43030 + Interview Questions in Mathematics

1.	The acute angle of intersection between the curves y2+x2=a2√2 and x2−y2=a2, is
Answer» The acute angle of intersection between the curves $y^{2} + x^{2} = a^{2} \sqrt{2}$ and $x^{2} - y^{2} = a^{2},$ is

Discussion

2.	The time taken to travel 20 km is 2 h, which can be represented as ordered pair (2,20). The time taken for every extra 1 km is 10 min. Find the expression for the time taken with resepect to the distance travelled.
Answer» The time taken to travel 20 km is 2 h, which can be represented as ordered pair (2,20). The time taken for every extra 1 km is 10 min. Find the expression for the time taken with resepect to the distance travelled.

Discussion

3.	If tan4θ+cot4θ, where θ is an acute angle, then the value of sin4θ+cos4θ is
Answer» If $t a n^{4} θ + c o t^{4} θ$ , where $θ$ is an acute angle, then the value of $s i n^{4} θ + c o s^{4} θ$ is

Discussion

4.	If A and B are two events such thati PA=13, PB=14 and PA∪B=512, then find PA\|B and PB\|A.ii PA=611, PB=511 and PA∪B=711, then find PA∩B, PA\|B and PB\|A.iii PA=713, PB=913 and PA∩B=413, then find PA\|B.iv PA=12, PB=13 and PA∩B=14, then find PA\|B, PB\|A, PA\|B and PA\|B. [NCERT EXEMPLAR]
Answer» If A and B are two events such that $(i) P (A) = \frac{1}{3}, P (B) = \frac{1}{4} and P (A \cup B) = \frac{5}{12}, then find P (A \| B) and P (B \| A) . (ii) P (A) = \frac{6}{11}, P (B) = \frac{5}{11} and P (A \cup B) = \frac{7}{11}, then find P (A \cap B), P (A \| B) and P (B \| A) . (iii) P (A) = \frac{7}{13}, P (B) = \frac{9}{13} and P (A \cap B) = \frac{4}{13}, then find P (A \| B) . (iv) P (A) = \frac{1}{2}, P (B) = \frac{1}{3} and P (A \cap B) = \frac{1}{4}, then find P (A \| B), P (B \| A), P (A \| B) and P (A \| B) .$ [NCERT EXEMPLAR]

Discussion

5.	How many squares are there in the figure below?
Answer» How many squares are there in the figure below?

Discussion

6.	For all values of θ, the lines represented by the equation (2 cos θ+3 sin θ)x+(3 cos θ−5 sin θ)y−(5 cos θ−2 sin θ)=0
Answer» For all values of $θ$ , the lines represented by the equation $(2 c o s θ + 3 s i n θ) x + (3 c o s θ - 5 s i n θ) y - (5 c o s θ - 2 s i n θ) = 0$

Discussion

7.	What is the derivation of the formula of( sine inverse (x)+sine inverse (y))
Answer» What is the derivation of the formula of( sine inverse (x)+sine inverse (y))

Discussion

8.	If the coefficients of three consecutive terms in the expansion of (1+x)n are 165,330 and 462 respectively, then the value of n is
Answer» If the coefficients of three consecutive terms in the expansion of $(1 + x)^{n}$ are $165, 330$ and $462$ respectively, then the value of $n$ is

Discussion

9.	Which of the following is/are a solution of the differential equation dydx=ex ?
Answer» $Which of the following is/are a solution of the differential equation \frac{dy}{dx} = e^{x} ?$

Discussion

10.	a(1) cos1sim1 -2
Answer» a(1) cos1sim1 -2

Discussion

11.	If a complex number z satisfies \|2z+10+10i\|≤5√3−5, then the least principle argument of z, is
Answer» If a complex number $z$ satisfies $\| 2 z + 10 + 10 i \| \leq 5 \sqrt{3} - 5,$ then the least principle argument of $z,$ is

Discussion

12.	The inverse Laplace transform of s+9s2+6s+13 is
Answer» The inverse Laplace transform of $\frac{s + 9}{s^{2} + 6 s + 13}$ is

Discussion

13.	Evaluate each of the following integrals:∫0π4tanxdx
Answer» Evaluate each of the following integrals: $\int_{0}^{\frac{π}{4}} \tan x d x$

Discussion

14.	Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).
Answer» Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Discussion

15.	If x>0 then prove that 1+xlog{x+√(x²+1)} > √(1+x²)
Answer» If x>0 then prove that 1+xlog{x+√(x²+1)} > √(1+x²)

Discussion

16.	If f(x) is differentiable and ∫t20xf(x)dx=25t5, then f(425) equals
Answer» If $f (x)$ is differentiable and $\int_{0}^{t^{2}} x f (x) d x = \frac{2}{5} t^{5}, then f (\frac{4}{25})$ equals

Discussion

17.	A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of B at a profit of ₹4. Find the production level per day for maximum profit graphically.
Answer» A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of B at a profit of ₹4. Find the production level per day for maximum profit graphically.

Discussion

18.	If x2+y2−2kx−2ky+3k2−6k+8=0 is a real circle, then the possible value(s) of k is/are
Answer» If $x^{2} + y^{2} - 2 k x - 2 k y + 3 k^{2} - 6 k + 8 = 0$ is a real circle, then the possible value(s) of $k$ is/are

Discussion

19.	16. Solve for x if tan inverse (1-x/1+x) =1/2tan inverse x
Answer» 16. Solve for x if tan inverse (1-x/1+x) =1/2tan inverse x

Discussion

20.	solve for x and y: (\log x)/3=(\log y)/2 and \log (xy)=5
Answer» solve for x and y: (\log x)/3=(\log y)/2 and \log (xy)=5

Discussion

21.	Question 130(ii)Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun.PlanetDistance from Sun (km)Distance from Sun(km) Standard NotationEarth1496000001.496×108Jupiter778300000Mars227900000Mercury57900000Neptune4497000000Pluto5900000000Saturn1427000000Uranus2870000000Venus108200000Order the planets from closest to the Sun to farthest from teh Sun.
Answer» Question 130(ii) Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun. $\begin{matrix} P l a n e t & D i s t a n c e f r o m S u n (k m) & D i s t a n c e f r o m S u n (k m) S t a n d a r d N o t a t i o n E a r t h & 149600000 & 1.496 \times 10^{8} J u p i t e r & 778300000 M a r s & 227900000 M e r c u r y & 57900000 N e p t u n e & 4497000000 P l u t o & 5900000000 S a t u r n & 1427000000 U r a n u s & 2870000000 V e n u s & 108200000 \end{matrix}$ Order the planets from closest to the Sun to farthest from teh Sun.

21.

Question 130(ii)Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun.PlanetDistance from Sun (km)Distance from Sun(km) Standard NotationEarth1496000001.496×108Jupiter778300000Mars227900000Mercury57900000Neptune4497000000Pluto5900000000Saturn1427000000Uranus2870000000Venus108200000Order the planets from closest to the Sun to farthest from teh Sun.

Answer»

Question 130(ii)

Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun.

$\begin{matrix} P l a n e t & D i s t a n c e f r o m S u n (k m) & D i s t a n c e f r o m S u n (k m) S t a n d a r d N o t a t i o n E a r t h & 149600000 & 1.496 \times 10^{8} J u p i t e r & 778300000 M a r s & 227900000 M e r c u r y & 57900000 N e p t u n e & 4497000000 P l u t o & 5900000000 S a t u r n & 1427000000 U r a n u s & 2870000000 V e n u s & 108200000 \end{matrix}$

Order the planets from closest to the Sun to farthest from teh Sun.

Discussion

22.	what is the chemical composition of zeolite
Answer» what is the chemical composition of zeolite

Discussion

23.	The probability that the 3N′s come consecutively in the arrangement of the letters of the word ′CONSTANTINOPLE′.
Answer» The probability that the $3 N^{'}$ s come consecutively in the arrangement of the letters of the word $^{'} C O N S T A N T I N O P L E^{'} .$

Discussion

24.	If xsin θcos θ-sin θ-x1cos θ1x=8, write the value of x.
Answer» If $\|\begin{matrix} x & \sin θ & \cos θ \\ - \sin θ & - x & 1 \\ \cos θ & 1 & x \end{matrix}\| = 8$ , write the value of x.

Discussion

25.	The perpendicular from the origin to the tangent at any point on the curve is equal to the abscissa of the point of contact. If equation of tangent to the curve at (1,3) is ax + by + 5 = 0, then value of a + b is equal to?
Answer» The perpendicular from the origin to the tangent at any point on the curve is equal to the abscissa of the point of contact. If equation of tangent to the curve at (1,3) is ax + by + 5 = 0, then value of a + b is equal to?

Discussion

26.	Given that x > 0, the sum ∑∞n=1(xx+1)n−1 equals
Answer» Given that x > 0, the sum $\sum_{n = 1}^{\infty} {(\frac{x}{x + 1})}^{n - 1}$ equals

Discussion

27.	If a>0 and the equation ax2+bx+c=0 has two real roots α and β such that \|α\|≤1, \|β\|≤1, then
Answer» If a>0 and the equation $a x^{2} + b x + c = 0$ has two real roots $α$ and $β$ such that $\| α \| \leq 1, \| β \| \leq 1,$ then

Discussion

28.	∫1x+x4dx
Answer» $\int \frac{1}{\sqrt{x} + \sqrt[4]{x}} d x$

Discussion

29.	If f(x) and g(x) are two differentiable function in (0,1). Such that f(1)=2,g(0)=−1,g(1)=1, then for atleast one value of c in (0,1), which of the following is correct
Answer» If $f (x)$ and $g (x)$ are two differentiable function in $(0, 1) .$ Such that $f (1) = 2, g (0) = - 1, g (1) = 1,$ then for atleast one value of $c$ in $(0, 1),$ which of the following is correct

Discussion

30.	The equation of sphere passing through (1,0,0),(0,1,0) and (0,0,1) and whose centre lies on the plane 3x−y+z=2 is
Answer» The equation of sphere passing through $(1, 0, 0), (0, 1, 0)$ and $(0, 0, 1)$ and whose centre lies on the plane $3 x - y + z = 2$ is

Discussion

31.	a + ib > c + id can be explained only when
Answer» a + ib > c + id can be explained only when

Discussion

32.	What is the value of (1+tanθ)(1+cotθ)(1−tanθ)(1−cotθ) when sinθ=810.
Answer» What is the value of $\frac{(1 + tan θ) (1 + cot θ)}{(1 - tan θ) (1 - cot θ)}$ when $sin θ = \frac{8}{10}$ .

Discussion

33.	If 1∫sinxt2f(t)dt=1−sinx, where x∈(0,π2), then the value of f(1√3) is
Answer» If $1 \int sin x t^{2} f (t) d t = 1 - sin x,$ where $x \in (0, \frac{π}{2}),$ then the value of $f (\frac{1}{\sqrt{3}})$ is

Discussion

34.	e^(sin x) - e^(-sin x) = 4 then find the number of real solutions
Answer» e^(sin x) - e^(-sin x) = 4 then find the number of real solutions

Discussion

35.	20.sin\|--sin-ı(--)\| İs equal to(D) 14
Answer» 20.sin\|--sin-ı(--)\| İs equal to(D) 14

Discussion

36.	If y=y(x) is the solution of the differential equation dydx+2ytanx=sinx,y(π3)=0, then the maximum value of the function y(x) over R is
Answer» If $y = y (x)$ is the solution of the differential equation $\frac{d y}{d x} + 2 y tan x = sin x, y (\frac{π}{3}) = 0,$ then the maximum value of the function $y (x)$ over $R$ is

Discussion

37.	Solve the inequalities: 2(2x+3)-10 < 6(x-2)
Answer» Solve the inequalities: 2(2x+3)-10 < 6(x-2)

Discussion

38.	Column 1 Column 2 Column 3(I)In a triangle ABC sin A, sin B, sin C(i)Latus rectum of ellipse(P)2 are in A.P., then sin(A2)sin(A2)sin(C2)is x216+y24=1 is equal to (II)In ΔABC if 2Δ+b2+c2=2bc+a2,(ii)Eccentricity of hyperbola(Q)3 then value of x which satisfy x2−5(sin (x−√2)22−y216=1 A+cos A)x+25 sin A cos A=0 is equal to is equal to (III)In ΔABC if a=7, b=3,c=√1312(iii)Radius of director circle ofR7and median AD meets circumcircle at x236+y213=1 is equal to E, then AE is greater than (IV)The point of contact of an inscribed circle of a right angled(iv)Minimum value of \|z1−z2\| where(S)4 triangle divides the hypotenuse in two \|z1\|=2 and \|z2−9\|=3 is equal to parts of lengths 4 and 7, then area of triangle is divisible by (where complex numbers in argand plane) Which of the following is the only correct combination?
Answer» $\begin{matrix} C o l u m n 1 & C o l u m n 2 & C o l u m n 3 (I) & I n a t r i a n g l e A B C s i n A, s i n B, s i n C & (i) & L a t u s r e c t u m o f e l l i p s e & (P) & 2 a r e i n A . P ., t h e n \frac{s i n (\frac{A}{2})}{s i n (\frac{A}{2}) s i n (\frac{C}{2}) i s} & \frac{x^{2}}{16} + \frac{y^{2}}{4} = 1 i s e q u a l t o (I I) & I n Δ A B C i f 2 Δ + b^{2} + c^{2} = 2 b c + a^{2}, & (i i) & E c c e n t r i c i t y o f h y p e r b o l a & (Q) & 3 t h e n v a l u e o f x w h i c h s a t i s f y x^{2} - 5 (s i n & \frac{(x - \sqrt{2})^{2}}{2} - \frac{y^{2}}{16} = 1 A + c o s A) x + 25 s i n A c o s A = 0 i s e q u a l t o & i s e q u a l t o (I I I) & I n Δ A B C i f a = 7, b = 3, c = \sqrt{\frac{131}{2}} & (i i i) & R a d i u s o f d i r e c t o r c i r c l e o f & R & 7 a n d m e d i a n A D m e e t s c i r c u m c i r c l e a t & \frac{x^{2}}{36} + \frac{y^{2}}{13} = 1 i s e q u a l t o E, t h e n A E i s g r e a t e r t h a n (I V) & T h e p o i n t o f c o n t a c t o f a n i n s c r i b e d c i r c l e o f a r i g h t a n g l e d & (i v) & M i n i m u m v a l u e o f \| z_{1} - z_{2} \| w h e r e & (S) & 4 t r i a n g l e d i v i d e s t h e h y p o t e n u s e i n t w o & \| z_{1} \| = 2 a n d \| z_{2} - 9 \| = 3 i s e q u a l t o p a r t s o f l e n g t h s 4 a n d 7, t h e n a r e a o f t r i a n g l e i s d i v i s i b l e b y & (w h e r e c o m p l e x n u m b e r s i n a r g a n d p l a n e) \end{matrix}$ Which of the following is the only correct combination?

Discussion

39.	The function f(x) = x2+2x has a local minimum at x = __________________.
Answer» The function f(x) = $\frac{x}{2} + \frac{2}{x}$ has a local minimum at x = __________________.

Discussion

40.	Spherical rain drop evaporates ata rate proportional to its surface area.The differential equation correspondingto the rate of change of the radius ofthe rain drop if the constant of proportionality is K>0 is .
Answer» $Spherical rain drop evaporates at a rate proportional to its surface area . The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K > 0 is$ .

Discussion

41.	Find the area bounded by x=at^2 ,y=2at between the ordinates corresponding to t=1 and t=2
Answer» Find the area bounded by x=at^2 ,y=2at between the ordinates corresponding to t=1 and t=2

Discussion

42.	The value of the parameter `a' such that the area bounded by y=a2x2+ax+1, positive coordinate axes and the line x=1 attains its least value, is equal to
Answer» The value of the parameter `a' such that the area bounded by $y = a^{2} x^{2} + a x + 1$ , positive coordinate axes and the line x=1 attains its least value, is equal to

Discussion

43.	In [1,3], Lagrange's mean value theorem is not applicable to
Answer» In $[1, 3],$ Lagrange's mean value theorem is not applicable to

Discussion

44.	sin x ⋅sin (cos x)
Answer» sin x ⋅ sin (cos x)

Discussion

45.	If fx=sin 3xx,if x≠0k2,if x=0is continuous at x = 0, then k is equal to _____________.
Answer» If $f (x) = \{\begin{matrix} \frac{\sin 3 x}{x}, & if x \neq 0 \\ \frac{k}{2}, & if x = 0 \end{matrix}$ is continuous at x = 0, then k is equal to _____________.

Discussion

46.	A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that getting 9 heads, then the probability of getting 3 heads is
Answer» A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that getting 9 heads, then the probability of getting 3 heads is

Discussion

47.	The value of ∫1√(x−1)2+(√2)2dx is
Answer» The value of $\int \frac{1}{\sqrt{{(x - 1)}^{2} + {(\sqrt{2})}^{2}}} d x$ is

Discussion

48.	Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) x2+2y2−2x+12y+10=0 (ii) x2+4y2−4x+24y+31=0 (iii) 4x2+y2−8x+2y+1=0 (iv) 3x2+4y2−12x−8y+4=0 (v) 4x2+16y2−24x−32y−12=0 (vi) x2+4y2−2x=0
Answer» Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) $x^{2} + 2 y^{2} - 2 x + 12 y + 10 = 0$ (ii) $x^{2} + 4 y^{2} - 4 x + 24 y + 31 = 0$ (iii) $4 x^{2} + y^{2} - 8 x + 2 y + 1 = 0$ (iv) $3 x^{2} + 4 y^{2} - 12 x - 8 y + 4 = 0$ (v) $4 x^{2} + 16 y^{2} - 24 x - 32 y - 12 = 0$ (vi) $x^{2} + 4 y^{2} - 2 x = 0$

Discussion

49.	∫0π4tan6x sec2x dx=________________.
Answer» $\int_{0}^{\frac{π}{4}} \tan^{6} x \sec^{2} x d x =$ ________________.

Discussion

50.	Solve the equation
Answer» Solve the equation

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The acute angle of intersection between the curves y2+x2=a2√2 and x2−y2=a2, is

The time taken to travel 20 km is 2 h, which can be represented as ordered pair (2,20). The time taken for every extra 1 km is 10 min. Find the expression for the time taken with resepect to the distance travelled.

If tan4θ+cot4θ, where θ is an acute angle, then the value of sin4θ+cos4θ is

If A and B are two events such thati PA=13, PB=14 and PA∪B=512, then find PA|B and PB|A.ii PA=611, PB=511 and PA∪B=711, then find PA∩B, PA|B and PB|A.iii PA=713, PB=913 and PA∩B=413, then find PA|B.iv PA=12, PB=13 and PA∩B=14, then find PA|B, PB|A, PA|B and PA|B. [NCERT EXEMPLAR]

How many squares are there in the figure below?

For all values of θ, the lines represented by the equation (2 cos θ+3 sin θ)x+(3 cos θ−5 sin θ)y−(5 cos θ−2 sin θ)=0

What is the derivation of the formula of( sine inverse (x)+sine inverse (y))

If the coefficients of three consecutive terms in the expansion of (1+x)n are 165,330 and 462 respectively, then the value of n is

Which of the following is/are a solution of the differential equation dydx=ex ?

a(1) cos1sim1 -2

If a complex number z satisfies |2z+10+10i|≤5√3−5, then the least principle argument of z, is

The inverse Laplace transform of s+9s2+6s+13 is

Evaluate each of the following integrals:∫0π4tanxdx

Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

If x>0 then prove that 1+xlog{x+√(x²+1)} > √(1+x²)

If f(x) is differentiable and ∫t20xf(x)dx=25t5, then f(425) equals

If x2+y2−2kx−2ky+3k2−6k+8=0 is a real circle, then the possible value(s) of k is/are

16. Solve for x if tan inverse (1-x/1+x) =1/2tan inverse x

solve for x and y: (\log x)/3=(\log y)/2 and \log (xy)=5

what is the chemical composition of zeolite

The probability that the 3N′s come consecutively in the arrangement of the letters of the word ′CONSTANTINOPLE′.

If xsin θcos θ-sin θ-x1cos θ1x=8, write the value of x.

The perpendicular from the origin to the tangent at any point on the curve is equal to the abscissa of the point of contact. If equation of tangent to the curve at (1,3) is ax + by + 5 = 0, then value of a + b is equal to?

Given that x &gt; 0, the sum ∑∞n=1(xx+1)n−1 equals

If a&gt;0 and the equation ax2+bx+c=0 has two real roots α and β such that |α|≤1, |β|≤1, then

∫1x+x4dx

If f(x) and g(x) are two differentiable function in (0,1). Such that f(1)=2,g(0)=−1,g(1)=1, then for atleast one value of c in (0,1), which of the following is correct

The equation of sphere passing through (1,0,0),(0,1,0) and (0,0,1) and whose centre lies on the plane 3x−y+z=2 is

a + ib &gt; c + id can be explained only when

What is the value of (1+tanθ)(1+cotθ)(1−tanθ)(1−cotθ) when sinθ=810.

If 1∫sinxt2f(t)dt=1−sinx, where x∈(0,π2), then the value of f(1√3) is

e^(sin x) - e^(-sin x) = 4 then find the number of real solutions

20.sin|--sin-ı(--)| İs equal to(D) 14

If y=y(x) is the solution of the differential equation dydx+2ytanx=sinx,y(π3)=0, then the maximum value of the function y(x) over R is

Solve the inequalities: 2(2x+3)-10 < 6(x-2)

The function f(x) = x2+2x has a local minimum at x = __________________.

Spherical rain drop evaporates ata rate proportional to its surface area.The differential equation correspondingto the rate of change of the radius ofthe rain drop if the constant of proportionality is K&gt;0 is .

Find the area bounded by x=at^2 ,y=2at between the ordinates corresponding to t=1 and t=2

The value of the parameter `a' such that the area bounded by y=a2x2+ax+1, positive coordinate axes and the line x=1 attains its least value, is equal to

In [1,3], Lagrange's mean value theorem is not applicable to

sin x ⋅sin (cos x)

If fx=sin 3xx,if x≠0k2,if x=0is continuous at x = 0, then k is equal to _____________.

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that getting 9 heads, then the probability of getting 3 heads is

The value of ∫1√(x−1)2+(√2)2dx is

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) x2+2y2−2x+12y+10=0 (ii) x2+4y2−4x+24y+31=0 (iii) 4x2+y2−8x+2y+1=0 (iv) 3x2+4y2−12x−8y+4=0 (v) 4x2+16y2−24x−32y−12=0 (vi) x2+4y2−2x=0

∫0π4tan6x sec2x dx=________________.

Solve the equation

Given that x > 0, the sum ∑∞n=1(xx+1)n−1 equals

If a>0 and the equation ax2+bx+c=0 has two real roots α and β such that |α|≤1, |β|≤1, then

a + ib > c + id can be explained only when

Spherical rain drop evaporates ata rate proportional to its surface area.The differential equation correspondingto the rate of change of the radius ofthe rain drop if the constant of proportionality is K>0 is .