43030 + Interview Questions in Mathematics

1.	∫π2π4 ex (log sin x+cot x)dx=
Answer» $\int_{\frac{π}{4}}^{\frac{π}{2}} e^{x} (l o g s i n x + c o t x) d x =$

Discussion

2.	2x1.+3)
Answer» 2x1.+3)

Discussion

3.	A line cutting off intercept –3 from the y-axis and the tangent of angle to the x-axis is 35, its equation is(a) 5y – 3x + 15 = 0(b) 3y – 5x + 15 = 0(c) 5y – 3x + 15 = 0(d) none of these
Answer» A line cutting off intercept –3 from the y-axis and the tangent of angle to the x-axis is $\frac{3}{5}$ , its equation is (a) 5y – 3x + 15 = 0 (b) 3y – 5x + 15 = 0 (c) 5y – 3x + 15 = 0 (d) none of these

Discussion

4.	An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?
Answer» An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?

Discussion

5.	If g is the inverse of function f and f′(x)=x1+x2, then g′(x)=
Answer» If $g$ is the inverse of function $f$ and $f^{'} (x) = \frac{x}{1 + x^{2}},$ then $g^{'} (x) =$

Discussion

6.	In a triangle ABC,AD and BE are medians drawn to BC and CA respectively. Given AD=4,∠DAB=π6 and∠ABE=π3. If the area of triangle ABC is p√3q, where p and q are co-prime, then the value of p+q is
Answer» In a triangle $A B C, A D$ and $B E$ are medians drawn to $B C$ and $C A$ respectively. Given $A D = 4, ∠ D A B = \frac{π}{6}$ and $∠ A B E = \frac{π}{3} .$ If the area of triangle $A B C$ is $\frac{p}{\sqrt{3} q},$ where $p$ and $q$ are co-prime, then the value of $p + q$ is

Discussion

7.	In triangle ABC which of the following is not true: A. B. C. D.
Answer» In triangle ABC which of the following is not true: A. B. C. D.

Discussion

8.	Integrate: (sin^6(x)/cos(x))dx
Answer» Integrate: (sin^6(x)/cos(x))dx

Discussion

9.	A signal which can be green or red with probability 23 and 15 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 34.If the signal received at station B is green, then the probability that the original signal was green is
Answer» A signal which can be green or red with probability $\frac{2}{3}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$ .If the signal received at station B is green, then the probability that the original signal was green is

Discussion

10.	The number of rational terms in (1+√2+8√3)6 is
Answer» The number of rational terms in ${(1 + \sqrt{2} + \sqrt[8]{3})}^{6} i s$

Discussion

11.	Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18. [NCERT EXEMPLAR]
Answer» Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18. [NCERT EXEMPLAR]

Discussion

12.	The range of f(x)=tan−1(x2+x+a) ∀ xϵ R is a subset of [0,π2) then the range of a is -
Answer» The range of $f (x) = t a n^{- 1} (x^{2} + x + a)$ $\forall x ϵ$ R is a subset of $[0, \frac{π}{2})$ then the range of a is -

Discussion

13.	Laplace transform of (a+bt)2 where 'a', and 'b' are constants is given by:
Answer» Laplace transform of $(a + b t)^{2}$ where 'a', and 'b' are constants is given by:

Discussion

14.	If ϕ(x)=cos(cosx) is an increasing function, then a possible interval for x is
Answer» If $ϕ (x) = cos (cos x)$ is an increasing function, then a possible interval for $x$ is

Discussion

15.	The sum of the slopes of the tangents to the parabola x2=16y from (5,1) is ′a′ and the product of the slopes is ′b′ then a−b is
Answer» The sum of the slopes of the tangents to the parabola $x^{2} = 16 y$ from $(5, 1)$ is $^{'} a^{'}$ and the product of the slopes is $^{'} b^{'}$ then $a - b$ is

Discussion

16.	If α=1+12+13+⋯⋯+1101 and β=99∑r=1r(102−r)(101−r), then the value of α+β is
Answer» If $α = 1 + \frac{1}{2} + \frac{1}{3} + \dots \dots + \frac{1}{101}$ and $β = 99 \sum r = 1 \frac{r}{(102 - r) (101 - r)}$ , then the value of $α + β$ is

Discussion

17.	For the quadratic expression y=ax2+bx+c,a<0. The maximum value of y occurs at
Answer» For the quadratic expression $y = a x^{2} + b x + c, a < 0.$ The maximum value of $y$ occurs at

Discussion

18.	Differentiate each of the following from first principles:(i) sin 2x(ii) sin xx(iii) cos xx(iv) x2 sin x(v) sin (3x+1)(vi) sin x + cos x(vii) x2 ex(viii) ex2+1(ix) e2x(x) eax+b(xi) ax(x) 3x2
Answer» Differentiate each of the following from first principles: (i) $\sqrt{\sin 2 x}$ (ii) $\frac{\sin x}{x}$ (iii) $\frac{\cos x}{x}$ (iv) x² sin x (v) $\sqrt{\sin (3 x + 1)}$ (vi) sin x + cos x (vii) x² e^x (viii) $e^{x^{2} + 1}$ (ix) $e^{\sqrt{2 x}}$ (x) $e^{\sqrt{a x + b}}$ (xi) $a^{\sqrt{x}}$ (x) $3^{x^{2}}$

Discussion

19.	Two dice are thorown together. The probability that at least one will show its digit greater than 3 is
Answer» Two dice are thorown together. The probability that at least one will show its digit greater than 3 is

Discussion

20.	The area between the curves y = x^3 and y = x + \| x \| is equal to
Answer» The area between the curves y = x^3 and y = x + \| x \| is equal to

Discussion

21.	30. The solution of differential equation Xdy/dx = -y/2-sin2x/2y is
Answer» 30. The solution of differential equation Xdy/dx = -y/2-sin2x/2y is

Discussion

22.	The value of 3∫0\|x−5\|dx is
Answer» The value of $3 \int 0 \| x - 5 \| d x$ is

Discussion

23.	The value of{40}_{C_{31 }}\overset{10}{\underset{r=0}{+∑}}{}^{40+r}C_{10+r} is equal to
Answer» The value of{40}_{C_{31 }}\overset{10}{\underset{r=0}{+∑}}{}^{40+r}C_{10+r} is equal to

Discussion

24.	The range of λ if the point (λ, λ+1) lies inside the parabola y2=14x
Answer» The range of $λ$ if the point $(λ, λ + 1)$ lies inside the parabola $y^{2} = 14 x$

Discussion

25.	Prove the following trigonometric identities.sin2 A+11+tan2 A=1
Answer» Prove the following trigonometric identities. $\sin^{2} A + \frac{1}{1 + \tan^{2} A} = 1$

Discussion

26.	Consider the frequency distribution of the given numbers Value1234Frequency546f If the mean is known to be 3, then the value of f is
Answer» Consider the frequency distribution of the given numbers $\begin{matrix} Value & 1 & 2 & 3 & 4 Frequency & 5 & 4 & 6 & f \end{matrix}$ If the mean is known to be 3, then the value of $f$ is

26.

Consider the frequency distribution of the given numbers Value1234Frequency546f If the mean is known to be 3, then the value of f is

Answer»

Consider the frequency distribution of the given numbers

$\begin{matrix} Value & 1 & 2 & 3 & 4 Frequency & 5 & 4 & 6 & f \end{matrix}$

If the mean is known to be 3, then the value of $f$ is

Discussion

27.	If alpha and beeta are the roots of the equation ax^2+bx+c=0, then write alpha^5+beeta^5 in terms of a,b,c
Answer» If alpha and beeta are the roots of the equation ax^2+bx+c=0, then write alpha^5+beeta^5 in terms of a,b,c

Discussion

28.	If f(x) = 2x2−5x+1 and g(x) = −x3−x2−3x+2, find g(x) - f(x).
Answer» If f(x) = $2 x^{2} - 5 x + 1$ and g(x) = $- x^{3} - x^{2} - 3 x + 2$ , find g(x) - f(x).

Discussion

29.	The dimensions for P = M L-1 T-1 Density = L-3 M surface tension = M T-2 Given T = P^a D^b S^c Powers of M = 0 Powers of L=0 Powers of T = 1 Powers of M = a+b+c =0 Powers of L = -a-3b = 0 3b = -a Powers of T = -a-2c = 1 Solving the three above equation we get a= -3/2 b= 1/2 c=1 In this how are the equations (in bold) solved. ? Let me know the steps involved while solving the 3 equations as I am not getting the required solution by solving the equations .
Answer» The dimensions for P = M L-1 T-1 Density = L-3 M surface tension = M T-2 Given T = P^a D^b S^c Powers of M = 0 Powers of L=0 Powers of T = 1 Powers of M = a+b+c =0 Powers of L = -a-3b = 0 3b = -a Powers of T = -a-2c = 1 Solving the three above equation we get a= -3/2 b= 1/2 c=1 In this how are the equations (in bold) solved. ? Let me know the steps involved while solving the 3 equations as I am not getting the required solution by solving the equations .

Discussion

30.	Solve }\vert-2x^2+1+e^x+\operatorname{sin}x\vert=\vert2x^2-1\vert+e^x+\vert\operatorname{sin}x\vert,x∈\lbrack0,2π\rbrack
Answer» Solve }\vert-2x^2+1+e^x+\operatorname{sin}x\vert=\vert2x^2-1\vert+e^x+\vert\operatorname{sin}x\vert,x∈\lbrack0,2π\rbrack

Discussion

31.	If a set has 7 proper subsets, then it contains ____ elements.
Answer» If a set has 7 proper subsets, then it contains ____ elements.

Discussion

32.	The number of permutations of the word AUROBIND in which vowels appear in the alphabetical order, is
Answer» The number of permutations of the word $A U R O B I N D$ in which vowels appear in the alphabetical order, is

Discussion

33.	If the order and degree of the differential equation satisfying √1−x2+√1−y2=b(x−y), where b is a parameter, is α and β respectively, then α+β is
Answer» If the order and degree of the differential equation satisfying $\sqrt{1 - x^{2}} + \sqrt{1 - y^{2}} = b (x - y),$ where $b$ is a parameter, is $α$ and $β$ respectively, then $α + β$ is

Discussion

34.	The equation of line perpendicular to 3x+5y=19 and passing through (3,2) is
Answer» The equation of line perpendicular to $3 x + 5 y = 19$ and passing through $(3, 2)$ is

Discussion

35.	If (→a×→b)2+(→a.→b)2=144 and \|→a\| , then \|→a\| =
Answer» If $(\to a \times \to b)^{2} + (\to a . \to b)^{2} = 144$ and $\| \to a \|$ , then $\| \to a \|$ =

Discussion

36.	lim0→x21−sinθ(x2−θ)cosθ is equal to
Answer» ${lim}_{0 \to \frac{x}{2}} \frac{1 - s i n θ}{(\frac{x}{2} - θ) c o s θ}$ is equal to

Discussion

37.	A function g defined for all real x > 0 satisfies g(1) = 1, for all x > 0, then g(4) equals
Answer» A function g defined for all real x > 0 satisfies g(1) = 1, for all x > 0, then g(4) equals

Discussion

38.	The order of a column matrix can be
Answer» The order of a column matrix can be

Discussion

39.	If x2−2hxy+y2=0 represents the equation of pair of straight lines both of which make an angle θ with the straight lines x+y=2, then
Answer» If $x^{2} - 2 h x y + y^{2} = 0$ represents the equation of pair of straight lines both of which make an angle $θ$ with the straight lines $x + y = 2,$ then

Discussion

40.	A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is a least one pair is equal to
Answer» A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is a least one pair is equal to

Discussion

41.	These people are ____.
Answer» These people are ____.

41.

These people are ____.

Answer»

These people are ____.

Discussion

42.	Find : ∫_0^1\sqrt{1+x^3}dx
Answer» Find : ∫_0^1\sqrt{1+x^3}dx

Discussion

43.	Show that the point (x, y) given by x=2at1+t2 and y=a1-t21+t2 lies on a circle for all real values of t such that -1≤t≤1, where a is any given real number. [NCERT EXEMPLAR]
Answer» Show that the point (x, y) given by $x = \frac{2 a t}{1 + t^{2}}$ and $y = a (\frac{1 - t^{2}}{1 + t^{2}})$ lies on a circle for all real values of t such that $- 1 \leq t \leq 1$ , where a is any given real number. [NCERT EXEMPLAR]

Discussion

44.	limx→0sin(3+x)−sin(3−x)x
Answer» ${lim}_{x \to 0} \frac{s i n (3 + x) - s i n (3 - x)}{x}$

Discussion

45.	Findthe domain of the function
Answer» Find the domain of the function

Discussion

46.	If [x2]+x−a=0 has a solution ( [.] represents the greatest integer function), where a∈N, a≤20, then the total number of distinct values of a is
Answer» If $[x^{2}] + x - a = 0$ has a solution $([.]$ represents the greatest integer function $)$ , where $a \in N, a \leq 20$ , then the total number of distinct values of $a$ is

Discussion

47.	Which of the following is/are true for nCr ?
Answer» Which of the following is/are true for $^{n} C_{r}$ ?

Discussion

48.	If y=cot−1√x2−1+sec−1x, x>1, then dydx is equal to
Answer» If $y = {cot}^{- 1} \sqrt{x^{2} - 1} + {sec}^{- 1} x, x > 1,$ then $\frac{d y}{d x}$ is equal to

Discussion

49.	The number of solution(s) of \vert\log\vert x\vert\vert+\vert x\vert=2 is equal to (1) 0 (2) 6 (3) 5 (4) 4
Answer» The number of solution(s) of \vert\log\vert x\vert\vert+\vert x\vert=2 is equal to (1) 0 (2) 6 (3) 5 (4) 4

Discussion

50.	Find the roots of the quadratic equation 3 x^2-2√6x+2=0 by quadratic method
Answer» Find the roots of the quadratic equation 3 x^2-2√6x+2=0 by quadratic method

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

∫π2π4 ex (log sin x+cot x)dx=

2x1.+3)

A line cutting off intercept –3 from the y-axis and the tangent of angle to the x-axis is 35, its equation is(a) 5y – 3x + 15 = 0(b) 3y – 5x + 15 = 0(c) 5y – 3x + 15 = 0(d) none of these

An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represent the number of black balls. What are the possible values of X? Is X a random variable?

If g is the inverse of function f and f′(x)=x1+x2, then g′(x)=

In a triangle ABC,AD and BE are medians drawn to BC and CA respectively. Given AD=4,∠DAB=π6 and∠ABE=π3. If the area of triangle ABC is p√3q, where p and q are co-prime, then the value of p+q is

In triangle ABC which of the following is not true: A. B. C. D.

Integrate: (sin^6(x)/cos(x))dx

The number of rational terms in (1+√2+8√3)6 is

Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18. [NCERT EXEMPLAR]

The range of f(x)=tan−1(x2+x+a) ∀ xϵ R is a subset of [0,π2) then the range of a is -

Laplace transform of (a+bt)2 where 'a', and 'b' are constants is given by:

If ϕ(x)=cos(cosx) is an increasing function, then a possible interval for x is

The sum of the slopes of the tangents to the parabola x2=16y from (5,1) is ′a′ and the product of the slopes is ′b′ then a−b is

If α=1+12+13+⋯⋯+1101 and β=99∑r=1r(102−r)(101−r), then the value of α+β is

For the quadratic expression y=ax2+bx+c,a&lt;0. The maximum value of y occurs at

Differentiate each of the following from first principles:(i) sin 2x(ii) sin xx(iii) cos xx(iv) x2 sin x(v) sin (3x+1)(vi) sin x + cos x(vii) x2 ex(viii) ex2+1(ix) e2x(x) eax+b(xi) ax(x) 3x2

Two dice are thorown together. The probability that at least one will show its digit greater than 3 is

The area between the curves y = x^3 and y = x + | x | is equal to

30. The solution of differential equation Xdy/dx = -y/2-sin2x/2y is

The value of 3∫0|x−5|dx is

The value of{40}_{C_{31 }}\overset{10}{\underset{r=0}{+∑}}{}^{40+r}C_{10+r} is equal to

The range of λ if the point (λ, λ+1) lies inside the parabola y2=14x

Prove the following trigonometric identities.sin2 A+11+tan2 A=1

Consider the frequency distribution of the given numbers Value1234Frequency546f If the mean is known to be 3, then the value of f is

If alpha and beeta are the roots of the equation ax^2+bx+c=0, then write alpha^5+beeta^5 in terms of a,b,c

If f(x) = 2x2−5x+1 and g(x) = −x3−x2−3x+2, find g(x) - f(x).

Solve }\vert-2x^2+1+e^x+\operatorname{sin}x\vert=\vert2x^2-1\vert+e^x+\vert\operatorname{sin}x\vert,x∈\lbrack0,2π\rbrack

If a set has 7 proper subsets, then it contains ____ elements.

The number of permutations of the word AUROBIND in which vowels appear in the alphabetical order, is

If the order and degree of the differential equation satisfying √1−x2+√1−y2=b(x−y), where b is a parameter, is α and β respectively, then α+β is

The equation of line perpendicular to 3x+5y=19 and passing through (3,2) is

If (→a×→b)2+(→a.→b)2=144 and |→a| , then |→a| =

lim0→x21−sinθ(x2−θ)cosθ is equal to

A function g defined for all real x &gt; 0 satisfies g(1) = 1, for all x &gt; 0, then g(4) equals

The order of a column matrix can be

If x2−2hxy+y2=0 represents the equation of pair of straight lines both of which make an angle θ with the straight lines x+y=2, then

A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is a least one pair is equal to

These people are ____.

Find : ∫_0^1\sqrt{1+x^3}dx

Show that the point (x, y) given by x=2at1+t2 and y=a1-t21+t2 lies on a circle for all real values of t such that -1≤t≤1, where a is any given real number. [NCERT EXEMPLAR]

limx→0sin(3+x)−sin(3−x)x

Findthe domain of the function

If [x2]+x−a=0 has a solution ( [.] represents the greatest integer function), where a∈N, a≤20, then the total number of distinct values of a is

Which of the following is/are true for nCr ?

If y=cot−1√x2−1+sec−1x, x&gt;1, then dydx is equal to

The number of solution(s) of \vert\log\vert x\vert\vert+\vert x\vert=2 is equal to (1) 0 (2) 6 (3) 5 (4) 4

Find the roots of the quadratic equation 3 x^2-2√6x+2=0 by quadratic method

For the quadratic expression y=ax2+bx+c,a<0. The maximum value of y occurs at

A function g defined for all real x > 0 satisfies g(1) = 1, for all x > 0, then g(4) equals

If y=cot−1√x2−1+sec−1x, x>1, then dydx is equal to