43030 + Interview Questions in Mathematics

1.	4^x-4^x-1=24 Then the value of (2x)^x
Answer» 4^x-4^x-1=24 Then the value of (2x)^x

Discussion

2.	A(a, 1), B(b, 3) and C(4, c) are the vertices of ΔABC. If its centroid lies on x–axis, then __________.
Answer» A(a, 1), B(b, 3) and C(4, c) are the vertices of ΔABC. If its centroid lies on x–axis, then __________.

Discussion

3.	Show that f : R → R, given by f(x) = x - [x], is neither one-one nor onto.
Answer» Show that f : R $\to$ R, given by f(x) = x $-$ [x], is neither one-one nor onto.

Discussion

4.	If I=∫10sin x√xdx and J=∫10cosx√xdx, then, which one of the following is true?
Answer» If $I = \int_{0}^{1} \frac{s i n x}{\sqrt{x}} d x a n d J = \int_{0}^{1} \frac{c o s x}{\sqrt{x}} d x,$ then, which one of the following is true?

Discussion

5.	f(x)=asinx+bcosxcsinx+dcosx is strictly increasing in its domain if
Answer» $f (x) = \frac{a sin x + b cos x}{c sin x + d cos x}$ is strictly increasing in its domain if

Discussion

6.	The graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image (i.e., reflection) along which line ?
Answer» The graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image (i.e., reflection) along which line ?

Discussion

7.	If the differential equation corresponding to the family of curves y=c(x−c)2, where c is an arbitrary constant, is 8y2=kxydydx−(dydx)3, then the value of 13∫limt→0ln⎛⎜⎝1tt∫0(1+k2sin3x)k/xdx⎞⎟⎠ is
Answer» If the differential equation corresponding to the family of curves $y = c (x - c)^{2},$ where $c$ is an arbitrary constant, is $8 y^{2} = k x y \frac{d y}{d x} - {(\frac{d y}{d x})}^{3},$ then the value of $\frac{1}{3} \int lim t \to 0 ln ⎛ ⎜ ⎝ \frac{1}{t} t \int 0 {(1 + \frac{k}{2} sin 3 x)}^{k / x} d x ⎞ ⎟ ⎠$ is

Discussion

8.	If log(x+3)(x2−x)<1, then the value of x lies in
Answer» If ${log}_{(x + 3)} (x^{2} - x) < 1$ , then the value of x lies in

Discussion

9.	Why LCM of fractions equals to LCM(of numerators)/ HCF (of denominators)?
Answer» Why LCM of fractions equals to LCM(of numerators)/ HCF (of denominators)?

Discussion

10.	Match the following with their conjugates to simplify them
Answer» Match the following with their conjugates to simplify them

Discussion

11.	Write the first five terms of the following sequence and obtain the corresponding series:
Answer» Write the first five terms of the following sequence and obtain the corresponding series:

11.

Write the first five terms of the following sequence and obtain the corresponding series:

Answer»

Write the first five terms of the following sequence and obtain the corresponding series:

Discussion

12.	Find dydx, if x and y are connected parametrically by the equations given in questions without eliminating the parameter. x=a(cos t+log tant2), y=a sin t.
Answer» Find $\frac{d y}{d x}$ , if x and y are connected parametrically by the equations given in questions without eliminating the parameter. $x = a (c o s t + l o g t a n \frac{t}{2}), y = a s i n t .$

12.

Find dydx, if x and y are connected parametrically by the equations given in questions without eliminating the parameter. x=a(cos t+log tant2), y=a sin t.

Answer»

Find $\frac{d y}{d x}$ , if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x = a (c o s t + l o g t a n \frac{t}{2}), y = a s i n t .$

Discussion

13.	The points on the curve y = 12x - x3 at which the gradient is zero are _______________.
Answer» The points on the curve y = 12x - x³ at which the gradient is zero are _______________.

Discussion

14.	10.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B i
Answer» 10.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B i

Discussion

15.	A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 12, respectively. If the probability that the student is successful, is 12, then
Answer» A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and $\frac{1}{2}$ , respectively. If the probability that the student is successful, is $\frac{1}{2}$ , then

Discussion

16.	Let →a=^i+2^j−^k,→b=^i−^j and →c=^i−^j−^k be three given vectors. If →r is a vector such that →r×→a=→c×→a and →r⋅→b=0, then →r⋅→a is equal to
Answer» Let $\to a =^i + 2^j -^k, \to b =^i -^j$ and $\to c =^i -^j -^k$ be three given vectors. If $\to r$ is a vector such that $\to r \times \to a = \to c \times \to a$ and $\to r \cdot \to b = 0$ , then $\to r \cdot \to a$ is equal to

Discussion

17.	If α,β are the roots of ax2+bx+c=0, the equation whose roots are 2+α,2+β is
Answer» If $α, β$ are the roots of $a x^{2} + b x + c = 0$ , the equation whose roots are $2 + α, 2 + β$ is

Discussion

18.	prove that p^1/n is irrational where p is prime
Answer» prove that p^1/n is irrational where p is prime

Discussion

19.	Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the x-axis.
Answer» Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the x-axis.

Discussion

20.	Taking axes of hyperbola as coordinate axes, find its equation when the distance between the foci is 16 and eccentricity is √2
Answer» Taking axes of hyperbola as coordinate axes, find its equation when the distance between the foci is $16$ and eccentricity is $\sqrt{2}$

Discussion

21.	If the line 3x+4y−24=0 intersects the x-axis at the point A and y-axis at the point B, then the incentre of the triangle OAB, where O is the origin is :
Answer» If the line $3 x + 4 y - 24 = 0$ intersects the x-axis at the point $A$ and y-axis at the point $B$ , then the incentre of the triangle $O A B$ , where $O$ is the origin is :

Discussion

22.	If f(x)=cosx−x∫0(x−t)f(t)dt, then f′′(x)+f(x) is equal to
Answer» If $f (x) = cos x - x \int 0 (x - t) f (t) d t$ , then $f^{''} (x) + f (x)$ is equal to

Discussion

23.	Find the derivative of f(x) = tan x at x = 0
Answer» Find the derivative of f(x) = tan x at x = 0

Discussion

24.	What part of speech does the underlined word belong to? The fox is very sly.
Answer» What part of speech does the underlined word belong to? The fox is very sly.

24.

What part of speech does the underlined word belong to? The fox is very sly.

Answer»

What part of speech does the underlined word belong to?

The fox is very sly.

Discussion

25.	Find the value of a³+6ap+p³-8 when p=2-a
Answer» Find the value of a³+6ap+p³-8 when p=2-a

Discussion

26.	Look at the following graphThe range of the graph is
Answer» Look at the following graph The range of the graph is

Discussion

27.	The number of ways in which 30 coins of one rupee each be given to six persons, so that none of them receives less than 4 rupees is
Answer» The number of ways in which 30 coins of one rupee each be given to six persons, so that none of them receives less than 4 rupees is

Discussion

28.	Question 66Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The height of Mount Everest is 20 times the height of Empire State building.
Answer» Question 66 Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement: The height of Mount Everest is 20 times the height of Empire State building.

28.

Question 66Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The height of Mount Everest is 20 times the height of Empire State building.

Answer»

Question 66

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

The height of Mount Everest is 20 times the height of Empire State building.

Discussion

29.	A function f is defined by f ( x ) = 2 x – 5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3)
Answer» A function f is defined by f ( x ) = 2 x – 5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3)

Discussion

30.	For all real permissible values of m, if the straight line y=mx+√9m2−4 is tangent to a hyperbola, then equation of the hyperbola can be
Answer» For all real permissible values of $m,$ if the straight line $y = m x + \sqrt{9 m^{2} - 4}$ is tangent to a hyperbola, then equation of the hyperbola can be

Discussion

31.	∫10dx[ax+b(1−x)]2=
Answer» $\int_{0}^{1} \frac{d x}{[a x + b (1 - x)]^{2}} =$

Discussion

32.	if U={x:x5-6x4+11x3-6x2=0}A={x:x2-x=0} and B={x:x2+x=0}then n(AintersectionB) is equal to
Answer» if U={x:x5-6x4+11x3-6x2=0} A={x:x2-x=0} and B={x:x2+x=0} then n(AintersectionB) is equal to

Discussion

33.	25. Least value \|z\|+\|z-1\|+\|z-i\|+\|z-3-4i\| Where z is a complex number
Answer» 25. Least value \|z\|+\|z-1\|+\|z-i\|+\|z-3-4i\| Where z is a complex number

Discussion

34.	If \|2x−7\|=\|9−2x\|, then the value of x is
Answer» If $\| 2^{x} - 7 \| = \| 9 - 2^{x} \|$ , then the value of $x$ is

Discussion

35.	Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.
Answer» Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

Discussion

36.	The value of x which satisfies ∣∣∣∣x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣∣∣=0 is:
Answer» The value of $x$ which satisfies $∣ ∣∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣∣ ∣ = 0$ is:

Discussion

37.	Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x+7y=12 is one diagonal.
Answer» Find the equations of the two straight lines through (1, 2) forming two sides of a square of which $4 x + 7 y = 12$ is one diagonal.

Discussion

38.	In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then the number of students who enrolled for English but not German is
Answer» In a class of $40$ students, $12$ enrolled for both English and German. $22$ enrolled for German. If the students of the class enrolled for at least one of the two subjects, then the number of students who enrolled for English but not German is

Discussion

39.	The number of values of x in [0, 2π] that satisfy the equation sin2 x-cos x=14(a) 1(b) 2(c) 3(d) 4
Answer» The number of values of x in [0, 2π] that satisfy the equation $\sin^{2} x - \cos x = \frac{1}{4}$ (a) 1 (b) 2 (c) 3 (d) 4

Discussion

40.	Which of the following interval(s) satisfy the inequality x20−x11+x6−x3+1>0
Answer» Which of the following interval(s) satisfy the inequality $x^{20} - x^{11} + x^{6} - x^{3} + 1 > 0$

Discussion

41.	The mean value of the function f(x)=2ex+1 on the interval [0,2] is :
Answer» The mean value of the function $f (x) = \frac{2}{e^{x} + 1}$ on the interval $[0, 2]$ is :

Discussion

42.	If Un=∫π01−cosnx1−cosxdx, where n is a non-negative integer, then which of the following is/are true
Answer» If $U_{n} = \int_{0}^{π} \frac{1 - cos n x}{1 - cos x} d x$ , where $n$ is a non-negative integer, then which of the following is/are true

Discussion

43.	SHM is described by equation x=A sin\pmt + A sin(\pmt+/3) Find maximum speed of particle.
Answer» SHM is described by equation x=A sin\pmt + A sin(\pmt+/3) Find maximum speed of particle.

Discussion

44.	∫π6π3tanx+cotx2dx
Answer» $\int_{\frac{π}{6}}^{\frac{π}{3}} {(\tan x + \cot x)}^{2} d x$

Discussion

45.	x– 2y≤3, 3x+ 4y≥12, x≥0, y≥1
Answer» x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

Discussion

46.	9. what is the range of 3cosx-sinx and 3sinx-cosx
Answer» 9. what is the range of 3cosx-sinx and 3sinx-cosx

Discussion

47.	The greatest value of x2y3 where x>0, y>0 and 3x+4y=5 is
Answer» The greatest value of $x^{2} y^{3}$ where $x > 0, y > 0$ and $3 x + 4 y = 5$ is

Discussion

48.	Tan20^°+2tan50^°-tan70^°
Answer» Tan20^°+2tan50^°-tan70^°

Discussion

49.	Find the principal and general solutions of the equation
Answer» Find the principal and general solutions of the equation

Discussion

50.	19. Find domain and range sin1 (1-\|x\|)/2
Answer» 19. Find domain and range sin1 (1-\|x\|)/2

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

4^x-4^x-1=24 Then the value of (2x)^x

A(a, 1), B(b, 3) and C(4, c) are the vertices of ΔABC. If its centroid lies on x–axis, then __________.

Show that f : R → R, given by f(x) = x - [x], is neither one-one nor onto.

If I=∫10sin x√xdx and J=∫10cosx√xdx, then, which one of the following is true?

f(x)=asinx+bcosxcsinx+dcosx is strictly increasing in its domain if

The graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image (i.e., reflection) along which line ?

If the differential equation corresponding to the family of curves y=c(x−c)2, where c is an arbitrary constant, is 8y2=kxydydx−(dydx)3, then the value of 13∫limt→0ln⎛⎜⎝1tt∫0(1+k2sin3x)k/xdx⎞⎟⎠ is

If log(x+3)(x2−x)&lt;1, then the value of x lies in

Why LCM of fractions equals to LCM(of numerators)/ HCF (of denominators)?

Match the following with their conjugates to simplify them

Write the first five terms of the following sequence and obtain the corresponding series:

Find dydx, if x and y are connected parametrically by the equations given in questions without eliminating the parameter. x=a(cos t+log tant2), y=a sin t.

The points on the curve y = 12x - x3 at which the gradient is zero are _______________.

A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II and III are p, q and 12, respectively. If the probability that the student is successful, is 12, then

Let →a=^i+2^j−^k,→b=^i−^j and →c=^i−^j−^k be three given vectors. If →r is a vector such that →r×→a=→c×→a and →r⋅→b=0, then →r⋅→a is equal to

If α,β are the roots of ax2+bx+c=0, the equation whose roots are 2+α,2+β is

prove that p^1/n is irrational where p is prime

Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the x-axis.

Taking axes of hyperbola as coordinate axes, find its equation when the distance between the foci is 16 and eccentricity is √2

If the line 3x+4y−24=0 intersects the x-axis at the point A and y-axis at the point B, then the incentre of the triangle OAB, where O is the origin is :

If f(x)=cosx−x∫0(x−t)f(t)dt, then f′′(x)+f(x) is equal to

Find the derivative of f(x) = tan x at x = 0

What part of speech does the underlined word belong to? The fox is very sly.

Find the value of a³+6ap+p³-8 when p=2-a

Look at the following graphThe range of the graph is

The number of ways in which 30 coins of one rupee each be given to six persons, so that none of them receives less than 4 rupees is

Question 66Choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The height of Mount Everest is 20 times the height of Empire State building.

A function f is defined by f ( x ) = 2 x – 5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3)

For all real permissible values of m, if the straight line y=mx+√9m2−4 is tangent to a hyperbola, then equation of the hyperbola can be

∫10dx[ax+b(1−x)]2=

if U={x:x5-6x4+11x3-6x2=0}A={x:x2-x=0} and B={x:x2+x=0}then n(AintersectionB) is equal to

25. Least value |z|+|z-1|+|z-i|+|z-3-4i| Where z is a complex number

If |2x−7|=|9−2x|, then the value of x is

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.

The value of x which satisfies ∣∣∣∣x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣∣∣=0 is:

Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x+7y=12 is one diagonal.

In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then the number of students who enrolled for English but not German is

The number of values of ​x in [0, 2π] that satisfy the equation sin2 x-cos x=14(a) 1(b) 2(c) 3(d) 4

Which of the following interval(s) satisfy the inequality x20−x11+x6−x3+1&gt;0

The mean value of the function f(x)=2ex+1 on the interval [0,2] is :

If Un=∫π01−cosnx1−cosxdx, where n is a non-negative integer, then which of the following is/are true

SHM is described by equation x=A sin\pmt + A sin(\pmt+/3) Find maximum speed of particle.

∫π6π3tanx+cotx2dx

x– 2y≤3, 3x+ 4y≥12, x≥0, y≥1

9. what is the range of 3cosx-sinx and 3sinx-cosx

The greatest value of x2y3 where x&gt;0, y&gt;0 and 3x+4y=5 is

Tan20^°+2tan50^°-tan70^°

Find the principal and general solutions of the equation

19. Find domain and range sin1 (1-|x|)/2

If log(x+3)(x2−x)<1, then the value of x lies in

The number of values of x in [0, 2π] that satisfy the equation sin2 x-cos x=14(a) 1(b) 2(c) 3(d) 4

Which of the following interval(s) satisfy the inequality x20−x11+x6−x3+1>0

The greatest value of x2y3 where x>0, y>0 and 3x+4y=5 is