43030 + Interview Questions in Mathematics

1.	The domain of the real function fx=x9−x2 is ___________.
Answer» The domain of the real function $f (x) = \frac{x}{\sqrt{9 - x^{2}}}$ is ___________.

Discussion

2.	If a, b, c are in A.P., then r1,r2,r3 are in
Answer» If $a, b, c$ are in $A . P .$ , then $r_{1}, r_{2}, r_{3}$ are in

Discussion

3.	The perpendicular form of the straight line y=x+4 is xcosα+ysinα=p. Then,
Answer» The perpendicular form of the straight line $y = x + 4$ is $x cos α + y sin α = p .$ Then,

Discussion

4.	If the line ax−by+2=0 belongs to both the family of lines (3+2λ)x+(1−3λ)y−1+14λ=0 and (2+t)x+(2t−1)y+3t+1=0.If f(x)=0 is a quadratic equation whose roots are ′a′ and ′b′ then number of real roots of f(\|x\|)=0 is
Answer» If the line $a x - b y + 2 = 0$ belongs to both the family of lines $(3 + 2 λ) x + (1 - 3 λ) y - 1 + 14 λ = 0$ and $(2 + t) x + (2 t - 1) y + 3 t + 1 = 0$ . If $f (x) = 0$ is a quadratic equation whose roots are $^{'} a^{'}$ and $^{'} b^{'}$ then number of real roots of $f (\| x \|) = 0$ is

Discussion

5.	The value of (cot x2−tan x2)2 (1-2 tan x cot 2x) is
Answer» The value of ${(c o t \frac{x}{2} - t a n \frac{x}{2})}^{2}$ (1-2 tan x cot 2x) is

Discussion

6.	Verify A(adj)(A)−(adj A)A=\|A\|In\|)in [23−4−6]
Answer» Verify $A (a d j) (A) - (a d j A) A = \| A \| I_{n} \|) i n$ $[\begin{matrix} 2 & 3 - 4 & - 6 \end{matrix}]$

6.

Verify A(adj)(A)−(adj A)A=|A|In|)in [23−4−6]

Answer»

Verify $A (a d j) (A) - (a d j A) A = | A | I_{n} |) i n$

$[\begin{matrix} 2 & 3 - 4 & - 6 \end{matrix}]$

Discussion

7.	What is the number that equals 512×4?(Apply lattice method of multiplication)
Answer» What is the number that equals $512 \times 4$ ? (Apply lattice method of multiplication)

Discussion

8.	The buckling load for the column (see figure) as kT approaches infinity is k. π2EIL2. The value of k (correct upto two decimal place) is___ 2
Answer» The buckling load for the column (see figure) as $k_{T}$ approaches infinity is k. $\frac{π^{2} E I}{L^{2}}$ . The value of k (correct upto two decimal place) is___ 2

Discussion

9.	Let x, y, z be positive reals. Which of the following implies x = y = z? (I) x3 + y3 + z3 = 3xyz (II) x3 + y2 z + yz2 = 3xyz (III) x3 + y2 z + z2 x = 3xyz (IV) (x + y + z)3 = 27xyz
Answer» Let x, y, z be positive reals. Which of the following implies x = y = z? (I) x $^{3}$ + y $^{3}$ + z $^{3}$ = 3xyz (II) x $^{3}$ + y $^{2}$ z + yz $^{2}$ = 3xyz (III) x $^{3}$ + y $^{2}$ z + z $^{2}$ x = 3xyz (IV) (x + y + z) $^{3}$ = 27xyz

9.

Let x, y, z be positive reals. Which of the following implies x = y = z? (I) x3 + y3 + z3 = 3xyz (II) x3 + y2 z + yz2 = 3xyz (III) x3 + y2 z + z2 x = 3xyz (IV) (x + y + z)3 = 27xyz

Answer»

Let x, y, z be positive reals. Which of the following implies x = y = z?

(I) x $^{3}$ + y $^{3}$ + z $^{3}$ = 3xyz

(II) x $^{3}$ + y $^{2}$ z + yz $^{2}$ = 3xyz

(III) x $^{3}$ + y $^{2}$ z + z $^{2}$ x = 3xyz

(IV) (x + y + z) $^{3}$ = 27xyz

Discussion

10.	If I=2∫11√2x3−9x2+12x+4 dx , then:
Answer» If $I = 2 \int 1 \frac{1}{\sqrt{2 x^{3} - 9 x^{2} + 12 x + 4}} d x$ , then:

Discussion

11.	The number of elements in the power set of A, where A={x:x∈W and x3−1≤7}
Answer» The number of elements in the power set of $A$ , where $A = {x : x \in W and x^{3} - 1 \leq 7}$

Discussion

12.	The integral of ∫dx(x−2)7/8(x+3)9/8 is:(where c is integration constant)
Answer» The integral of $\int \frac{d x}{(x - 2)^{7 / 8} (x + 3)^{9 / 8}}$ is: (where $c$ is integration constant)

Discussion

13.	If A is a 4×4 matrix such that \|3⋅adjA\|=3, then \|A\| is equal to
Answer» If $A$ is a $4 \times 4$ matrix such that $\| 3 \cdot a d j A \| = 3,$ then $\| A \|$ is equal to

Discussion

14.	A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes?
Answer» A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes?

Discussion

15.	If the tangent at the point P(2,4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R, then the sum of the coordinates of the mid point of QR is
Answer» If the tangent at the point $P (2, 4)$ to the parabola $y^{2} = 8 x$ meets the parabola $y^{2} = 8 x + 5$ at $Q$ and $R$ , then the sum of the coordinates of the mid point of $Q R$ is

Discussion

16.	Express 0.621 in form of p/q
Answer» Express 0.621 in form of p/q

Discussion

17.	Question 68Count the number of cubes in the given shapes.
Answer» Question 68 Count the number of cubes in the given shapes.

Discussion

18.	The maximum value of sinx1 + 2sinx2 + 3sinx3 is
Answer» The maximum value of sinx1 + 2sinx2 + 3sinx3 is

Discussion

19.	If sinA=1213,cosB=−35,0<A<π2, π<B<3π2, then the value of sin(A+B) is
Answer» If $sin A = \frac{12}{13}, cos B = - \frac{3}{5}, 0 < A < \frac{π}{2},$ $π < B < \frac{3 π}{2}$ , then the value of $sin (A + B)$ is

Discussion

20.	Let a seven digit number be formed using 1,2,3,4,5,6,7 without repetition such that they are not divisible by 5. If the numbers are arranged in increasing order, then the 1994th number is
Answer» Let a seven digit number be formed using $1, 2, 3, 4, 5, 6, 7$ without repetition such that they are not divisible by $5$ . If the numbers are arranged in increasing order, then the $1994^{t h}$ number is

Discussion

21.	limn→∞sin(a2n)sin(b2n)
Answer» ${lim}_{n \to \infty} \frac{s i n (\frac{a}{2^{n}})}{s i n (\frac{b}{2^{n}})}$

Discussion

22.	Sin(alfa -1080 degree)
Answer» Sin(alfa -1080 degree)

Discussion

23.	If cx = 4, and 7+97(3c - 4x)^2 * 56 * 56% =kthen find 1. k^2 + 3/98 2. k(6k-7)^5
Answer» If cx = 4, and 7+97(3c - 4x)^2 * 56 * 56% =k then find 1. k^2 + 3/98 2. k(6k-7)^5

Discussion

24.	Evaluate the following integrals:∫-π/2π/2sin x+cos x dx
Answer» Evaluate the following integrals: $\int_{- π / 2}^{π / 2} \{\sin \|x\| + \cos \|x\|\} d x$

Discussion

25.	A b c + b a c = d a d c .find the value of a b c d
Answer» A b c + b a c = d a d c .find the value of a b c d

Discussion

26.	If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation
Answer» $I f [\begin{matrix} α & β γ & - α \end{matrix}] is the square root of second order unit matrix, T h e n α, β a n d γ should satisfy the relation$

Discussion

27.	A slip of paper is given to a person A who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is 13. A passes the slip to B, who may either leave it alone or change the sign before passing it to C. Next C passes the slip to D after perhaps changing the sign. Finally D passes it to a referee after perhaps changing the sign. B, C, D each change the sign with probability 23. The probability that the referee observes a plus sign on the slip if it is known that A wrote a plus sign is
Answer» A slip of paper is given to a person A who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is $\frac{1}{3}$ . A passes the slip to B, who may either leave it alone or change the sign before passing it to C. Next C passes the slip to D after perhaps changing the sign. Finally D passes it to a referee after perhaps changing the sign. B, C, D each change the sign with probability $\frac{2}{3}$ . The probability that the referee observes a plus sign on the slip if it is known that A wrote a plus sign is

Discussion

28.	The solution of the differential equation (1+y2)+(x−etan−1y)dydx=0, is
Answer» The solution of the differential equation $(1 + y^{2}) + (x - e^{t a n^{- 1} y}) \frac{d y}{d x} = 0$ , is

Discussion

29.	Given that the 4th term in the expansion of (2+3x8)10 has the maximum numerical value, then x lies in the interval
Answer» Given that the 4th term in the expansion of ${(2 + \frac{3 x}{8})}^{10}$ has the maximum numerical value, then x lies in the interval

Discussion

30.	If the vectors →a=(clog2x)^i−6^j+2^k and →b=(log2x)^i+2^j+3(clog2x)^k make an obtuse angle for any x∈(0,∞) then c belongs to
Answer» If the vectors $\to a = (c l o g_{2} x)^i - 6^j + 2^k$ and $\to b = (l o g_{2} x)^i + 2^j + 3 (c l o g_{2} x)^k$ make an obtuse angle for any $x \in (0, \infty)$ then c belongs to

Discussion

31.	Which of the following is a correct representation 3×14?
Answer» Which of the following is a correct representation $3 \times \frac{1}{4} ?$

Discussion

32.	,xin quadrant II
Answer» , x in quadrant II

Discussion

33.	In a △OAB, where O is origin and vertex B is (3,4). If the orthocentre of the triangle is P(1,4) and coordinates of vertex A is (h,k), then the value of 4k+h is
Answer» In a $△ O A B$ , where $O$ is origin and vertex $B$ is $(3, 4)$ . If the orthocentre of the triangle is $P (1, 4)$ and coordinates of vertex $A$ is $(h, k)$ , then the value of $4 k + h$ is

Discussion

34.	If 3 - 5i is one root of the equation -x2 + ax + b = 0, find a + b, where a,b∈ R
Answer» If 3 - 5i is one root of the equation - $x^{2}$ + ax + b = 0, find a + b, where a,b∈ R

Discussion

35.	Thegiven figure shows a relationship between the sets P and Q. writethis relation(i) inset-builder form (ii) in roster form. Whatis its domain and range?
Answer» The given figure shows a relationship between the sets P and Q. write this relation (i) in set-builder form (ii) in roster form. What is its domain and range?

35.

Thegiven figure shows a relationship between the sets P and Q. writethis relation(i) inset-builder form (ii) in roster form. Whatis its domain and range?

Answer»

The
given figure shows a relationship between the sets P and Q. write
this relation

(i) in
set-builder form (ii) in roster form.

What
is its domain and range?

Discussion

36.	If lines px+qy+r=0,qx+ry+p=0 and rx+py+q=0 are concurrent, then the value of p+q+r is: (where p,q,r are distinct).
Answer» If lines $p x + q y + r = 0, q x + r y + p = 0$ and $r x + p y + q = 0$ are concurrent, then the value of $p + q + r$ is: (where $p, q, r$ are distinct).

Discussion

37.	how to solve ouestions which con†an two or more modulus in linear inequalities
Answer» how to solve ouestions which con†an two or more modulus in linear inequalities

Discussion

38.	the sum of first 8 term of an ap is 100 and sum of its 19 term is 511 then find its ap
Answer» the sum of first 8 term of an ap is 100 and sum of its 19 term is 511 then find its ap

Discussion

39.	For any complex number Z, the min value of \|Z\|+\|Z+3i\| isA)2B)4C)9D)3^(1/2)
Answer» For any complex number Z, the min value of \|Z\|+\|Z+3i\| is A)2 B)4 C)9 D)3^(1/2)

Discussion

40.	[[Q]]Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥3, x, y ≥ 0
Answer» [[Q]] Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

40.

[[Q]]Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥3, x, y ≥ 0

Answer»

[[Q]]

Solve the following system of inequalities graphically:

4x + 3y ≤ 60, y ≥ 2x, x ≥
3, x, y ≥ 0

Discussion

41.	(i) If A=[3√32420] and B=[2−12124], verify that (A′)′=A.(ii) If A=[3√32420] and B=[2−12124], verify that (A+B)′=A′+B′.(iii) If A=[3√32420] and B=[2−12124], verify that (kB)′=(kB′) where k is any constant.
Answer» $(i)$ If $A = [\begin{matrix} 3 & \sqrt{3} & 2 4 & 2 & 0 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 1 & 2 1 & 2 & 4 \end{matrix}]$ , verify that $(A^{'})^{'} = A .$ $(i i)$ If $A = [\begin{matrix} 3 & \sqrt{3} & 2 4 & 2 & 0 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 1 & 2 1 & 2 & 4 \end{matrix}]$ , verify that $(A + B)^{'} = A^{'} + B^{'} .$ $(i i i)$ If $A = [\begin{matrix} 3 & \sqrt{3} & 2 4 & 2 & 0 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 1 & 2 1 & 2 & 4 \end{matrix}]$ , verify that $(k B)^{'} = (k B^{'})$ where $k$ is any constant.

Discussion

42.	A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.
Answer» A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.

Discussion

43.	Line joining the points (0, 3) and (5, -2) isa tangent to the curve y ax/1+x, then a∈\varnothing?
Answer» Line joining the points (0, 3) and (5, -2) isa tangent to the curve y ax/1+x, then a∈\varnothing?

Discussion

44.	Find a vector in the direction of vector which has magnitude 8 units.
Answer» Find a vector in the direction of vector which has magnitude 8 units.

Discussion

45.	(sinθ,cosθ) and (3,2) lies on the same side of the line x+y=1, then θ lies between
Answer» $(s i n θ, c o s θ)$ and (3,2) lies on the same side of the line x+y=1, then $θ$ lies between

Discussion

46.	A normal is drawn on the hyperbola x216−y29=1 at a point given by parameter π3.What is the x-intercept of the normal.
Answer» A normal is drawn on the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ at a point given by parameter $\frac{π}{3}$ . What is the x-intercept of the normal.

46.

A normal is drawn on the hyperbola x216−y29=1 at a point given by parameter π3.What is the x-intercept of the normal.

Answer»

A normal is drawn on the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ at a point given by parameter $\frac{π}{3}$ .

What is the x-intercept of the normal.

Discussion

47.	The equation of the image of circle x2+y2−4x+6y+10=0 in the line 4x−3y+8=0 is
Answer» The equation of the image of circle $x^{2} + y^{2} - 4 x + 6 y + 10 = 0$ in the line $4 x - 3 y + 8 = 0$ is

Discussion

48.	If for x≥0 , y=y(x) is the solution of the differential equation (1+x)dy=[(1+x)2+y−3]dx,y(2)=0, then y(3) is equal to
Answer» If for $x \geq 0$ , $y = y (x)$ is the solution of the differential equation $(1 + x) d y = [(1 + x)^{2} + y - 3] d x, y (2) = 0,$ then $y (3)$ is equal to

Discussion

49.	If the system of linear equations2x+py+6z=8 x+2y+qz=5x+y+3z=4has 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

50.	Let f:(0,∞)→R and F(x)=∫x0tf(t)dt.If F(x2)=x4+x5, then 12∑r=1f(r2) is equal to
Answer» Let $f : (0, \infty) \to R$ and $F (x) = \int_{0}^{x} t f (t) d t$ . If $F (x^{2}) = x^{4} + x^{5}$ , then $12 \sum r = 1 f (r^{2})$ is equal to

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The domain of the real function fx=x9−x2 is ___________.

If a, b, c are in A.P., then r1,r2,r3 are in

The perpendicular form of the straight line y=x+4 is xcosα+ysinα=p. Then,

If the line ax−by+2=0 belongs to both the family of lines (3+2λ)x+(1−3λ)y−1+14λ=0 and (2+t)x+(2t−1)y+3t+1=0.If f(x)=0 is a quadratic equation whose roots are ′a′ and ′b′ then number of real roots of f(|x|)=0 is

The value of (cot x2−tan x2)2 (1-2 tan x cot 2x) is

Verify A(adj)(A)−(adj A)A=|A|In|)in [23−4−6]

What is the number that equals 512×4?(Apply lattice method of multiplication)

The buckling load for the column (see figure) as kT approaches infinity is k. π2EIL2. The value of k (correct upto two decimal place) is___ 2

Let x, y, z be positive reals. Which of the following implies x = y = z? (I) x3 + y3 + z3 = 3xyz (II) x3 + y2 z + yz2 = 3xyz (III) x3 + y2 z + z2 x = 3xyz (IV) (x + y + z)3 = 27xyz

If I=2∫11√2x3−9x2+12x+4 dx , then:

The number of elements in the power set of A, where A={x:x∈W and x3−1≤7}

The integral of ∫dx(x−2)7/8(x+3)9/8 is:(where c is integration constant)

If A is a 4×4 matrix such that |3⋅adjA|=3, then |A| is equal to

A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes?

If the tangent at the point P(2,4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R, then the sum of the coordinates of the mid point of QR is ​​

Express 0.621 in form of p/q

Question 68Count the number of cubes in the given shapes.

The maximum value of sinx1 + 2sinx2 + 3sinx3 is

If sinA=1213,cosB=−35,0&lt;A&lt;π2, π&lt;B&lt;3π2, then the value of sin(A+B) is

Let a seven digit number be formed using 1,2,3,4,5,6,7 without repetition such that they are not divisible by 5. If the numbers are arranged in increasing order, then the 1994th number is

limn→∞sin(a2n)sin(b2n)

Sin(alfa -1080 degree)

If cx = 4, and 7+97(3c - 4x)^2 * 56 * 56% =kthen find 1. k^2 + 3/98 2. k(6k-7)^5

Evaluate the following integrals:∫-π/2π/2sin x+cos x dx

A b c + b a c = d a d c .find the value of a b c d

If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation

The solution of the differential equation (1+y2)+(x−etan−1y)dydx=0, is

Given that the 4th term in the expansion of (2+3x8)10 has the maximum numerical value, then x lies in the interval

If the vectors →a=(clog2x)^i−6^j+2^k and →b=(log2x)^i+2^j+3(clog2x)^k make an obtuse angle for any x∈(0,∞) then c belongs to

Which of the following is a correct representation 3×14?

,xin quadrant II

In a △OAB, where O is origin and vertex B is (3,4). If the orthocentre of the triangle is P(1,4) and coordinates of vertex A is (h,k), then the value of 4k+h is

If 3 - 5i is one root of the equation -x2 + ax + b = 0, find a + b, where a,b∈ R

Thegiven figure shows a relationship between the sets P and Q. writethis relation(i) inset-builder form (ii) in roster form. Whatis its domain and range?

If lines px+qy+r=0,qx+ry+p=0 and rx+py+q=0 are concurrent, then the value of p+q+r is: (where p,q,r are distinct).

how to solve ouestions which con†an two or more modulus in linear inequalities

the sum of first 8 term of an ap is 100 and sum of its 19 term is 511 then find its ap

For any complex number Z, the min value of |Z|+|Z+3i| isA)2B)4C)9D)3^(1/2)

[[Q]]Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥3, x, y ≥ 0

(i) If A=[3√32420] and B=[2−12124], verify that (A′)′=A.(ii) If A=[3√32420] and B=[2−12124], verify that (A+B)′=A′+B′.(iii) If A=[3√32420] and B=[2−12124], verify that (kB)′=(kB′) where k is any constant.

A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.

Line joining the points (0, 3) and (5, -2) isa tangent to the curve y ax/1+x, then a∈\varnothing?

Find a vector in the direction of vector which has magnitude 8 units.

(sinθ,cosθ) and (3,2) lies on the same side of the line x+y=1, then θ lies between

A normal is drawn on the hyperbola x216−y29=1 at a point given by parameter π3.What is the x-intercept of the normal.

The equation of the image of circle x2+y2−4x+6y+10=0 in the line 4x−3y+8=0 is

If for x≥0 , y=y(x) is the solution of the differential equation (1+x)dy=[(1+x)2+y−3]dx,y(2)=0, then y(3) is equal to

If the system of linear equations2x+py+6z=8 x+2y+qz=5x+y+3z=4has infinitely many solutions, then a possible pair of p and q is

Let f:(0,∞)→R and F(x)=∫x0tf(t)dt.If F(x2)=x4+x5, then 12∑r=1f(r2) is equal to

If the tangent at the point P(2,4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R, then the sum of the coordinates of the mid point of QR is

If sinA=1213,cosB=−35,0<A<π2, π<B<3π2, then the value of sin(A+B) is