43030 + Interview Questions in Mathematics

1.	If the normal to the rectangular hyperbola xy=c2 at the point (ct,ct) meets the curve again at (ct′,ct′), then
Answer» If the normal to the rectangular hyperbola $x y = c^{2}$ at the point $(c t, \frac{c}{t})$ meets the curve again at $(c t^{'}, {\frac{c}{t}}^{'}),$ then

Discussion

2.	If α,β,γ are the roots of x3−3x+7=0, then the equation whose roots are α+β−γ,β+γ−α,γ+α−β is
Answer» If $α, β, γ$ are the roots of $x^{3} - 3 x + 7 = 0$ , then the equation whose roots are $α + β - γ, β + γ - α, γ + α - β$ is

Discussion

3.	if y= 2/sin theta + root 3 cos theta ,then minimum value of y is
Answer» if y= 2/sin theta + root 3 cos theta ,then minimum value of y is

Discussion

4.	258.Given a vector A-31-4). Which of thefollowing is perpendicular to it ?(A) 3i(B) 4j(C) 4i+3)(D) 3i +4j
Answer» 258.Given a vector A-31-4). Which of thefollowing is perpendicular to it ?(A) 3i(B) 4j(C) 4i+3)(D) 3i +4j

Discussion

5.	In huckels rule 4n+2π rule what is n
Answer» In huckels rule 4n+2π rule what is n

Discussion

6.	Find the radian measures corresponding to the following degree measure (1)39^°22'30"
Answer» Find the radian measures corresponding to the following degree measure (1)39^°22'30"

Discussion

7.	34. If the equation x⁴-4x³+ax²+bx+1=0 has 4 positive roots, then the value of (\|a\|+\|b\|)/(a+b) is. 5/3/-5/-3
Answer» 34. If the equation x⁴-4x³+ax²+bx+1=0 has 4 positive roots, then the value of (\|a\|+\|b\|)/(a+b) is. 5/3/-5/-3

Discussion

8.	If →a,→b and →c are non-coplanar vectors and →a×→c is perpendicular to →a×(→b×→c), then the value of [→a×(→b×→c)]×→c is equal to
Answer» $If \to a, \to b and \to c$ are non-coplanar vectors and $\to a \times \to c$ is perpendicular to $\to a \times (\to b \times \to c),$ then the value of $[\to a \times (\to b \times \to c)] \times \to c$ is equal to

Discussion

9.	Match the following:Column AColumn B1. A={x:x is an odd natural number}a. {12,13,23,34,35,57}2. B={x:x=(n2),n∈N and x<100}b. {1,4,9,16,25,........10000}3. C={x:x=nn+2,n∈N and 1≤n≤6}c.{1,4,9,16,25,36,49,64,81}4. D={x:x is a letter of the word TRIGONOMETRY}d. {G,E,I,M,N,O,R,T,Y} e. {1,3,5,7,9,...............}
Answer» Match the following: $\begin{matrix} Column A & Column B 1. A = {x : x i s a n o d d n a t u r a l n u m b e r} & a . {\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{3}{4}, \frac{3}{5}, \frac{5}{7}} 2. B = {x : x = (n^{2}), n \in N a n d x < 100} & b . {1, 4, 9, 16, 25, . . . . . . . .10000} 3. C = {x : x = \frac{n}{n + 2}, n \in N a n d 1 \leq n \leq 6} & c . {1, 4, 9, 16, 25, 36, 49, 64, 81} 4. D = {x : x i s a l e t t e r o f t h e w o r d T R I G O N O M E T R Y} & d . {G, E, I, M, N, O, R, T, Y} e . {1, 3, 5, 7, 9, . . . . . . . . . . . . . . .} \end{matrix}$

Discussion

10.	Find the values of x for which is an increasing function.
Answer» Find the values of x for which is an increasing function.

Discussion

11.	If (p ∧∼q)∧(p∧r)→ ∼p ∨q is false, then the truth values of p,q and r are, repectively :
Answer» If $(p \land \sim q) \land (p \land r) \to \sim p \lor q$ is false, then the truth values of $p, q$ and $r$ are, repectively :

Discussion

12.	10.x, rs, x,n terms (ifx # ± 1).
Answer» 10.x, rs, x,n terms (ifx # ± 1).

Discussion

13.	The random variable X has probability distribution P(X) of the following form, where k is some number: (a) Determine the value of k . (b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).
Answer» The random variable X has probability distribution P(X) of the following form, where k is some number: (a) Determine the value of k . (b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

Discussion

14.	The sides of a rectangle of the greatest area which can be inscribed into an ellipse x2/25 + y2/9 = 1 are
Answer» The sides of a rectangle of the greatest area which can be inscribed into an ellipse x²/25 + y²/9 = 1 are

Discussion

15.	Find the area of the region bounded bythe ellipse
Answer» Find the area of the region bounded by the ellipse

Discussion

16.	Let →a,→c be unit vectors and \|→b\|=4. The angle between →a and →c is cos−1(14). Then the positive integral value of λ such that →b−2→c=λ→a is ___
Answer» Let $\to a, \to c$ be unit vectors and $\| \to b \| = 4$ . The angle between $\to a a n d \to c$ is ${c o s}^{- 1} (\frac{1}{4})$ . Then the positive integral value of $λ$ such that $\to b - 2 \to c = λ \to a$ is ___

Discussion

17.	Write the following decimal in the place value table: 205.9
Answer» Write the following decimal in the place value table: 205.9

17.

Write the following decimal in the place value table: 205.9

Answer»

Write the following decimal in the place value table:

205.9

Discussion

18.	Pick out the personal pronoun from the sentence. They were afraid of confessing their mistake before everyone.
Answer» Pick out the personal pronoun from the sentence. They were afraid of confessing their mistake before everyone.

18.

Pick out the personal pronoun from the sentence. They were afraid of confessing their mistake before everyone.

Answer»

Pick out the personal pronoun from the sentence.

They were afraid of confessing their mistake before everyone.

Discussion

19.	If y=(tan22x−tan2x1−tan22xtan2x)cot3x, then y′(π4)=
Answer» If $y = (\frac{{tan}^{2} 2 x - {tan}^{2} x}{1 - {tan}^{2} 2 x {tan}^{2} x}) cot 3 x,$ then $y^{'} (\frac{π}{4}) =$

Discussion

20.	For allreal values of x, the minimum value of is(A) 0 (B) 1(C) 3 (D)
Answer» For all real values of x, the minimum value of is (A) 0 (B) 1 (C) 3 (D)

20.

For allreal values of x, the minimum value of is(A) 0 (B) 1(C) 3 (D)

Answer»

For all
real values of x, the minimum value of

is

(A) 0 (B) 1

(C) 3 (D)

Discussion

21.	1+7i(2−i)2=
Answer» $\frac{1 + 7 i}{(2 - i)^{2}}$ =

Discussion

22.	If α,β are the eccentric angles of the extremities of a focal chord of an ellipse, then eccentricity of the ellipse is
Answer» If $α, β$ are the eccentric angles of the extremities of a focal chord of an ellipse, then eccentricity of the ellipse is

Discussion

23.	(2nC0)2−(2nC1)2+(2nC2)2−…(2nC2n)2=
Answer» $(^{2 n} C_{0})^{2} - (^{2 n} C_{1})^{2} + (^{2 n} C_{2})^{2} - \dots (^{2 n} C_{2 n})^{2} =$

Discussion

24.	The value of π4∫π6cosecx dx is;
Answer» The value of $\frac{π}{4} \int \frac{π}{6} cosec x d x$ is;

Discussion

25.	If the roots of the equation (a²+b²)x² -2b(a+c)x + (b²+c²) = 0 are equal, thenA. 2b = a+cB. b² = acC. b = 2ac/ a+cD. b = ac
Answer» If the roots of the equation (a²+b²)x² -2b(a+c)x + (b²+c²) = 0 are equal, then A. 2b = a+c B. b² = ac C. b = 2ac/ a+c D. b = ac

Discussion

26.	The square of distance between the point of intersection of the lines represented by the equation ax2+2hxy+by2+2gx+2fy+c=0 and origin, is
Answer» The square of distance between the point of intersection of the lines represented by the equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ and origin, is

Discussion

27.

Construct price index number of the following data by using:(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method. Items Base Year Current Year Quantity Price Quantity Price A B C D 3 7 4 6 5 4 7 6 2 5 3 5 8 6 10 7

Answer» Construct price index number of the following data by using:

(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.

Items	Base Year		Current Year
Items	Quantity	Price	Quantity	Price
A B C D	3 7 4 6	5 4 7 6	2 5 3 5	8 6 10 7

Discussion

28.	The standard deviation of the observations 6,5,9,13,12,8,10 is
Answer» The standard deviation of the observations 6,5,9,13,12,8,10 is

Discussion

29.	If 2 cos x +sin x =1 then 7 cos x +6 sin x=___
Answer» If 2 cos x +sin x =1 then 7 cos x +6 sin x=___

Discussion

30.	Inverse of the matrix⎡⎢⎣3−2−1−41−1201⎤⎥⎦ is [MP PET 1990]
Answer» $\begin{matrix} I n v e r s e o f t h e m a t r i x ⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & - 1 - 4 & 1 & - 1 2 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ \end{matrix}$ is [MP PET 1990]

30.

Inverse of the matrix⎡⎢⎣3−2−1−41−1201⎤⎥⎦ is [MP PET 1990]

Answer»

$\begin{matrix} I n v e r s e o f t h e m a t r i x ⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & - 1 - 4 & 1 & - 1 2 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ \end{matrix}$ is [MP PET 1990]

Discussion

31.	sin 25° sin 50° sin 90° sec 40° sec 65° = ___.
Answer» sin 25° sin 50° sin 90° sec 40° sec 65° = ___.

Discussion

32.	∫π20sin4xsin4x+cos4x dx=
Answer» $\int_{0}^{\frac{π}{2}} \frac{s i n^{4} x}{s i n^{4} x + c o s^{4} x} d x =$

Discussion

33.	The points (3, 9), (4, 8) and (5, 7) are _____
Answer» The points (3, 9), (4, 8) and (5, 7) are _____

Discussion

34.	Find the equation of the circle with radius 5 whose centre lies on x -axis and passes through the point (2, 3).
Answer» Find the equation of the circle with radius 5 whose centre lies on x -axis and passes through the point (2, 3).

Discussion

35.	The relation R defined on the set A={1,2,3,4,5} as R={(a,b):\|a2−b2\|<16} has cardinality equal to
Answer» The relation $R$ defined on the set $A = {1, 2, 3, 4, 5}$ as $R = {(a, b) : \| a^{2} - b^{2} \| < 16}$ has cardinality equal to

Discussion

36.	19. If x R, then find the max. And min. Values of x-6x+4/x+2x+4 are?
Answer» 19. If x R, then find the max. And min. Values of x-6x+4/x+2x+4 are?

Discussion

37.	If f(x)=11−x, show that f[f{f(x)}]=x.
Answer» If $f (x) = \frac{1}{1 - x}$ , show that $f [f {f (x)}] = x$ .

Discussion

38.	If , find a unit vector parallel to the vector .
Answer» If , find a unit vector parallel to the vector .

Discussion

39.	The degree of the differential equation 1+d2ydx2=dydx+x is ______________.
Answer» The degree of the differential equation $\sqrt{1 + \frac{d^{2} y}{d x^{2}}} = \frac{d y}{d x} + x$ is ______________.

Discussion

40.	Choose the correct alternative in the following question:If A and B are two events associated to a random experiment such that PA∩B=710 and PB=1720, then P(A\|B) =a 1417 b 1720 c 78 d 18
Answer» Choose the correct alternative in the following question: If A and B are two events associated to a random experiment such that $P (A \cap B) = \frac{7}{10} and P (B) = \frac{17}{20}$ , then P(A\|B) = $(a) \frac{14}{17} (b) \frac{17}{20} (c) \frac{7}{8} (d) \frac{1}{8}$

Discussion

41.	If f(x)=x√1−x2,g(x)=x√1+x2 then ddx(fog)(x)=
Answer» $I f f (x) = \frac{x}{\sqrt{1 - x^{2}}}, g (x) = \frac{x}{\sqrt{1 + x^{2}}} t h e n \frac{d}{d x} (f o g) (x) =$

Discussion

42.	For a biased die, the probability of getting an even number is twice the probability of getting an odd number. The die is thrown twice and the sum of the outcomes is even. Then the probability that both the outcomes on the die is an odd number is
Answer» For a biased die, the probability of getting an even number is twice the probability of getting an odd number. The die is thrown twice and the sum of the outcomes is even. Then the probability that both the outcomes on the die is an odd number is

Discussion

43.	lim to 0+ sin(root)/root(sin)=
Answer» lim to 0+ sin(root)/root(sin)=

Discussion

44.	17. c_c_b_aca_cac_b(1) acaab(2) abcab(3) aacba(4) abcca
Answer» 17. c_c_b_aca_cac_b (1) acaab (2) abcab (3) aacba (4) abcca

Discussion

45.	Int (e^x){(1+sin 2x)/(1-sin 2x)
Answer» Int (e^x){(1+sin 2x)/(1-sin 2x)

Discussion

46.	29. Find Arg( sin8Π/5 + i [ 1+ cos 8Π/5] )
Answer» 29. Find Arg( sin8Π/5 + i [ 1+ cos 8Π/5] )

Discussion

47.	If x=sint,y=tcost. Then dydx is equal to
Answer» If $x = sin t, y = t cos t .$ Then $\frac{d y}{d x}$ is equal to

Discussion

48.	Let X={n∈N:1≤n≤50}. If A={n∈X:n is a multiple of 2} and B={n∈X:n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is
Answer» Let $X = {n \in N : 1 \leq n \leq 50}$ . If $A = {n \in X : n is a multiple of 2}$ and $B = {n \in X : n is a multiple of 7}$ , then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

Discussion

49.	Let y=g(x) be the solution of differential equation dydx+y=2xe−x1+yex such that g(0)=1. If [.] denotes the greatest integer function, then [g(−1)e] is equal to
Answer» Let $y = g (x)$ be the solution of differential equation $\frac{d y}{d x} + y = \frac{2 x e^{- x}}{1 + y e^{x}}$ such that $g (0) = 1.$ If $[.]$ denotes the greatest integer function, then $[\frac{g (- 1)}{e}]$ is equal to

Discussion

50.	If graph of y=ax2−bx+c is following, then sign of a, b, c are
Answer» If graph of $y = a x^{2} - b x + c$ is following, then sign of $a, b, c$ are

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the normal to the rectangular hyperbola xy=c2 at the point (ct,ct) meets the curve again at (ct′,ct′), then

If α,β,γ are the roots of x3−3x+7=0, then the equation whose roots are α+β−γ,β+γ−α,γ+α−β is

if y= 2/sin theta + root 3 cos theta ,then minimum value of y is

258.Given a vector A-31-4). Which of thefollowing is perpendicular to it ?(A) 3i(B) 4j(C) 4i+3)(D) 3i +4j

In huckels rule 4n+2π rule what is n

Find the radian measures corresponding to the following degree measure (1)39^°22'30"

34. If the equation x⁴-4x³+ax²+bx+1=0 has 4 positive roots, then the value of (|a|+|b|)/(a+b) is. 5/3/-5/-3

If →a,→b and →c are non-coplanar vectors and →a×→c is perpendicular to →a×(→b×→c), then the value of [→a×(→b×→c)]×→c is equal to

Find the values of x for which is an increasing function.

If (p ∧∼q)∧(p∧r)→ ∼p ∨q is false, then the truth values of p,q and r are, repectively :

10.x, rs, x,n terms (ifx # ± 1).

The random variable X has probability distribution P(X) of the following form, where k is some number: (a) Determine the value of k . (b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

The sides of a rectangle of the greatest area which can be inscribed into an ellipse x​​​​​​2/25 + y​​​​​​2/9 = 1 are

Find the area of the region bounded bythe ellipse

Let →a,→c be unit vectors and |→b|=4. The angle between →a and →c is cos−1(14). Then the positive integral value of λ such that →b−2→c=λ→a is ___

Write the following decimal in the place value table: 205.9

Pick out the personal pronoun from the sentence. They were afraid of confessing their mistake before everyone.

If y=(tan22x−tan2x1−tan22xtan2x)cot3x, then y′(π4)=

For allreal values of x, the minimum value of is(A) 0 (B) 1(C) 3 (D)

1+7i(2−i)2=

If α,β are the eccentric angles of the extremities of a focal chord of an ellipse, then eccentricity of the ellipse is

(2nC0)2−(2nC1)2+(2nC2)2−…(2nC2n)2=

The value of π4∫π6cosecx dx is;

If the roots of the equation (a²+b²)x² -2b(a+c)x + (b²+c²) = 0 are equal, thenA. 2b = a+cB. b² = acC. b = 2ac/ a+cD. b = ac

The square of distance between the point of intersection of the lines represented by the equation ax2+2hxy+by2+2gx+2fy+c=0 and origin, is

Construct price index number of the following data by using:(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method. Items Base Year Current Year Quantity Price Quantity Price A B C D 3 7 4 6 5 4 7 6 2 5 3 5 8 6 10 7

The standard deviation of the observations 6,5,9,13,12,8,10 is

If 2 cos x +sin x =1 then 7 cos x +6 sin x=___

Inverse of the matrix⎡⎢⎣3−2−1−41−1201⎤⎥⎦ is [MP PET 1990]

sin 25° sin 50° sin 90° sec 40° sec 65° = ___.

∫π20sin4xsin4x+cos4x dx=

The points (3, 9), (4, 8) and (5, 7) are _____

Find the equation of the circle with radius 5 whose centre lies on x -axis and passes through the point (2, 3).

The relation R defined on the set A={1,2,3,4,5} as R={(a,b):|a2−b2|&lt;16} has cardinality equal to

19. If x R, then find the max. And min. Values of x-6x+4/x+2x+4 are?

If f(x)=11−x, show that f[f{f(x)}]=x.

If , find a unit vector parallel to the vector .

The degree of the differential equation 1+d2ydx2=dydx+x is ______________.

Choose the correct alternative in the following question:If A and B are two events associated to a random experiment such that PA∩B=710 and PB=1720, then P(A|B) =a 1417 b 1720 c 78 d 18

If f(x)=x√1−x2,g(x)=x√1+x2 then ddx(fog)(x)=

For a biased die, the probability of getting an even number is twice the probability of getting an odd number. The die is thrown twice and the sum of the outcomes is even. Then the probability that both the outcomes on the die is an odd number is

lim to 0+ sin(root)/root(sin)=

17. c_c_b_aca_cac_b(1) acaab(2) abcab(3) aacba(4) abcca

Int (e^x){(1+sin 2x)/(1-sin 2x)

29. Find Arg( sin8Π/5 + i [ 1+ cos 8Π/5] )

If x=sint,y=tcost. Then dydx is equal to

Let X={n∈N:1≤n≤50}. If A={n∈X:n is a multiple of 2} and B={n∈X:n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is

Let y=g(x) be the solution of differential equation dydx+y=2xe−x1+yex such that g(0)=1. If [.] denotes the greatest integer function, then [g(−1)e] is equal to

If graph of y=ax2−bx+c is following, then sign of a, b, c are

The sides of a rectangle of the greatest area which can be inscribed into an ellipse x2/25 + y2/9 = 1 are

The relation R defined on the set A={1,2,3,4,5} as R={(a,b):|a2−b2|<16} has cardinality equal to