43030 + Interview Questions in Mathematics

1.	If x satisfies \|x−1\|+\|x−2\|+\|x−3\|≥6, then
Answer» If $x$ satisfies $\| x - 1 \| + \| x - 2 \| + \| x - 3 \| \geq 6$ , then

Discussion

2.	The equation of the plane which makes the intercepts 3, 4, 12 with X-axis, Y-axis and Z-axis respectively is:
Answer» The equation of the plane which makes the intercepts 3, 4, 12 with X-axis, Y-axis and Z-axis respectively is:

Discussion

3.	If Z is a compresibility factor, van der waals equation at low pressure can be written as:
Answer» If $Z$ is a compresibility factor, van der waals equation at low pressure can be written as:

Discussion

4.	Write the first fiveterms of the sequences whose nth term is
Answer» Write the first five terms of the sequences whose n^th term is

Discussion

5.	Will the consequate of √5 will be -√5 or√5
Answer» Will the consequate of √5 will be -√5 or√5

Discussion

6.	Let →r=(→a×→b)sinx+(→b×→c)cosy+(→c×→a) where →a,→b and →c are non zero, non coplanar vectors. If →r is orthogonal to 3→a+5→b+2→c, then the value of sec2y+cosec2x+secy⋅cosecx is:
Answer» Let $\to r = (\to a \times \to b) sin x + (\to b \times \to c) cos y + (\to c \times \to a)$ where $\to a, \to b$ and $\to c$ are non zero, non coplanar vectors. If $\to r$ is orthogonal to $3 \to a + 5 \to b + 2 \to c$ , then the value of ${sec}^{2} y + {cosec}^{2} x + sec y \cdot cosec x$ is:

Discussion

7.	Equation of the line in the plane P:x+3y−z=9, which is perpendicular to the line L:→r=^i+^j+^k+λ(2^i+^j−^k) and passing through a point where the plane P meets the given line L, is
Answer» Equation of the line in the plane $P : x + 3 y - z = 9,$ which is perpendicular to the line $L : \to r =^i +^j +^k + λ (2^i +^j -^k)$ and passing through a point where the plane $P$ meets the given line $L,$ is

Discussion

8.	Amit and Nisha appear for an interview for two vacancies in a company. The probability of Amit's selection is 15 and that of Nisha's selection is 16. Then the probability that both of them are selected is:
Answer» Amit and Nisha appear for an interview for two vacancies in a company. The probability of Amit's selection is $\frac{1}{5}$ and that of Nisha's selection is $\frac{1}{6}$ . Then the probability that both of them are selected is:

Discussion

9.	What is the remainder when 123×124×125is divisible by 9?
Answer» What is the remainder when 123×124×125is divisible by 9?

Discussion

10.	The value of cos2(π16)+cos2(3π16)+cos2(5π16)+cos2(7π16) is
Answer» The value of ${cos}^{2} (\frac{π}{16}) + {cos}^{2} (\frac{3 π}{16}) + {cos}^{2} (\frac{5 π}{16}) + {cos}^{2} (\frac{7 π}{16})$ is

Discussion

11.	If LMVT holds for the function f(x)=lnx on the interval [1,3] at x=c, then which of the following is not true
Answer» If LMVT holds for the function $f (x) = ln x$ on the interval $[1, 3]$ at $x = c,$ then which of the following is not true

Discussion

12.	If y=x√2−8√2 is a normal chord to y2=8x.Then its length (in units) is
Answer» If $y = x \sqrt{2} - 8 \sqrt{2}$ is a normal chord to $y^{2} = 8 x$ .Then its length (in units) is

Discussion

13.	Given that x2+x−6 is a factor of 2x4+x3−ax2+bx+a+b−1, then which of the following is/are true?
Answer» Given that $x^{2} + x - 6$ is a factor of $2 x^{4} + x^{3} - a x^{2} + b x + a + b - 1,$ then which of the following is/are true?

Discussion

14.	Prove that A-(BnC)=(A-B)U (A-C)
Answer» Prove that A-(BnC)=(A-B)U (A-C)

Discussion

15.	A six faced die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of the two numbers thrown is even is:
Answer» A six faced die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of the two numbers thrown is even is:

Discussion

16.	The average of 80 numbers is 42. When 5 more numbers are included, then the average of 85 numbers becomes 45. The average of 5 numbers is
Answer» The average of $80$ numbers is $42.$ When $5$ more numbers are included, then the average of $85$ numbers becomes $45.$ The average of $5$ numbers is

Discussion

17.	If →b and →c are two non-collinear unit vectors and →a is any vector, then (→a⋅→b)→b+(→a⋅→c)→c+→a⋅(→b×→c)\|→b×→c\|2(→b×→c)=
Answer» If $\to b and \to c$ are two non-collinear unit vectors and $\to a$ is any vector, then $(\to a \cdot \to b) \to b + (\to a \cdot \to c) \to c + \frac{\to a \cdot (\to b \times \to c)}{\| \to b \times \to c \|^{2}} (\to b \times \to c) =$

Discussion

18.	45. TRIGONOMETRIC EQUATIONS: If sin²4x + cos²x = 2 sin4x cos²x, then x = A. n(pie) /2 B. (2n+1)pie/2 C. (2n+1)pie D. None of these
Answer» 45. TRIGONOMETRIC EQUATIONS: If sin²4x + cos²x = 2 sin4x cos²x, then x = A. n(pie) /2 B. (2n+1)pie/2 C. (2n+1)pie D. None of these

Discussion

19.	In an A.P., let Tn denotes the nth term and Sn denotes the sum of first n terms. If T7=19 and T9=17, then the value of S63 is
Answer» In an A.P., let $T_{n}$ denotes the $n^{t h}$ term and $S_{n}$ denotes the sum of first $n$ terms. If $T_{7} = \frac{1}{9}$ and $T_{9} = \frac{1}{7},$ then the value of $S_{63}$ is

Discussion

20.	Find the distance of a point (2,4,-1) from the line. x+51=y+34=z−6−9.
Answer» Find the distance of a point (2,4,-1) from the line. $\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{- 9}$ .

Discussion

21.	If 3iZ25Z1 is purely real, then 5∣∣3Z1+7Z23Z1−7Z2∣∣ is -
Answer» If $\frac{3 i Z_{2}}{5 Z_{1}}$ is purely real, then $5 ∣ ∣ \frac{3 Z_{1} + 7 Z_{2}}{3 Z_{1} - 7 Z_{2}} ∣ ∣$ is -

Discussion

22.	If f(x)=xαsinx when x≠0, and f(0)=0. If Rolle's theorem can be applied to f in [0,π] then value(s) of α can be
Answer» If $f (x) = x^{α} sin x$ when $x \neq 0,$ and $f (0) = 0.$ If Rolle's theorem can be applied to $f$ in $[0, π]$ then value(s) of $α$ can be

Discussion

23.	Find the roots of the quadratic equation x2−3x+2=0, using factorisation method.
Answer» Find the roots of the quadratic equation $x^{2} - 3 x + 2 = 0$ , using factorisation method.

Discussion

24.	When a system of linear equations has no solution, what does it mean?
Answer» When a system of linear equations has no solution, what does it mean?

Discussion

25.	The equation of normal to the curve x=asin2θ , y=acosθ at θ=π6 is
Answer» The equation of normal to the curve $x = a sin 2 θ, y = a cos θ$ at $θ = \frac{π}{6}$ is

Discussion

26.	Write each of the statements in the form “if p , then q ”. (i) p : It is necessary to have a password to log on to the server. (ii) q : There is traffic jam whenever it rains. (iii) r : You can access the website only if you pay a subscription fee.
Answer» Write each of the statements in the form “if p , then q ”. (i) p : It is necessary to have a password to log on to the server. (ii) q : There is traffic jam whenever it rains. (iii) r : You can access the website only if you pay a subscription fee.

Discussion

27.	Obtain the differential equation of the family of circles having centre at (0, b) and passing through the points (a, 0) and (-a, 0), where 'b' is the arbitrary constant.
Answer» Obtain the differential equation of the family of circles having centre at (0, b) and passing through the points (a, 0) and (-a, 0), where 'b' is the arbitrary constant.

Discussion

28.	If 3sin A + 5 cosA= 5 prove that 5sinA-3cosA = +-3
Answer» If 3sin A + 5 cosA= 5 prove that 5sinA-3cosA = +-3

Discussion

29.	Find value of X, 1/a+b+X=1/a+1/b+1/x
Answer» Find value of X, 1/a+b+X=1/a+1/b+1/x

Discussion

30.	Let X and Y be two arbitrary, 3×3, non-zero, skew symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
Answer» Let $X$ and $Y$ be two arbitrary, $3 \times 3$ , non-zero, skew symmetric matrices and $Z$ be an arbitrary $3 \times 3$ , non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

Discussion

31.	The solution of a differential equation y′′+3y′+2y=0 is of the form
Answer» The solution of a differential equation $y^{''} + 3 y^{'} + 2 y = 0$ is of the form

Discussion

32.	The value of 9∑r=1sin2rπ18 is
Answer» The value of $9 \sum r = 1 {sin}^{2} \frac{r π}{18}$ is

Discussion

33.	If the value's of m for which the line y=mx+2√5 touches the hyperbola 16x2−9y2=144 are roots of the equation x2−(a+b)x−4=0, then the value of a+b=
Answer» If the value's of $m$ for which the line $y = m x + 2 \sqrt{5}$ touches the hyperbola $16 x^{2} - 9 y^{2} = 144$ are roots of the equation $x^{2} - (a + b) x - 4 = 0$ , then the value of $a + b =$

Discussion

34.	If △ABC is an acute angle triangle, then the minimum value of tanA+tanB+tanC is
Answer» If $△ A B C$ is an acute angle triangle, then the minimum value of $tan A + tan B + tan C$ is

Discussion

35.	A group of 10 persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table.The total number of possible arrangements, if ''Manager'', ''Assistant manager'' and ''Secretory'' had to sit together is
Answer» A group of $10$ persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table. The total number of possible arrangements, if ''Manager'', ''Assistant manager'' and ''Secretory'' had to sit together is

Discussion

36.	9. x cos-1 x
Answer» 9. x cos-1 x

Discussion

37.	In the Taylor series expansion of ex about x=2, the coefficient of (x−2)4
Answer» In the Taylor series expansion of $e^{x}$ about $x = 2$ , the coefficient of $(x - 2)^{4}$

Discussion

38.	Evaluate each of the following integrals:(i) ∫x4dx(ii) ∫x54dx(iii) ∫1x5dx(iv) ∫1x3/2dx(v) ∫3xdx(vi) ∫1x23dx(vii) ∫32 log3 xdx(viii) ∫logxxdx
Answer» Evaluate each of the following integrals: (i) $\int x^{4} d x$ (ii) $\int x^{\frac{5}{4}} d x$ (iii) $\int \frac{1}{x^{5}} d x$ (iv) $\int \frac{1}{x^{3 / 2}} d x$ (v) $\int 3^{x} d x$ (vi) $\int \frac{1}{\sqrt[3]{x^{2}}} d x$ (vii) $\int 3^{2 \log_{3}}^{x} d x$ (viii) $\int \log_{x} x d x$

Discussion

39.	If verify that A 3 − 6 A 2 + 9 A − 4 I = O and hence find A −1
Answer» If verify that A 3 − 6 A 2 + 9 A − 4 I = O and hence find A −1

Discussion

40.	For a sequence, Σ100r=1ar=α,Σ50r=1a2r−1=β. Find Σ50r=1a2r
Answer» For a sequence, $Σ_{r = 1}^{100} a_{r} = α, Σ_{r = 1}^{50} a_{2 r - 1} = β . F i n d Σ_{r = 1}^{50} a_{2 r}$

Discussion

41.	The value of integral ∫xdx(1−x4)3/2 is(where C is constant of integration)
Answer» The value of integral $\int \frac{x d x}{{(1 - x^{4})}^{3 / 2}}$ is (where $C$ is constant of integration)

Discussion

42.	If x=3tant and y=3sect, then the value of d2ydx2 at t=π4, is :
Answer» If $x = 3 tan t$ and $y = 3 sec t$ , then the value of $\frac{d^{2} y}{d x^{2}} at t = \frac{π}{4}$ , is :

Discussion

43.	Question 96Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data.BrandNumber of pairs of shoes soldA130B120C90D40E20
Answer» Question 96 Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data. $\begin{matrix} B r a n d & N u m b e r o f p a i r s o f s h o e s s o l d A & 130 B & 120 C & 90 D & 40 E & 20 \end{matrix}$

43.

Question 96Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data.BrandNumber of pairs of shoes soldA130B120C90D40E20

Answer»

Question 96

Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data.

$\begin{matrix} B r a n d & N u m b e r o f p a i r s o f s h o e s s o l d A & 130 B & 120 C & 90 D & 40 E & 20 \end{matrix}$

Discussion

44.	Angle between 2 planes will be same as
Answer» Angle between 2 planes will be same as

Discussion

45.	If cosx+cos(k+x)−cos(k−x)=2 has real solutions, then
Answer» $If cos x + cos (k + x) - cos (k - x) = 2$ has real solutions, then

Discussion

46.	Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
Answer» Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?

Discussion

47.	if x-1/x=2 then x2+1/x2=
Answer» if x-1/x=2 then x2+1/x2=

Discussion

48.	find next term 0,6,24,60,120,
Answer» find next term 0,6,24,60,120,

Discussion

49.	Numerically greatest term in the expansion of (2+3x)9, where x=32 is
Answer» Numerically greatest term in the expansion of $(2 + 3 x)^{9},$ where $x = \frac{3}{2}$ is

Discussion

50.	If the 2nd and 5th terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______.
Answer» If the $2^{n d}$ and $5^{t h}$ terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If x satisfies |x−1|+|x−2|+|x−3|≥6, then

The equation of the plane which makes the intercepts 3, 4, 12 with X-axis, Y-axis and Z-axis respectively is:

If Z is a compresibility factor, van der waals equation at low pressure can be written as:

Write the first fiveterms of the sequences whose nth term is

Will the consequate of √5 will be -√5 or√5

Let →r=(→a×→b)sinx+(→b×→c)cosy+(→c×→a) where →a,→b and →c are non zero, non coplanar vectors. If →r is orthogonal to 3→a+5→b+2→c, then the value of sec2y+cosec2x+secy⋅cosecx is:

Equation of the line in the plane P:x+3y−z=9, which is perpendicular to the line L:→r=^i+^j+^k+λ(2^i+^j−^k) and passing through a point where the plane P meets the given line L, is

Amit and Nisha appear for an interview for two vacancies in a company. The probability of Amit's selection is 15 and that of Nisha's selection is 16. Then the probability that both of them are selected is:

What is the remainder when 123×124×125is divisible by 9?

The value of cos2(π16)+cos2(3π16)+cos2(5π16)+cos2(7π16) is

If LMVT holds for the function f(x)=lnx on the interval [1,3] at x=c, then which of the following is not true

If y=x√2−8√2 is a normal chord to y2=8x.Then its length (in units) is

Given that x2+x−6 is a factor of 2x4+x3−ax2+bx+a+b−1, then which of the following is/are true?

Prove that A-(BnC)=(A-B)U (A-C)

A six faced die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of the two numbers thrown is even is:

The average of 80 numbers is 42. When 5 more numbers are included, then the average of 85 numbers becomes 45. The average of 5 numbers is

If →b and →c are two non-collinear unit vectors and →a is any vector, then (→a⋅→b)→b+(→a⋅→c)→c+→a⋅(→b×→c)|→b×→c|2(→b×→c)=

45. TRIGONOMETRIC EQUATIONS: If sin²4x + cos²x = 2 sin4x cos²x, then x = A. n(pie) /2 B. (2n+1)pie/2 C. (2n+1)pie D. None of these

In an A.P., let Tn denotes the nth term and Sn denotes the sum of first n terms. If T7=19 and T9=17, then the value of S63 is

Find the distance of a point (2,4,-1) from the line. x+51=y+34=z−6−9.

If 3iZ25Z1 is purely real, then 5∣∣3Z1+7Z23Z1−7Z2∣∣ is -

If f(x)=xαsinx when x≠0, and f(0)=0. If Rolle's theorem can be applied to f in [0,π] then value(s) of α can be

Find the roots of the quadratic equation x2−3x+2=0, using factorisation method.

When a system of linear equations has no solution, what does it mean?

The equation of normal to the curve x=asin2θ , y=acosθ at θ=π6 is

Write each of the statements in the form “if p , then q ”. (i) p : It is necessary to have a password to log on to the server. (ii) q : There is traffic jam whenever it rains. (iii) r : You can access the website only if you pay a subscription fee.

Obtain the differential equation of the family of circles having centre at (0, b) and passing through the points (a, 0) and (-a, 0), where 'b' is the arbitrary constant.

If 3sin A + 5 cosA= 5 prove that 5sinA-3cosA = +-3

Find value of X, 1/a+b+X=1/a+1/b+1/x

Let X and Y be two arbitrary, 3×3, non-zero, skew symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

The solution of a differential equation y′′+3y′+2y=0 is of the form

The value of 9∑r=1sin2rπ18 is

If the value's of m for which the line y=mx+2√5 touches the hyperbola 16x2−9y2=144 are roots of the equation x2−(a+b)x−4=0, then the value of a+b=

If △ABC is an acute angle triangle, then the minimum value of tanA+tanB+tanC is

A group of 10 persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table.The total number of possible arrangements, if ''Manager'', ''Assistant manager'' and ''Secretory'' had to sit together is

9. x cos-1 x

In the Taylor series expansion of ex about x=2, the coefficient of (x−2)4

Evaluate each of the following integrals:(i) ∫x4dx(ii) ∫x54dx(iii) ∫1x5dx(iv) ∫1x3/2dx(v) ∫3xdx(vi) ∫1x23dx(vii) ∫32 log3 xdx(viii) ∫logxxdx

If verify that A 3 − 6 A 2 + 9 A − 4 I = O and hence find A −1

For a sequence, Σ100r=1ar=α,Σ50r=1a2r−1=β. Find Σ50r=1a2r

The value of integral ∫xdx(1−x4)3/2 is(where C is constant of integration)

If x=3tant and y=3sect, then the value of d2ydx2 at t=π4, is :

Question 96Shoes of the following brands are sold in November 2007 at a shoe store. Construct a pie chart for the given data.BrandNumber of pairs of shoes soldA130B120C90D40E20

Angle between 2 planes will be same as

If cosx+cos(k+x)−cos(k−x)=2 has real solutions, then

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?

if x-1/x=2 then x2+1/x2=

find next term 0,6,24,60,120,

Numerically greatest term in the expansion of (2+3x)9, where x=32 is

If the 2nd and 5th terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______​.

If the 2nd and 5th terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______.