43030 + Interview Questions in Mathematics

1.	For a function f:A→B, let the number of elements in set A and B be 4 and 5 respectively. If the number of many one functions are N, then value of N101 is
Answer» For a function $f : A \to B,$ let the number of elements in set $A$ and $B$ be $4$ and $5$ respectively. If the number of many one functions are $N,$ then value of $\frac{N}{101}$ is

Discussion

2.	If α,β,γ are roots of equation x3−x−1=0, then the equation whose roots are 1β+γ,1γ+α,1α+β is -
Answer» If $α, β, γ$ are roots of equation $x^{3} - x - 1 = 0$ , then the equation whose roots are $\frac{1}{β + γ}, \frac{1}{γ + α}, \frac{1}{α + β}$ is -

Discussion

3.	1. Check the bijectivity of the function f: R-->R given by f(x) = 3-2sinx.
Answer» 1. Check the bijectivity of the function f: R-->R given by f(x) = 3-2sinx.

Discussion

4.	Prove that tan−1√x=12cos−1(1−x1+x),x∈[0,1]
Answer» Prove that ${tan}^{- 1} \sqrt{x} = \frac{1}{2} {cos}^{- 1} (\frac{1 - x}{1 + x}), x \in [0, 1]$

Discussion

5.	Prove the following by using the principle of mathematical induction for all n∈N.1+3+32+⋯+3n−1=(3n−1)2.
Answer» Prove the following by using the principle of mathematical induction for all $n \in N$ . $1 + 3 + 3^{2} + \dots + 3^{n - 1} = \frac{(3^{n} - 1)}{2}$ .

Discussion

6.	Let S=121.3+223.5+325.7+......+5002999.1001 then the number of positive divisors of [S] is (where [.] denotes the greatest integer function)
Answer» Let $S = \frac{1^{2}}{1.3} + \frac{2^{2}}{3.5} + \frac{3^{2}}{5.7} + . . . . . . + \frac{500^{2}}{999.1001}$ then the number of positive divisors of $[S]$ is (where $[.]$ denotes the greatest integer function)

Discussion

7.	Find the derivative of ea cos-1 x
Answer» Find the derivative of e^{a cos-1 x}

Discussion

8.	find the domain and range of y=\sqrt{x^2-3x+2
Answer» find the domain and range of y=\sqrt{x^2-3x+2

Discussion

9.	The solution of the differential equation dydx+1+x2x=0 is
Answer» The solution of the differential equation $\frac{d y}{d x} + \frac{1 + x^{2}}{x} = 0$ is

9.

The solution of the differential equation dydx+1+x2x=0 is

Answer»

The solution of the differential equation $\frac{d y}{d x} + \frac{1 + x^{2}}{x} = 0$ is

Discussion

10.	The integer part of the number 44∑k=01cosk∘cos(k+1)∘ is
Answer» The integer part of the number $44 \sum k = 0 \frac{1}{cos k^{\circ} cos (k + 1)^{\circ}}$ is

Discussion

11.	11. Correct increasing order of e/m value is 1- alpha < p < e - < n 2- p < alpha < e - < n 3- n < alpha < p < e - 4- alpha < n < p < e-
Answer» 11. Correct increasing order of e/m value is 1- alpha < p < e - < n 2- p < alpha < e - < n 3- n < alpha < p < e - 4- alpha < n < p < e-

Discussion

12.	Find the area of the minor segment of the circle x2+y2=a2 cut off by the line x=a2.
Answer» Find the area of the minor segment of the circle $x^{2} + y^{2} = a^{2}$ cut off by the line $x = \frac{a}{2}$ .

Discussion

13.	6. e sin 5x
Answer» 6. e sin 5x

Discussion

14.	Let α,β be the values of m for which the equation (1+m)x2−2(1+3m)x+(1+8m) has equal roots. Find the equation whose roots are α+2 and β+2.
Answer» Let $α, β$ be the values of m for which the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m)$ has equal roots. Find the equation whose roots are $α + 2$ and $β + 2$ .

Discussion

15.	There are 8 intermediate stations on a railway line from one terminus to another. Find the number of ways in which a train can stop at 3 stations such that two of the stations are consecutive.
Answer» There are $8$ intermediate stations on a railway line from one terminus to another. Find the number of ways in which a train can stop at $3$ stations such that two of the stations are consecutive.

Discussion

16.	The curve between absolute temperature & V2rmsis:
Answer» The curve between absolute temperature & $V_{r m s}^{2}$ is:

Discussion

17.	If < l, m, n> and are the direction cosines of two straight lines then find the maximum value of the expression lp + mq + nr + (mr-qn)² + (np- rl)² + (lq - pm)².
Answer» If < l, m, n> and are the direction cosines of two straight lines then find the maximum value of the expression lp + mq + nr + (mr-qn)² + (np- rl)² + (lq - pm)².

Discussion

18.	A circle has radius 3 units and its centre lies on the line y=x-1 . if it passes through (7,3), then its equation is ?
Answer» A circle has radius 3 units and its centre lies on the line y=x-1 . if it passes through (7,3), then its equation is ?

Discussion

19.	Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = { ( x , y ): 3 x – y = 0, where x , y ∈ A}. Write down its domain, codomain and range.
Answer» Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = { ( x , y ): 3 x – y = 0, where x , y ∈ A}. Write down its domain, codomain and range.

Discussion

20.	The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, in which subject did the student score 105 marks?
Answer» The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, in which subject did the student score 105 marks?

Discussion

21.	{ 43. From the point }(1,1) tangents are drawn to the curve }}{ represented parametrically as }x=2t-t^2 and }y=t+t^2 . }} The distance between the points of contact is
Answer» { 43. From the point }(1,1) tangents are drawn to the curve }}{ represented parametrically as }x=2t-t^2 and }y=t+t^2 . }} The distance between the points of contact is

Discussion

22.	List I has four entries and List II has five entries. Each entry of List I is to be correctly matched with one or more than one entries of List II. List IList II (A)Let f:A→B be a function defined by (P)−1 f(x)=log(x2−7\|x\|+12). If C=Z−A is a set, then an element in C is (B)A solution of the inequation(Q)0∣∣∣2x−4∣∣∣>1 is(C)If f(x)=log(1−\|x\|\|x−2\|), then an(R)1integer which is not in the domainof f, is(D)An element in the domain of the (S)2function f(x)=ex−4x2√4x−x2 is(T)3Which of the following is the only INCORRECT combination?
Answer» $List I$ has four entries and $List II$ has five entries. Each entry of $List I$ is to be correctly matched with one or more than one entries of $List II .$ $\begin{matrix} List I & List II (A) & Let f : A \to B be a function defined by & (P) & - 1 f (x) = log (x^{2} - 7 \| x \| + 12) . If C = Z - A is a set, then an element in C is (B) & A solution of the inequation & (Q) & 0 ∣ ∣ ∣ \frac{2}{x - 4} ∣ ∣ ∣ > 1 is (C) & If f (x) = log (\frac{1 - \| x \|}{\| x - 2 \|}), then an & (R) & 1 integer which is not in the domain of f, is (D) & An element in the domain of the & (S) & 2 function f (x) = \frac{e^{x - 4 x^{2}}}{\sqrt{4 x - x^{2}}} is (T) & 3 \end{matrix}$ Which of the following is the only INCORRECT combination?

Discussion

23.	Two cutting tools with tool life equations given below are being compared: Tool 1 : VT0.1 = 150 Too1 2 : VT0.3 = 300 where V is cutting sped in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is m/minute.
Answer» Two cutting tools with tool life equations given below are being compared: Tool 1 : $V T^{0.1}$ = 150 Too1 2 : $V T^{0.3}$ = 300 where V is cutting sped in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is m/minute.

Discussion

24.	if x+1x = p+q and x-1/x = p-q where x is not equal to 0,1 then which of the following is correct
Answer» if x+1x = p+q and x-1/x = p-q where x is not equal to 0,1 then which of the following is correct

Discussion

25.	The value of (cosθ+sinθ+1)(cosθ+sinθ−1)−2sinθcosθ is
Answer» The value of $(cos θ + sin θ + 1) (cos θ + sin θ - 1) - 2 sin θ cos θ$ is

Discussion

26.	How to find the degree and order of differential equation?
Answer» How to find the degree and order of differential equation?

Discussion

27.	Choose the correct alternative in the following question:If PA=310, PB=25 and PA∪B=35, then PA\|B+PB\|A equalsa 14 b 712 c 512 d 13
Answer» Choose the correct alternative in the following question: $If P (A) = \frac{3}{10}, P (B) = \frac{2}{5} and P (A \cup B) = \frac{3}{5}, then P (A \| B) + P (B \| A) equals (a) \frac{1}{4} (b) \frac{7}{12} (c) \frac{5}{12} (d) \frac{1}{3}$

Discussion

28.	If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
Answer» If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Discussion

29.	Find sets A, B and C such that A∩B, B∩C and A∩C are non-empty sets and A∩B∩C=Φ.
Answer» Find sets A, B and C such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C = Φ .$

Discussion

30.	Nick and Amy are practicing graph translations by moving y=2x on the coordinate plane. Nick moved the graph by 5 units to the left and a units downward and obtained L1. Amy moved the graph by b units to the right and 3 units upward and obtained L2.If L1 and L2 are graphically represented as shown in the diagram below,then value of a+2b is
Answer» Nick and Amy are practicing graph translations by moving $y = 2 x$ on the coordinate plane. Nick moved the graph by $5$ units to the left and $a$ units downward and obtained $L_{1} .$ Amy moved the graph by $b$ units to the right and $3$ units upward and obtained $L_{2} .$ If $L_{1}$ and $L_{2}$ are graphically represented as shown in the diagram below,then value of $a + 2 b$ is

Discussion

31.	A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
Answer» A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?

Discussion

32.	The real part of (1−cosθ+isinθ)−1 is
Answer» The real part of $(1 - cos θ + i sin θ)^{- 1}$ is

Discussion

33.	If 599 is divided by 13, then the remainder is
Answer» If $5^{99}$ is divided by $13$ , then the remainder is

Discussion

34.	In a ΔABC, cosA⋅cosC=λ(c2−a2)3ac, where AD is the median through A and AD⊥AC, then the value of λ is
Answer» In a $Δ A B C, cos A \cdot cos C = \frac{λ (c^{2} - a^{2})}{3 a c}$ , where $A D$ is the median through $A$ and $A D ⊥ A C$ , then the value of $λ$ is

Discussion

35.	If the odds against an event be 2 : 3, then the probability of its occurrence is
Answer» If the odds against an event be 2 : 3, then the probability of its occurrence is

Discussion

36.	If 2x ≤ 7 and 2x > 3, what is the possible range of values for x?
Answer» If 2x $\leq$ 7 and 2x > 3, what is the possible range of values for x?

Discussion

37.	If x = cy + bz, y = az + cx, z = bx + ay (where x, y, z are not all zero) have a solution other than x = 0, y = 0, z = 0, then a, b and c are connected by the relation
Answer» If x = cy + bz, y = az + cx, z = bx + ay (where x, y, z are not all zero) have a solution other than x = 0, y = 0, z = 0, then a, b and c are connected by the relation

Discussion

38.	Let y=xxx..., then dydx is equal to
Answer» Let $y = x^{x^{x^{.^{.^{.}}}}}$ , then $\frac{d y}{d x}$ is equal to

Discussion

39.	Coefficient of xn in (x+nC0)(x+3nCl)(x+5nC2)⋯(x+(2n+1)nCn) is
Answer» Coefficient of $x^{n}$ in $(x +^{n} C_{0}) (x + 3^{n} C_{l}) (x + 5^{n} C_{2}) \dots (x + (2 n + 1)^{n} C_{n})$ is

Discussion

40.	42. The distance between the foci of an ellipse is 10 and length of latus rectum is 15; find its equation referred to its axes as axes of co-ordinates
Answer» 42. The distance between the foci of an ellipse is 10 and length of latus rectum is 15; find its equation referred to its axes as axes of co-ordinates

Discussion

41.	Choose the correct answer in each of the question. ∫x(x−1)(x−2)dx equals (a)log∣∣∣(x−1)2x−2∣∣∣+C(b)log∣∣∣(x−2)2x−1∣∣∣+C(c)log∣∣(x−1x−2)2∣∣(d)log\|((x−1)(x−2))\|+C
Answer» Choose the correct answer in each of the question. $\int \frac{x}{(x - 1) (x - 2)} d x$ equals $(a) l o g ∣ ∣ ∣ \frac{(x - 1)^{2}}{x - 2} ∣ ∣ ∣ + C (b) l o g ∣ ∣ ∣ \frac{(x - 2)^{2}}{x - 1} ∣ ∣ ∣ + C (c) l o g ∣ ∣ (\frac{x - 1}{x - 2})^{2} ∣ ∣ (d) l o g \| ((x - 1) (x - 2)) \| + C$

Discussion

42.	43.14.vertices (±7,0), e=
Answer» 43.14.vertices (±7,0), e=

Discussion

43.	Prove that:1-cos 2x1+cos 2x=tan x
Answer» Prove that: $\sqrt{\frac{1 - \cos 2 x}{1 + \cos 2 x}} = \tan x$

Discussion

44.	If in the determinant Δ = ∣∣∣∣a1b1c1a2b2c2a3b3c3∣∣∣∣, A1, B1, C1 etc. be the co-factors of a1, b1, c1 etc., then which of the following relations is incorrect
Answer» If in the determinant $Δ = ∣ ∣∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣∣ ∣, A_{1}, B_{1}, C_{1}$ etc. be the co-factors of $a_{1}, b_{1}, c_{1}$ etc., then which of the following relations is incorrect

Discussion

45.	68. If root of x/y + root of y/x equals to 10/3 . Then find xy .
Answer» 68. If root of x/y + root of y/x equals to 10/3 . Then find xy .

Discussion

46.	Solution of differential equation (1+x)(1+y^2)dx+(1+y)(1+x^2)dy=0 is
Answer» Solution of differential equation (1+x)(1+y^2)dx+(1+y)(1+x^2)dy=0 is

Discussion

47.	Let adj(X) denote the adjoint of matrix X. If A is a non-singular matrix of order 2 such that ∣∣A+\|A\|adj(A)∣∣=0, then the value of ∣∣A−\|A\|adj(A)∣∣ is
Answer» Let $adj (X)$ denote the adjoint of matrix $X .$ If $A$ is a non-singular matrix of order $2$ such that $∣ ∣ A + \| A \| adj (A) ∣ ∣ = 0,$ then the value of $∣ ∣ A - \| A \| adj (A) ∣ ∣$ is

Discussion

48.	Suppose C is the closed curve defined as the circle x2+y2=1 with C oriented anti clockwise. The value of ∮(xy2dx+x2ydy) over the curve C equals ______0
Answer» Suppose C is the closed curve defined as the circle $x^{2} + y^{2} = 1$ with C oriented anti clockwise. The value of $\oint (x y^{2} d x + x^{2} y d y)$ over the curve C equals ______ 0

Discussion

49.	If x and (20+y)∘ are the supplementary angles and difference between them is 60∘, then the value of y is
Answer» If $x$ and $(20 + y)^{\circ}$ are the supplementary angles and difference between them is $60^{\circ}$ , then the value of $y$ is

Discussion

50.	Figure shows a 11.7 ft wide ditch with the approach roads at an angle of 150 with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch ? Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach.
Answer» Figure shows a 11.7 ft wide ditch with the approach roads at an angle of $15^{0}$ with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch ? Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach.

50.

Figure shows a 11.7 ft wide ditch with the approach roads at an angle of 150 with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch ? Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach.

Answer»

Figure shows a 11.7 ft wide ditch with the approach roads at an angle of $15^{0}$ with the horizontal. With what minimum speed should a motorbike be moving on the road so that it safely crosses the ditch ?

Assume that the length of the bike is 5 ft, and it leaves the road when the front part runs out of the approach.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

For a function f:A→B, let the number of elements in set A and B be 4 and 5 respectively. If the number of many one functions are N, then value of N101 is

If α,β,γ are roots of equation x3−x−1=0, then the equation whose roots are 1β+γ,1γ+α,1α+β is -

1. Check the bijectivity of the function f: R-->R given by f(x) = 3-2sinx.

Prove that tan−1√x=12cos−1(1−x1+x),x∈[0,1]

Prove the following by using the principle of mathematical induction for all n∈N.1+3+32+⋯+3n−1=(3n−1)2.

Let S=121.3+223.5+325.7+......+5002999.1001 then the number of positive divisors of [S] is (where [.] denotes the greatest integer function)

Find the derivative of ea cos-1 x

find the domain and range of y=\sqrt{x^2-3x+2

The solution of the differential equation dydx+1+x2x=0 is

The integer part of the number 44∑k=01cosk∘cos(k+1)∘ is

11. Correct increasing order of e/m value is 1- alpha < p < e - < n 2- p < alpha < e - < n 3- n < alpha < p < e - 4- alpha < n < p < e-

Find the area of the minor segment of the circle x2+y2=a2 cut off by the line x=a2.

6. e sin 5x

Let α,β be the values of m for which the equation (1+m)x2−2(1+3m)x+(1+8m) has equal roots. Find the equation whose roots are α+2 and β+2.

There are 8 intermediate stations on a railway line from one terminus to another. Find the number of ways in which a train can stop at 3 stations such that two of the stations are consecutive.

The curve between absolute temperature &amp; V2rmsis:

If < l, m, n> and are the direction cosines of two straight lines then find the maximum value of the expression lp + mq + nr + (mr-qn)² + (np- rl)² + (lq - pm)².

A circle has radius 3 units and its centre lies on the line y=x-1 . if it passes through (7,3), then its equation is ?

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = { ( x , y ): 3 x – y = 0, where x , y ∈ A}. Write down its domain, codomain and range.

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, in which subject did the student score 105 marks?

{ 43. From the point }(1,1) tangents are drawn to the curve }}{ represented parametrically as }x=2t-t^2 and }y=t+t^2 . }} The distance between the points of contact is

Two cutting tools with tool life equations given below are being compared: Tool 1 : VT0.1 = 150 Too1 2 : VT0.3 = 300 where V is cutting sped in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is m/minute.

if x+1x = p+q and x-1/x = p-q where x is not equal to 0,1 then which of the following is correct

The value of (cosθ+sinθ+1)(cosθ+sinθ−1)−2sinθcosθ is

How to find the degree and order of differential equation?

Choose the correct alternative in the following question:If PA=310, PB=25 and PA∪B=35, then PA|B+PB|A equalsa 14 b 712 c 512 d 13

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Find sets A, B and C such that A∩B, B∩C and A∩C are non-empty sets and A∩B∩C=Φ.

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?

The real part of (1−cosθ+isinθ)−1 is

If 599 is divided by 13, then the remainder is

In a ΔABC, cosA⋅cosC=λ(c2−a2)3ac, where AD is the median through A and AD⊥AC, then the value of λ is

If the odds against an event be 2 : 3, then the probability of its occurrence is

If 2x ≤ 7 and 2x &gt; 3, what is the possible range of values for x?

If x = cy + bz, y = az + cx, z = bx + ay (where x, y, z are not all zero) have a solution other than x = 0, y = 0, z = 0, then a, b and c are connected by the relation

Let y=xxx..., then dydx is equal to

Coefficient of xn in (x+nC0)(x+3nCl)(x+5nC2)⋯(x+(2n+1)nCn) is

42. The distance between the foci of an ellipse is 10 and length of latus rectum is 15; find its equation referred to its axes as axes of co-ordinates

Choose the correct answer in each of the question. ∫x(x−1)(x−2)dx equals (a)log∣∣∣(x−1)2x−2∣∣∣+C(b)log∣∣∣(x−2)2x−1∣∣∣+C(c)log∣∣(x−1x−2)2∣∣(d)log|((x−1)(x−2))|+C

43.14.vertices (±7,0), e=

Prove that:1-cos 2x1+cos 2x=tan x

If in the determinant Δ = ∣∣∣∣a1b1c1a2b2c2a3b3c3∣∣∣∣, A1, B1, C1 etc. be the co-factors of a1, b1, c1 etc., then which of the following relations is incorrect

68. If root of x/y + root of y/x equals to 10/3 . Then find xy .

Solution of differential equation (1+x)(1+y^2)dx+(1+y)(1+x^2)dy=0 is

Let adj(X) denote the adjoint of matrix X. If A is a non-singular matrix of order 2 such that ∣∣A+|A|adj(A)∣∣=0, then the value of ∣∣A−|A|adj(A)∣∣ is

Suppose C is the closed curve defined as the circle x2+y2=1 with C oriented anti clockwise. The value of ∮(xy2dx+x2ydy) over the curve C equals ______0

If x and (20+y)∘ are the supplementary angles and difference between them is 60∘, then the value of y is

The curve between absolute temperature & V2rmsis:

If 2x ≤ 7 and 2x > 3, what is the possible range of values for x?