43030 + Interview Questions in Mathematics

1.	The point which lies in the half plane 3x−2y−2≥0 is
Answer» The point which lies in the half plane $3 x - 2 y - 2 \geq 0$ is

Discussion

2.	16.Cot 70+4cos 70 = ?
Answer» 16.Cot 70+4cos 70 = ?

Discussion

3.	Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4
Answer» Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4

Discussion

4.	The function f(x)=ex+x being differentiable and has a differentiable inverse f−1(x). The value of ddx(f−1) at the point f(ln2) is
Answer» The function $f (x) = e^{x} + x$ being differentiable and has a differentiable inverse $f^{- 1} (x)$ . The value of $\frac{d}{d x} (f^{- 1})$ at the point $f (ln 2)$ is

Discussion

5.	Find theequation of the lines through the point (3, 2) which make an angle of45° with the line x–2y = 3.
Answer» Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Discussion

6.	A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. Then the probability that he will win a prize exactly once is:
Answer» A person buys a lottery ticket in $50$ lotteries, in each of which his chance of winning a prize is $1 / 100$ . Then the probability that he will win a prize exactly once is:

Discussion

7.	The area of the region (in sq. unit) bounded by the curve y=\|x−1\| and y=1 is equal to
Answer» The area of the region (in sq. unit) bounded by the curve $y = \| x - 1 \|$ and $y = 1$ is equal to

Discussion

8.	If x=2+3, find the value of x3+1x3.
Answer» If $x = 2 + \sqrt{3}$ , find the value of $x^{3} + \frac{1}{x^{3}}$ .

Discussion

9.	The value of integral ∞∫0[n⋅e−x]dx is equal to (where [⋅] denotes the greatest integer function and n∈N,n>1)
Answer» The value of integral $\infty \int 0 [n \cdot e^{- x}] d x$ is equal to $($ where $[\cdot]$ denotes the greatest integer function and $n \in N, n > 1)$

Discussion

10.	What is the the maximum electrons that can fill the L shell?
Answer» What is the the maximum electrons that can fill the L shell?

Discussion

11.	If a,b,c ϵ R, then the number of real roots of the equation Δ=∣∣∣∣xc−b−cxab−ax∣∣∣∣=0 is
Answer» If $a, b, c ϵ R,$ then the number of real roots of the equation $Δ = ∣ ∣∣ ∣ \begin{matrix} x & c & - b - c & x & a b & - a & x \end{matrix} ∣ ∣∣ ∣ = 0$ is

Discussion

12.	60.If P vector + Q vector = P vector - Q vector then Q vector
Answer» 60.If P vector + Q vector = P vector - Q vector then Q vector

Discussion

13.	The parabolic arc y=√x,1≤×≤2 is resloved around the x−axis. The volume of the solid of revolution is
Answer» The parabolic arc $y = \sqrt{x}, 1 \leq \times \leq 2$ is resloved around the $x -$ axis. The volume of the solid of revolution is

Discussion

14.	If x+iy=a+iba−ib, prove that x2+y2=1
Answer» If $x + i y = \frac{a + i b}{a - i b}$ , prove that $x^{2} + y^{2} = 1$

Discussion

15.	The value of the determinant, ∣∣∣∣∣2sinAcosAsin(A+B)sin(A+C)sin(A+B)2sinBcosBsin(B+C)sin(A+C)sin(B+C)2sinCcosC∣∣∣∣∣ is:
Answer» The value of the determinant, $∣ ∣∣∣ ∣ \begin{matrix} 2 sin A cos A & sin (A + B) & sin (A + C) sin (A + B) & 2 sin B cos B & sin (B + C) sin (A + C) & sin (B + C) & 2 sin C cos C \end{matrix} ∣ ∣∣∣ ∣$ is:

Discussion

16.	If f:N→R is a function defined as f(x)=2x2+1, then the image of 5 under f is
Answer» If $f : N \to R$ is a function defined as $f (x) = 2 x^{2} + 1$ , then the image of $5$ under $f$ is

Discussion

17.	List I has four entries and List II has five entries. Each entry of List I is to be matched with one entry of List II. List IList II (A)The minimum value of ab if roots ofx3−ax2+bx−2=0 are positive, is(P)36(B)The number of quadrilateral formed in an octagon having two sides common(Q)24with the octagon, is(C)If 2nC4, 2nC5 and 2nC6 are in A.P.,then the value of 2n is (R)18(D)The value of 72sinπ18sin5π18sin7π18 is(S)14(T)9 Which of the following is the only CORRECT combination?
Answer» $List I$ has four entries and $List II$ has five entries. Each entry of $List I$ is to be matched with one entry of $List II .$ $\begin{matrix} List I & List II (A) & The minimum value of a b if roots of x^{3} - a x^{2} + b x - 2 = 0 are positive, is & (P) & 36 (B) & The number of quadrilateral formed in an octagon having two sides common & (Q) & 24 with the octagon, is (C) & If^{2 n} C_{4},^{2 n} C_{5} and^{2 n} C_{6} are in A . P ., then the value of 2 n is & (R) & 18 (D) & The value of 72 sin \frac{π}{18} sin \frac{5 π}{18} sin \frac{7 π}{18} is & (S) & 14 (T) & 9 \end{matrix}$ Which of the following is the only CORRECT combination?

Discussion

18.	Let U be the set of all boys and girls in a school, G be the set of all girls in theschool, B be the set of all boys in the school, and S be the set of all students in theschool who take swimming. Some, but not all, students in the school takeswimming. Draw a Venn diagram showing one of the possible interrelationshipamong sets U, G, B and S.12. For all sets A, B and C, show that (A – B) n (C – B) = A – (B . C)
Answer» Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S. 12. For all sets A, B and C, show that (A – B) n (C – B) = A – (B . C)

Discussion

19.	The position of a particle x depends on timet according to the relation xof the particle at t 2 s is(3 m/s) t (1 m/s2) f. The speed\vert(1) -1 m/s(2) -2 m/s(3) 2 m/s(4) 1 m/s
Answer» The position of a particle x depends on timet according to the relation xof the particle at t 2 s is(3 m/s) t (1 m/s2) f. The speed\vert(1) -1 m/s(2) -2 m/s(3) 2 m/s(4) 1 m/s

Discussion

20.	sin( 75o)
Answer» sin( 75^o)

Discussion

21.	The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is[EAMCET 2003]
Answer» The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is [EAMCET 2003]

21.

The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is[EAMCET 2003]

Answer»

The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is

[EAMCET 2003]

Discussion

22.	find the equation of a circle which has the portion of the line 3x+4y=14 intercepted by the limnes x-y=0 and 11x-4y=0 as diameter
Answer» find the equation of a circle which has the portion of the line 3x+4y=14 intercepted by the limnes x-y=0 and 11x-4y=0 as diameter

Discussion

23.	(x-2√6)(5√3+5√2)÷5√3-5√2=1
Answer» (x-2√6)(5√3+5√2)÷5√3-5√2=1

Discussion

24.	∫x3sin3x dx=
Answer» $\int x^{3} sin 3 x d x =$

Discussion

25.	ntProve that the planes bx-ay=n, cy-bz=L, az-cx=m intersect in a line if aL+bm+cn=0n
Answer» ntProve that the planes bx-ay=n, cy-bz=L, az-cx=m intersect in a line if aL+bm+cn=0n

Discussion

26.	Prove that: ∣∣∣∣∣y2z2yzy+zz2x2zxz+xx2y2xyx+y∣∣∣∣∣=0
Answer» Prove that: $∣ ∣∣∣ ∣ \begin{matrix} y^{2} z^{2} & y z & y + z z^{2} x^{2} & z x & z + x x^{2} y^{2} & x y & x + y \end{matrix} ∣ ∣∣∣ ∣ = 0$

Discussion

27.	If \|z+4\|≤3, then the maximum value of \|z+1\| is
Answer» If $\| z + 4 \| \leq 3,$ then the maximum value of $\| z + 1 \|$ is

Discussion

28.	If f(x)=∣∣∣∣∣tan xsin xcos xtan xsec x+cos xcos2xcos2xcosec2x1cos2xcos2x∣∣∣∣∣ Then −π∫+πf(x)dx=2kπ. Therefore, the value of k is
Answer» If $f (x) = ∣ ∣∣∣ ∣ \begin{matrix} tan x & sin x cos x & tan x sec x + cos x {cos}^{2} x & {cos}^{2} x & {c o s e c}^{2} x 1 & {cos}^{2} x & {cos}^{2} x \end{matrix} ∣ ∣∣∣ ∣$ Then $- π \int + π f (x) d x = 2 k π$ . Therefore, the value of $k$ is

Discussion

29.	If sum of n terms of an A.P. is 3n2+5n and Tm=164, then the value of m is
Answer» If sum of $n$ terms of an A.P. is $3 n^{2} + 5 n$ and $T_{m} = 164$ , then the value of $m$ is

Discussion

30.	If P(A) = 0.8, P(B) = 0.5 and P(B\|A) = 0.4, find (i) P(A ∩ B) (ii) P(A\|B) (iii) P(A ∪ B)
Answer» If P(A) = 0.8, P(B) = 0.5 and P(B\|A) = 0.4, find (i) P(A ∩ B) (ii) P(A\|B) (iii) P(A ∪ B)

Discussion

31.	∫exsecx(1+tanx) dx is equal to(where c is integration constant)
Answer» $\int e^{x} sec x (1 + tan x) d x$ is equal to (where $c$ is integration constant)

Discussion

32.	A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is:
Answer» A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is:

Discussion

33.	limx→0tan8xsin2x
Answer» ${lim}_{x \to 0} \frac{t a n 8 x}{s i n 2 x}$

Discussion

34.	If x and y are two real numbers such that x > 0 and xy = 1. The the minimum value of x + y is ________________.
Answer» If x and y are two real numbers such that x > 0 and xy = 1. The the minimum value of x + y is ________________.

Discussion

35.	The power of (2,1) with respect to the circle 2x2+2y2−8x−6y+k = 0 is positive if
Answer» The power of (2,1) with respect to the circle $2 x^{2} + 2 y^{2} - 8 x - 6 y + k$ = 0 is positive if

Discussion

36.	If x∈R, then the range of f(x)=sin√2x2+4x+3 is
Answer» If $x \in R,$ then the range of $f (x) = sin \sqrt{2 x^{2} + 4 x + 3}$ is

Discussion

37.	15.how to find out what color will be imparted by a compound.
Answer» 15.how to find out what color will be imparted by a compound.

Discussion

38.	If (a+i)22a−i=p+iq, where a∈R, then the value of p2+q2 is
Answer» If $\frac{(a + i)^{2}}{2 a - i} = p + i q,$ where $a \in R,$ then the value of $p^{2} + q^{2}$ is

Discussion

39.	The value of ∫(sin2x+2cos2x)dx is(where C is constant of integration)
Answer» The value of $\int ({sin}^{2} x + 2 {cos}^{2} x) d x$ is (where $C$ is constant of integration)

Discussion

40.	If a-b=3 and a+b+x=2 then the value of [a-b] [x^(3)-2ax^(2)+a^(2)x-(a+b)b^(2)] is
Answer» If a-b=3 and a+b+x=2 then the value of [a-b] [x^(3)-2ax^(2)+a^(2)x-(a+b)b^(2)] is

Discussion

41.	23. tan
Answer» 23. tan

Discussion

42.	If P(vector) = Q(vector), then which of the following is NOT correct? { P(vector) and Q(vector) are unit vectors and P & Q are magnitudes of P(vector) and Q(vector) }(1) P = Q(2) \|P(vector)\| = \|Q(vector)\|(3) P(vector) + Q(vector) = P + Q(4) \|P(vector) + Q(vector)\| = P + Q
Answer» If P(vector) = Q(vector), then which of the following is NOT correct? { P(vector) and Q(vector) are unit vectors and P & Q are magnitudes of P(vector) and Q(vector) } (1) P = Q (2) \|P(vector)\| = \|Q(vector)\| (3) P(vector) + Q(vector) = P + Q (4) \|P(vector) + Q(vector)\| = P + Q

Discussion

43.	The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
Answer» The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Discussion

44.	Let f:[2,7]→[0,∞) be a continuous and differentiable function such that (f(7)−f(2))(f(7))2+(f(2))2+f(7)f(2)3=kf2(c)f′(c), where c∈(2,7). Then the value of k is
Answer» Let $f : [2, 7] \to [0, \infty)$ be a continuous and differentiable function such that $(f (7) - f (2)) \frac{(f (7))^{2} + (f (2))^{2} + f (7) f (2)}{3} = k f^{2} (c) f^{'} (c),$ where $c \in (2, 7) .$ Then the value of $k$ is

Discussion

45.	Find the coordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, −1, 3) and C(2, −3, −1). [NCERT EXEMPLAR]
Answer» Find the coordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, −1, 3) and C(2, −3, −1). [NCERT EXEMPLAR]

Discussion

46.	If f,g:-R be define respectively by f(x)=3x+2 and g(x)=6x+5.find f-g.[hint; (f-g)x=f(x)-g(x)]
Answer» If f,g:-R be define respectively by f(x)=3x+2 and g(x)=6x+5.find f-g. [hint; (f-g)x=f(x)-g(x)]

Discussion

47.	30 pencil has to be divided into 7 boxes equally. How many Pencils are left?
Answer» 30 pencil has to be divided into 7 boxes equally. How many Pencils are left?

Discussion

48.	If x4+1x4= 194, find x3+1x3, x2+1x2 and x+1x
Answer» If $x^{4} + \frac{1}{x^{4}} = 194,$ find $x^{3} + \frac{1}{x^{3}}, x^{2} + \frac{1}{x^{2}}$ and $x + \frac{1}{x}$

Discussion

49.	If ∫π20 f(sin 2x) sin x dx=λ√24 ∫π40 f(cos 2x) cos x dx then the value of λ must be ___
Answer» If $\int_{0}^{\frac{π}{2}} f (s i n 2 x) s i n x d x = \frac{λ \sqrt{2}}{4} \int_{0}^{\frac{π}{4}} f (c o s 2 x) c o s x d x$ then the value of $λ$ must be ___

Discussion

50.	If 2f(x2)+3f(1x2)=x2−1, then the domain of the function f is
Answer» If $2 f (x^{2}) + 3 f (\frac{1}{x^{2}}) = x^{2} - 1,$ then the domain of the function $f$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The point which lies in the half plane 3x−2y−2≥0 is

16.Cot 70+4cos 70 = ?

Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4

The function f(x)=ex+x being differentiable and has a differentiable inverse f−1(x). The value of ddx(f−1) at the point f(ln2) is

Find theequation of the lines through the point (3, 2) which make an angle of45° with the line x–2y = 3.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. Then the probability that he will win a prize exactly once is:

The area of the region (in sq. unit) bounded by the curve y=|x−1| and y=1 is equal to

If x=2+3, find the value of x3+1x3.

The value of integral ∞∫0[n⋅e−x]dx is equal to (where [⋅] denotes the greatest integer function and n∈N,n&gt;1)

What is the the maximum electrons that can fill the L shell?

If a,b,c ϵ R, then the number of real roots of the equation Δ=∣∣∣∣xc−b−cxab−ax∣∣∣∣=0 is

60.If P vector + Q vector = P vector - Q vector then Q vector

The parabolic arc y=√x,1≤×≤2 is resloved around the x−axis. The volume of the solid of revolution is

If x+iy=a+iba−ib, prove that x2+y2=1

The value of the determinant, ∣∣∣∣∣2sinAcosAsin(A+B)sin(A+C)sin(A+B)2sinBcosBsin(B+C)sin(A+C)sin(B+C)2sinCcosC∣∣∣∣∣ is:

If f:N→R is a function defined as f(x)=2x2+1, then the image of 5 under f is

The position of a particle x depends on timet according to the relation xof the particle at t 2 s is(3 m/s) t (1 m/s2) f. The speed\vert(1) -1 m/s(2) -2 m/s(3) 2 m/s(4) 1 m/s

sin( 75o)

The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is[EAMCET 2003]

find the equation of a circle which has the portion of the line 3x+4y=14 intercepted by the limnes x-y=0 and 11x-4y=0 as diameter

(x-2√6)(5√3+5√2)÷5√3-5√2=1

∫x3sin3x dx=

ntProve that the planes bx-ay=n, cy-bz=L, az-cx=m intersect in a line if aL+bm+cn=0n

Prove that: ∣∣∣∣∣y2z2yzy+zz2x2zxz+xx2y2xyx+y∣∣∣∣∣=0

If |z+4|≤3, then the maximum value of |z+1| is

If f(x)=∣∣∣∣∣tan xsin xcos xtan xsec x+cos xcos2xcos2xcosec2x1cos2xcos2x∣∣∣∣∣ Then −π∫+πf(x)dx=2kπ. Therefore, the value of k is

If sum of n terms of an A.P. is 3n2+5n and Tm=164, then the value of m is

If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find (i) P(A ∩ B) (ii) P(A|B) (iii) P(A ∪ B)

∫exsecx(1+tanx) dx is equal to(where c is integration constant)

A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is:

limx→0tan8xsin2x

If x and y are two real numbers such that x > 0 and xy = 1. The the minimum value of x + y is ________________.

The power of (2,1) with respect to the circle 2x2+2y2−8x−6y+k = 0 is positive if

If x∈R, then the range of f(x)=sin√2x2+4x+3 is

15.how to find out what color will be imparted by a compound.

If (a+i)22a−i=p+iq, where a∈R, then the value of p2+q2 is

The value of ∫(sin2x+2cos2x)dx is(where C is constant of integration)

If a-b=3 and a+b+x=2 then the value of [a-b] [x^(3)-2ax^(2)+a^(2)x-(a+b)b^(2)] is

23. tan

If P(vector) = Q(vector), then which of the following is NOT correct? { P(vector) and Q(vector) are unit vectors and P & Q are magnitudes of P(vector) and Q(vector) }(1) P = Q(2) |P(vector)| = |Q(vector)|(3) P(vector) + Q(vector) = P + Q(4) |P(vector) + Q(vector)| = P + Q

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Let f:[2,7]→[0,∞) be a continuous and differentiable function such that (f(7)−f(2))(f(7))2+(f(2))2+f(7)f(2)3=kf2(c)f′(c), where c∈(2,7). Then the value of k is

Find the coordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, −1, 3) and C(2, −3, −1). [NCERT EXEMPLAR]

If f,g:-R be define respectively by f(x)=3x+2 and g(x)=6x+5.find f-g.[hint; (f-g)x=f(x)-g(x)]

30 pencil has to be divided into 7 boxes equally. How many Pencils are left?

If x4+1x4= 194, find x3+1x3, x2+1x2 and x+1x

If ∫π20 f(sin 2x) sin x dx=λ√24 ∫π40 f(cos 2x) cos x dx then the value of λ must be ___

If 2f(x2)+3f(1x2)=x2−1, then the domain of the function f is

The value of integral ∞∫0[n⋅e−x]dx is equal to (where [⋅] denotes the greatest integer function and n∈N,n>1)