2} - 4 x + 6 y - 1 = 0$ then the coordinates of centre are

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

For two 3×3 matrices A and B, let A+B=2B′ and 3A+2B=I3, where B′ is the transpose of B and I3 is 3×3 identity matrix, then

the position of a particle moving in a straight line along x axis varies with time t as x =12t-3t^2m, where t is in seconds .the distance covered by particle in irst 5 seconds is

Consider a triangle Δ whose two sides lie on the x−axis and the line x+y+1=0. If the orthocenter of Δ is (1,1), then the equation of the circle passing through the vertices of the triangle Δ is

If α,β,γ are the roots of equation x3−6x2+11x−6=0, then find the equation whose roots are α2+β2,β2+γ2,γ2+α2 is

49.Solve for x: yAl +xH^+=yAl^{3+} + zH_2

There are three distinct positive integers whose sum is equal to the product of the largest two of them. Find the product of these three integers.

Let f:R→R given by f(x)=(3−x3)1/3. Then fof(x) is

If system of equations ax + y + z = a, x + by + z = b and x + y + cz = c is inconsistent, then which of the following is correct?

The value of 108 sinπ9-144 sin3π9 is ____________.

The arithmetic mean of a and b is an+bnan−1+bn−1. The value of n is

34. In Triangle ABC, ANGLE BISECTS ANGLE A AND ANGLE C >ANGLE B. PROVE THAT ANGLE ADB>ANGLE ADC

If ∫xexcosx dx=aex(b(1−x)sinx+cxcosx)+d, (where d is constant of integration), then

what are coordination number

There are 12 points (A1,A2,...,A12) in a plane, where (A1,A2,A3,A4) are collinear to each other and (A5,A6,A7,A8) are collinear to each other. If no points other than these two set of points are collinear, then the total number of straight lines that can be formed using these 12 points is

The number of words not starting and ending with vowels formed using all the letters of the word 'UNIVERSITY' such that all the vowels are in alphabetical order is

A flood having a return period of 50 years . The risk that this flood may occur in next 20 years will be ___________0.33

1x dx

Inverse of x+1/x+2

A perpendicular is drawn from the point A(1,8,4) to the line joining the points B(0,−1,3) and C(2,−3,−1). The co-ordinates of the foot of the perpendicular is:

Which of the following is/are true, if z, z1, z2 are complex numbers?

Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:Omar helps his mother 1 hour more than his sister does.

If n≠3k and 1,ω,ω2​ are the cube roots of unity, then Δ=∣∣∣∣∣1ωnω2nω2n1ωnωnω2n1∣∣∣∣∣ has the value

Prove that sin2x+2sin4x+sin6x=4cos2xsin4x

How many 6-letter words can be formed from the letters of the word WEDNESDAY such that vowel A is always included in each arrangement?Also, find out the combinations of such words.

A basket has 5 yellow and 12 black balls. Find probability that second ball drawn is black in the first ball is yellow.

The value of π/2∫0dx1+tan4x is

Prove that x2n−1+y2n−1 is divisible by x+y for all n∈N.

Question 11 (iv)State whether the following are true or false. Justify your answer. (iv) cot A is the product of cot and A.

Evaluate ∫1−cot2x1+cot2xdx(where C is constant of integration)

limn→∞1⋅n2+2(n−1)2+3(n−2)2 +⋯+ n⋅1213+23 +⋯+ n3 is equal to

If area of a triangle whose vertices in argand plane are z, iz, z+iz is 16 square units, find |z|

If the system of linear equations 2x+py+6z=8 x+2y+qz=5 x+y+3z=4 has infinitely many solutions, then a possible pair of p and q is

Slope of the normal at (1,1) to the curve x3+3xy+y3=5 is

The number of points having position vector a^i+b^j+c^k where a,b,c∈{1,2,3,4,5} such that 2a+3b+5c is divisible by 4, is

If the equations x2+2x+3=0 and ax2+bx+c=0,a,b,c∈R, have a common root, then a:b:c is

Represent to solution set of each of the following in equations graphically in two dimensional plane : −3x+2y≤6

f(x)=1+[cos x]x,in 0&lt;x⩽π2

The sum of 10 terms of the series 2⋅5+5⋅8+8⋅11+… is

In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. The probability that a student chosen randomly studies in class XII, given that the chosen student is a girl, is given by a) 43/100 b) 1/43 c) 1/10 d) 10/43

Some students went for the picnic. The bugdet for the food is Rs 240. Because 4students failed to go the cost of food to each student will increase Rs 5 . So how many students went for the picnic?

x+5&gt;4x-10

Minimize Z = 3x + 5y, subject to constraints are x + 3y ≥ 3, x+y≥2 and x, y ≥0.

Maximum number of real roots does the equation ax¹⁰-bx⁸+cx²+e=0 ,a,b,c,e>0 can have.

Express each of the following as the product of sinces and cosines (i) sin12θ+sin4θ (ii) sin5θ−sinθ (iii) cos12θ−cos4θ (iv) sin2θ+cos4θ

find the range of f(x) = 1 + x

a group consist of 4 girls and 7 boys in how many ways can a team of 5 members be selected if the team has 1) no girl 2)atlest one boy and one girl 3)at least 3 girls

An urn contains 9 red balls and x green balls. If the probability of picking a red ball is thrice that of picking a green ball, then x = ________.

If the equation of a circle is λx2+(2λ−3) y2−4x+6y−1=0 then the coordinates of centre are

If n≠3k and 1,ω,ω2 are the cube roots of unity, then Δ=∣∣∣∣∣1ωnω2nω2n1ωnωnω2n1∣∣∣∣∣ has the value

f(x)=1+[cos x]x,in 0<x⩽π2

x+5>4x-10