43030 + Interview Questions in Mathematics

1.	The domain of f(x) is [0,1], then the domain of y=f(ex)+f(\|[x]\|) is (where [.] denotes greatest integer function)
Answer» The domain of $f (x)$ is $[0, 1]$ , then the domain of $y = f (e^{x}) + f (\| [x] \|)$ is (where [.] denotes greatest integer function)

Discussion

2.	If the latus rectum of an hyperbola be 8 and eccentricity be 3√5 , then the equation of the hyperbola is
Answer» If the latus rectum of an hyperbola be 8 and eccentricity be $\frac{3}{\sqrt{5}}$ , then the equation of the hyperbola is

Discussion

3.	tan[π4+12cos−1ab]+tan[π4+12cos−1ab] [MP PET 1999]
Answer» $t a n [\frac{π}{4} + \frac{1}{2} c o s^{- 1} \frac{a}{b}] + t a n [\frac{π}{4} + \frac{1}{2} c o s^{- 1} \frac{a}{b}]$ [MP PET 1999]

3.

tan[π4+12cos−1ab]+tan[π4+12cos−1ab] [MP PET 1999]

Answer»

$t a n [\frac{π}{4} + \frac{1}{2} c o s^{- 1} \frac{a}{b}] + t a n [\frac{π}{4} + \frac{1}{2} c o s^{- 1} \frac{a}{b}]$
[MP PET 1999]

Discussion

4.	For a stationary ergodic process X(t), the autocorrelation function RX(τ) is given by, RX(τ)=τ22+9τ2The magnitude of the mean value of X(t) i.e., \|¯¯¯¯¯X\| is ______0.33
Answer» For a stationary ergodic process $X (t),$ the autocorrelation function $R_{X} (τ)$ is given by, $R_{X} (τ) = \frac{τ^{2}}{2 + 9 τ^{2}}$ The magnitude of the mean value of $X (t)$ i.e., $\| ¯ ¯¯¯ ¯ X \|$ is ______ 0.33

Discussion

5.	If f(x) is continuous and f(92)=29, then 27limx→0f(1−cos3xx2) is equal to
Answer» If $f (x)$ is continuous and $f (\frac{9}{2}) = \frac{2}{9},$ then $27 lim x \to 0 f (\frac{1 - cos 3 x}{x^{2}})$ is equal to

Discussion

6.	The sum of sin22π7+sin24π7+sin28π7 is S, the value of 4S is
Answer» The sum of ${sin}^{2} \frac{2 π}{7} + {sin}^{2} \frac{4 π}{7} + {sin}^{2} \frac{8 π}{7}$ is $S$ , the value of $4 S$ is

Discussion

7.	The graph of the quadratic polynomial y=ax2+bx+c has its vertex at (4,−5) and two x intercepts, one positive and one negative. Which of the following hold(s) good?
Answer» The graph of the quadratic polynomial $y = a x^{2} + b x + c$ has its vertex at $(4, - 5)$ and two $x$ intercepts, one positive and one negative. Which of the following hold(s) good?

Discussion

8.	A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is
Answer» A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is

Discussion

9.	∫5cosx−3sinx3cosx+5sinxdx is equal to
Answer» $\int \frac{5 cos x - 3 sin x}{3 cos x + 5 sin x} d x$ is equal to

Discussion

10.	If and , find k so that
Answer» If and , find k so that

Discussion

11.	If limx→0kx cosec x = limx→0x cosec kx , then k =
Answer» If $l i m_{x \to 0}$ kx cosec x = $l i m_{x \to 0}$ x cosec kx , then k =

Discussion

12.	In a random experiment of drawing a card from a well-shuffled pack of 52 cards,let A,B,C & D are the events of drawing an ace,a spade, a heart and a diamond respectively.Show that the events A & B , C& A, A& D are not manually exclusive while the event B & C, C & D, B& D are manually exclusive.Show also that the events A,B,C,D are not exhaustive.
Answer» In a random experiment of drawing a card from a well-shuffled pack of 52 cards,let A,B,C & D are the events of drawing an ace,a spade, a heart and a diamond respectively.Show that the events A & B , C& A, A& D are not manually exclusive while the event B & C, C & D, B& D are manually exclusive.Show also that the events A,B,C,D are not exhaustive.

Discussion

13.	Find the sum of theproducts of the corresponding terms of the sequences 2, 4, 8, 16, 32and 128, 32, 8, 2, .
Answer» Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

Discussion

14.	The degree of the polynomial function f(x)=5x4+6x−2 is
Answer» The degree of the polynomial function $f (x) = 5 x^{4} + 6 x - 2$ is

Discussion

15.	The radius of Na+ is 95 pm and that of Cl− is 181 pm. The edge length of unit cell in NaCl would be
Answer» The radius of $N a^{+}$ is 95 pm and that of $C l^{-}$ is 181 pm. The edge length of unit cell in NaCl would be

Discussion

16.	If α,β are the roots of the equation 2x2−35x+2=0, then the value of √(2α−35)3(2β−35)3 is
Answer» If $α, β$ are the roots of the equation $2 x^{2} - 35 x + 2 = 0,$ then the value of $\sqrt{(2 α - 35)^{3} (2 β - 35)^{3}}$ is

Discussion

17.	Choose the correct answer. If x , y , z are nonzero real numbers, then the inverse of matrix is A. B. C. D.
Answer» Choose the correct answer. If x , y , z are nonzero real numbers, then the inverse of matrix is A. B. C. D.

Discussion

18.	If cosx+sinx=12, where x∈(0,π), then the maximum possible value of tanx is
Answer» If $cos x + sin x = \frac{1}{2}$ , where $x \in (0, π)$ , then the maximum possible value of $tan x$ is

Discussion

19.	Evaluate P (A ∪ B), if 2P (A) = P (B) = and P(A\|B) =
Answer» Evaluate P (A ∪ B), if 2P (A) = P (B) = and P(A\|B) =

Discussion

20.	36.Motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstreeam resp. the time required by the boat to cover this distance i still water is:
Answer» 36.Motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstreeam resp. the time required by the boat to cover this distance i still water is:

Discussion

21.	Which of the following holds true in a Right angled triangle?
Answer» Which of the following holds true in a Right angled triangle?

Discussion

22.	The coefficient of two consecutive terms in the expansion of (1+x)n will be equal, if
Answer» The coefficient of two consecutive terms in the expansion of $(1 + x)^{n}$ will be equal, if

Discussion

23.	The order of the differential equation whose solution is y=a cos x+b sin x+ce−x is
Answer» The order of the differential equation whose solution is $y = a c o s x + b s i n x + c e^{- x}$ is

Discussion

24.	Consider a △PQR in a circle x2+y2=16 such that Q≡(2√2,2√2) and R≡(−2,2√3). Then the measure of ∠QPR is
Answer» Consider a $△ P Q R$ in a circle $x^{2} + y^{2} = 16$ such that $Q \equiv (2 \sqrt{2}, 2 \sqrt{2})$ and $R \equiv (- 2, 2 \sqrt{3}) .$ Then the measure of $∠ Q P R$ is

Discussion

25.	If a function f(x) satisfies f(x)+f(y)f(x+y)=1,where x,y∈R and f(2) is the mean of roots of x2−6x+8=0, then the value of 3sin(f(3)π)+4cos(f(1)π) is
Answer» If a function $f (x)$ satisfies $\frac{f (x) + f (y)}{f (x + y)} = 1,$ where $x, y \in R$ and $f (2)$ is the mean of roots of $x^{2} - 6 x + 8 = 0,$ then the value of $3 sin (f (3) π) + 4 cos (f (1) π)$ is

Discussion

26.	Mark the correct alternative in each of the following:If fx=1+x+x22+ ... +x100100, then f'1 is equal to(a) 1100 (b) 100 (c) 50 (d) 0
Answer» Mark the correct alternative in each of the following: If $f (x) = 1 + x + \frac{x^{2}}{2} + . . . + \frac{x^{100}}{100}$ , then $f' (1)$ is equal to (a) $\frac{1}{100}$ (b) 100 (c) 50 (d) 0

Discussion

27.	Prove that the function given by f(x) =cos3x is neither increasing nor decreasing on (0, π/2)
Answer» Prove that the function given by f(x) =cos3x is neither increasing nor decreasing on (0, π/2)

Discussion

28.	Integrate : 3x-1/x^2+4x+4
Answer» Integrate : 3x-1/x^2+4x+4

Discussion

29.	The no.of integral values of k for which the equation 7cosx+5sinx=2k+1has a solution is
Answer» The no.of integral values of k for which the equation 7cosx+5sinx=2k+1has a solution is

Discussion

30.	Write the coordinates of the point P which is five-sixth of the way from A(-2, 0, 6) to B (10, -6, -12).
Answer» Write the coordinates of the point P which is five-sixth of the way from A(-2, 0, 6) to B (10, -6, -12).

30.

Write the coordinates of the point P which is five-sixth of the way from A(-2, 0, 6) to B (10, -6, -12).

Answer»

Write the coordinates of the point P which is five-sixth of the way from

A(-2, 0, 6) to B (10, -6, -12).

Discussion

31.	The value of limn→∞3n+2n3n−2nis
Answer» $The value of l i m n \to \infty \frac{3^{n} + 2^{n}}{3^{n} - 2^{n}} is$

Discussion

32.	The length of a rectangle is decreasing at the rate of 3 cm/min and its width is increasing at the rate of 2 cm/min. If length is 10 cm, width is 6 cm and P,A represent the perimeter and area of the rectangle respectively, then which of the following is/are true
Answer» The length of a rectangle is decreasing at the rate of $3 cm / min$ and its width is increasing at the rate of $2 cm / min .$ If length is $10 cm,$ width is $6 cm$ and $P, A$ represent the perimeter and area of the rectangle respectively, then which of the following is/are true

Discussion

33.	y=sin−11√x+1 Find dydx
Answer» $y = s i n^{- 1} \frac{1}{\sqrt{x + 1}}$ Find $\frac{d y}{d x}$

Discussion

34.	The value of ∞∫0tan(x+1x)logxx2+1dx is
Answer» The value of $\infty \int 0 tan (x + \frac{1}{x}) \frac{log x}{x^{2} + 1} d x$ is

Discussion

35.	Which among the following functions is not injective
Answer» Which among the following functions is not injective

Discussion

36.	If.For what integers m and n does and exist?
Answer» If. For what integers m and n does and exist?

Discussion

37.	The value of p if the lines x+p=0,y−2=0 and 3x+2y+5=0 are concurrent is
Answer» The value of $p$ if the lines $x + p = 0, y - 2 = 0$ and $3 x + 2 y + 5 = 0$ are concurrent is

Discussion

38.	The line 6x + 8y = 48 intersects the coordinate axes at A and B respectively. A line L bisects the area and the perimeter of the triangle OAB where O is the origin. The slope of the line L can be
Answer» The line 6x + 8y = 48 intersects the coordinate axes at A and B respectively. A line L bisects the area and the perimeter of the triangle OAB where O is the origin. The slope of the line L can be

Discussion

39.	Given the parametric equations x=f(t),y=g(t), then d2ydx2 equals
Answer» Given the parametric equations $x = f (t), y = g (t)$ , then $\frac{d^{2} y}{d x^{2}}$ equals

Discussion

40.	The complex number z which satisfies the condition i+zi-z=1 lies on(a) circle x2 + y2 = 1(b) the x−axis(c) the y−axis(d) the line x + y = 1
Answer» The complex number z which satisfies the condition $\|\frac{i + z}{i - z}\| = 1$ lies on (a) circle x² + y² = 1 (b) the x−axis (c) the y−axis (d) the line x + y = 1

Discussion

41.	{ Two vectors }\vec A and }\vec B are inclined at an angle }θ. It }}{(\vec A+\vec B) and }(\vec A-\vec B) make angles }α and }B}{ respectively with }\vec A , then value of }(\operatorname{tan}α+\operatorname{tan}β) will }} be
Answer» { Two vectors }\vec A and }\vec B are inclined at an angle }θ. It }}{(\vec A+\vec B) and }(\vec A-\vec B) make angles }α and }B}{ respectively with }\vec A , then value of }(\operatorname{tan}α+\operatorname{tan}β) will }} be

Discussion

42.	Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?
Answer» Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?

Discussion

43.	Derivation of lambda = h/root of 2×m× Q×V
Answer» Derivation of lambda = h/root of 2×m× Q×V

Discussion

44.	If U={2, 4, 6, 8, 12, 14, 17}, where U is the universal set and some set A={1, 4, 6, 11, 12}. The set A' is
Answer» If U={2, 4, 6, 8, 12, 14, 17}, where U is the universal set and some set A={1, 4, 6, 11, 12}. The set A' is

Discussion

45.	Find theequation of a line drawn perpendicular to the line throughthe point, where it meets the y-axis.
Answer» Find the equation of a line drawn perpendicular to the line through the point, where it meets the y-axis.

Discussion

46.	Find the equation of the plane passing through ( a , b , c ) and parallel to the plane
Answer» Find the equation of the plane passing through ( a , b , c ) and parallel to the plane

Discussion

47.	For observations x1,x2,x3,..........,xn, if ∑ni=1(xi+1)2=9n and ∑ni=1(xi−1)2=5n., then standard deviation of the data is
Answer» For observations $x_{1}, x_{2}, x_{3}, . . . . . . . . . ., x_{n},$ if $\sum_{i = 1}^{n} (x_{i} + 1)^{2} = 9 n$ and $\sum_{i = 1}^{n} (x_{i} - 1)^{2} = 5 n .$ , then standard deviation of the data is

Discussion

48.	∫sec2x(secx+tanx)9/2dx equals(where C is constant of integration)
Answer» $\int \frac{{sec}^{2} x}{{(sec x + tan x)}^{9 / 2}} d x$ equals (where $C$ is constant of integration)

Discussion

49.	48. If the points P(x, y) is eqidistance from point A (a+b, b-a) and B (a-b, a+b). Prove that, bx=ay.
Answer» 48. If the points P(x, y) is eqidistance from point A (a+b, b-a) and B (a-b, a+b). Prove that, bx=ay.

Discussion

50.	Let C be a circle passing through the origin and making an intercept of √10 on the line y=2x+5√2. If the line subtends an angle of 45∘ at the origin, then the equation of circle C is/are
Answer» Let $C$ be a circle passing through the origin and making an intercept of $\sqrt{10}$ on the line $y = 2 x + \frac{5}{\sqrt{2}}$ . If the line subtends an angle of $45^{\circ}$ at the origin, then the equation of circle $C$ is/are

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The domain of f(x) is [0,1], then the domain of y=f(ex)+f(|[x]|) is (where [.] denotes greatest integer function)

If the latus rectum of an hyperbola be 8 and eccentricity be 3√5 , then the equation of the hyperbola is

tan[π4+12cos−1ab]+tan[π4+12cos−1ab] [MP PET 1999]

For a stationary ergodic process X(t), the autocorrelation function RX(τ) is given by, RX(τ)=τ22+9τ2The magnitude of the mean value of X(t) i.e., |¯¯¯¯¯X| is ______0.33

If f(x) is continuous and f(92)=29, then 27limx→0f(1−cos3xx2) is equal to

The sum of sin22π7+sin24π7+sin28π7 is S, the value of 4S is ​​​​​​​

The graph of the quadratic polynomial y=ax2+bx+c has its vertex at (4,−5) and two x intercepts, one positive and one negative. Which of the following hold(s) good?

A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is

∫5cosx−3sinx3cosx+5sinxdx is equal to

If and , find k so that

If limx→0kx cosec x = limx→0x cosec kx , then k =

Find the sum of theproducts of the corresponding terms of the sequences 2, 4, 8, 16, 32and 128, 32, 8, 2, .

The degree of the polynomial function f(x)=5x4+6x−2 is

The radius of Na+ is 95 pm and that of Cl− is 181 pm. The edge length of unit cell in NaCl would be

If α,β are the roots of the equation 2x2−35x+2=0, then the value of √(2α−35)3(2β−35)3 is

Choose the correct answer. If x , y , z are nonzero real numbers, then the inverse of matrix is A. B. C. D.

If cosx+sinx=12, where x∈(0,π), then the maximum possible value of tanx is

Evaluate P (A ∪ B), if 2P (A) = P (B) = and P(A|B) =

36.Motorboat covers the distance between two spots on the river in 8h and 12h downstream and upstreeam resp. the time required by the boat to cover this distance i still water is:

Which of the following holds true in a Right angled triangle?

The coefficient of two consecutive terms in the expansion of (1+x)n will be equal, if

The order of the differential equation whose solution is y=a cos x+b sin x+ce−x is

Consider a △PQR in a circle x2+y2=16 such that Q≡(2√2,2√2) and R≡(−2,2√3). Then the measure of ∠QPR is

If a function f(x) satisfies f(x)+f(y)f(x+y)=1,where x,y∈R and f(2) is the mean of roots of x2−6x+8=0, then the value of 3sin(f(3)π)+4cos(f(1)π) is

Mark the correct alternative in each of the following:If fx=1+x+x22+ ... +x100100, then f'1 is equal to(a) 1100 (b) 100 (c) 50 (d) 0

Prove that the function given by f(x) =cos3x is neither increasing nor decreasing on (0, π/2)

Integrate : 3x-1/x^2+4x+4

The no.of integral values of k for which the equation 7cosx+5sinx=2k+1has a solution is

Write the coordinates of the point P which is five-sixth of the way from A(-2, 0, 6) to B (10, -6, -12).

The value of limn→∞3n+2n3n−2nis

The length of a rectangle is decreasing at the rate of 3 cm/min and its width is increasing at the rate of 2 cm/min. If length is 10 cm, width is 6 cm and P,A represent the perimeter and area of the rectangle respectively, then which of the following is/are true

y=sin−11√x+1 Find dydx

The value of ∞∫0tan(x+1x)logxx2+1dx is

Which among the following functions is not injective

If.For what integers m and n does and exist?

The value of p if the lines x+p=0,y−2=0 and 3x+2y+5=0 are concurrent is

The line 6x + 8y = 48 intersects the coordinate axes at A and B respectively. A line L bisects the area and the perimeter of the triangle OAB where O is the origin. The slope of the line L can be

Given the parametric equations x=f(t),y=g(t), then d2ydx2 equals

The complex number z which satisfies the condition i+zi-z=1 lies on(a) circle x2 + y2 = 1(b) the x−axis(c) the y−axis(d) the line x + y = 1

{ Two vectors }\vec A and }\vec B are inclined at an angle }θ. It }}{(\vec A+\vec B) and }(\vec A-\vec B) make angles }α and }B}{ respectively with }\vec A , then value of }(\operatorname{tan}α+\operatorname{tan}β) will }} be

Derivation of lambda = h/root of 2×m× Q×V

If U={2, 4, 6, 8, 12, 14, 17}, where U is the universal set and some set A={1, 4, 6, 11, 12}. The set A' is

Find theequation of a line drawn perpendicular to the line throughthe point, where it meets the y-axis.

Find the equation of the plane passing through ( a , b , c ) and parallel to the plane

For observations x1,x2,x3,..........,xn, if ∑ni=1(xi+1)2=9n and ∑ni=1(xi−1)2=5n., then standard deviation of the data is

∫sec2x(secx+tanx)9/2dx equals(where C is constant of integration)

48. If the points P(x, y) is eqidistance from point A (a+b, b-a) and B (a-b, a+b). Prove that, bx=ay.

Let C be a circle passing through the origin and making an intercept of √10 on the line y=2x+5√2. If the line subtends an angle of 45∘ at the origin, then the equation of circle C is/are

The sum of sin22π7+sin24π7+sin28π7 is S, the value of 4S is