43030 + Interview Questions in Mathematics

1.	There are total 18 balls in a bag. Out of them, 6 are red in colour, 4 are green in colour and 8 are blue in colour. If Vishal picks three balls randomly from the bag, then what is the probability that all the three balls are not of the same colour?
Answer» There are total $18$ balls in a bag. Out of them, $6$ are red in colour, $4$ are green in colour and $8$ are blue in colour. If Vishal picks three balls randomly from the bag, then what is the probability that all the three balls are not of the same colour?

Discussion

2.	What's the equation of a tangent on the parabolay2=5x at the point (5, 5)
Answer» What's the equation of a tangent on the parabola $y^{2} = 5 x$ at the point (5, 5)

Discussion

3.	20.Graph of x+integral value of x
Answer» 20.Graph of x+integral value of x

Discussion

4.	If limx→1(2x+22x+23x+⋯+2nx)=126 (n∈N), then the value of n is equal to
Answer» If $lim x \to 1 (2^{x} + 2^{2 x} + 2^{3 x} + \dots + 2^{n x}) = 126 (n \in N),$ then the value of $n$ is equal to

Discussion

5.	A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is 332, then n is equal to ___.
Answer» A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is $\frac{3}{32}$ , then n is equal to ___.

Discussion

6.	limx→0 x2cosx1-cosx is(a) 2 (b) 32 (c) -32 (d) 1
Answer» $\lim_{x \to 0} \frac{x^{2} \cos x}{1 - \cos x} is$ (a) 2 (b) $\frac{3}{2}$ (c) $- \frac{3}{2}$ (d) 1

Discussion

7.	Let x0 be the point of Local maxima of f(x)=→a⋅(→b×→c), where →a=x^i−2^j+3^k,→b=−2^i+x^j−^k and →c=7^i−2^j+x^k. Then the value of →a⋅→b+→b⋅→c+→c⋅→a at x=x0 is
Answer» Let $x_{0}$ be the point of Local maxima of $f (x) =$ $\to a \cdot (\to b \times \to c),$ where $\to a = x^i - 2^j + 3^k, \to b = - 2^i + x^j -^k$ and $\to c = 7^i - 2^j + x^k$ . Then the value of $\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a$ at $x = x_{0}$ is

Discussion

8.	The range of f(x)=x2−81x−9 is
Answer» The range of $f (x) = \frac{x^{2} - 81}{x - 9}$ is

Discussion

9.	If g(x) = 2f(x) + x + log (f(x)) then d(g(x))d(f(x))_________
Answer» If g(x) = 2f(x) + x + log (f(x)) then $\frac{d (g (x))}{d (f (x))}$ _________

Discussion

10.	ABC is a right angle triangle at B and BC=10. If 100 points L1,L2,L3,…,L100 on AB are such that AB is divided into 101 equal parts and L1M1,L2M2,…,L100M100 are line segments parallel to BC and points M1,M2,M3,…,M100 are on AC, then the sum of L1M1,L2M2,…,L100M100 is
Answer» $A B C$ is a right angle triangle at $B$ and $B C = 10.$ If $100$ points $L_{1}, L_{2}, L_{3}, \dots, L_{100}$ on $A B$ are such that $A B$ is divided into $101$ equal parts and $L_{1} M_{1}, L_{2} M_{2}, \dots, L_{100} M_{100}$ are line segments parallel to $B C$ and points $M_{1}, M_{2}, M_{3}, \dots, M_{100}$ are on $A C,$ then the sum of $L_{1} M_{1}, L_{2} M_{2}, \dots, L_{100} M_{100}$ is

Discussion

11.	The area of the quadrilateral formed by the lines 4x−3y−a=0,3x−4y+a=0, 4x−3y−3a=0 and 3x−4y+2a=0 is
Answer» The area of the quadrilateral formed by the lines $4 x - 3 y - a = 0, 3 x - 4 y + a = 0$ , $4 x - 3 y - 3 a = 0$ and $3 x - 4 y + 2 a = 0$ is

Discussion

12.	Equation of curve through point(1,0) which satisfies the differential equation (1+y2)dx−xydy=0, is
Answer» Equation of curve through point(1,0) which satisfies the differential equation $(1 + y^{2}) d x - x y d y = 0$ , is

Discussion

13.	If a + ib =,prove that a2 + b2 =
Answer» If a + ib =, prove that a² + b² =

Discussion

14.	If I1=∫102x2 dx, I2=∫102x3dx, I3=∫212x2dx and I4=∫212x3 dx then
Answer» $I f I_{1} = \int_{0}^{1} 2^{x^{2}} d x, I_{2} = \int_{0}^{1} 2^{x^{3}} d x, I_{3} = \int_{1}^{2} 2^{x^{2}} d x a n d I_{4} = \int_{1}^{2} 2 x^{3} d x t h e n$

Discussion

15.

The lengths and bearing of a traverse PQRS are: Segment Length(m) Bearing PQ 40 80∘ QR 50 10∘ RS 30 210∘ The length of line segment SP (in m, round off to two decimal places), is44.79

Answer» The lengths and bearing of a traverse PQRS are:

Segment	Length(m)	Bearing
PQ	40	$80^{\circ}$
QR	50	$10^{\circ}$
RS	30	$210^{\circ}$

The length of line segment SP (in m, round off to two decimal places), is

44.79

Discussion

16.	Show that the linesandareperpendicular to each other.
Answer» Show that the lines and are perpendicular to each other.

Discussion

17.	Given that and . What can you conclude about the vectors ?
Answer» Given that and . What can you conclude about the vectors ?

Discussion

18.	An aeroplane flying at a height of 9000 m vertically above from the ground, passes another aeroplane when the angles of elevation of the two aeroplanes from a point on the ground are 60∘ and 30∘ respectively. Then the vertical distance between the aeroplanes at that instant is
Answer» An aeroplane flying at a height of $9000 m$ vertically above from the ground, passes another aeroplane when the angles of elevation of the two aeroplanes from a point on the ground are $60^{\circ}$ and $30^{\circ}$ respectively. Then the vertical distance between the aeroplanes at that instant is

Discussion

19.	An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]
Answer» An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]

19.

An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]

Answer»

An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is

[CEE 1993; IIT Screening]

Discussion

20.	In Argand plane, assume +x, -x, +y, -y as East, West, North & South respectively. A man walks a distance of 6 units from the Origin towards the north-east direction. From there, he walks a distance of 8 units towards the north-west direction to reach a point P. The position of P in the Argand plane is given by (a+ib)eiπ4. Then, a+b=
Answer» In Argand plane, assume +x, -x, +y, -y as East, West, North & South respectively. A man walks a distance of $6$ units from the Origin towards the north-east direction. From there, he walks a distance of $8$ units towards the north-west direction to reach a point P. The position of P in the Argand plane is given by $(a + i b) e^{i \frac{π}{4}}$ . Then, $a + b =$

Discussion

21.	If, in a right angled triangle ABC, the hypotenuse AB = p, then AB . AC + BC . BA + CA . CB =
Answer» If, in a right angled triangle ABC, the hypotenuse AB = p, then AB . AC + BC . BA + CA . CB =

Discussion

22.	The equation of chord to the parabola y2=4x whose sum of ordinates and product of abscissas of the endpoints of the chord is 4 and 9 respectively, is :
Answer» The equation of chord to the parabola $y^{2} = 4 x$ whose sum of ordinates and product of abscissas of the endpoints of the chord is $4$ and $9$ respectively, is :

Discussion

23.	The eccentricity of a hyperbola passing through the points (3, 0),(3√2,2) will be
Answer» The eccentricity of a hyperbola passing through the points (3, 0), $(3 \sqrt{2}, 2)$ will be

Discussion

24.	22.The interval on which f(x)=2x3+9x2+12x-1 is decreasing in interval
Answer» 22.The interval on which f(x)=2x3+9x2+12x-1 is decreasing in interval

Discussion

25.	If 20C1+(22)20C2+(32)20C3+.....+(202)20C20=A(2β), then the ordered pair (A,β) is equal to:
Answer» If $^{20} C_{1} + (2^{2})^{20} C_{2} + (3^{2})^{20} C_{3} + . . . . . + (20^{2})^{20} C_{20} = A (2^{β})$ , then the ordered pair $(A, β)$ is equal to:

Discussion

26.	Number of 2 digit even numbers that can be formed using the digits 1, 2, 3, 4, 5, if the digits can be repeated is
Answer» Number of $2$ digit even numbers that can be formed using the digits $1, 2, 3, 4, 5,$ if the digits can be repeated is

Discussion

27.	The Partnership agreement between Maneesh and Girish provides that (i) Profits will be shared equally; (ii) Maneesh will be allowed a salary of Rs 400 pm; (iii) Girish who manages the sales department will be allowed a commission equal to 10% of the net profits, after allowing Maneesh's salary; (iv) 7% interest will be allowed on partner's fixed capital; (v) 5% interest will be charged on partner's annual drawings; (vi) The fixed capitals of Maneesh and Girish are Rs 1,00,000 and Rs 80,000 respectively. Their annual drawings were Rs 16,000 and Rs 14,000 respectively. The net profit for the year ending March 31, 2006 amounted to Rs 40,000; Prepare firm's profit and toss appropriation account.
Answer» The Partnership agreement between Maneesh and Girish provides that (i) Profits will be shared equally; (ii) Maneesh will be allowed a salary of Rs 400 pm; (iii) Girish who manages the sales department will be allowed a commission equal to 10% of the net profits, after allowing Maneesh's salary; (iv) 7% interest will be allowed on partner's fixed capital; (v) 5% interest will be charged on partner's annual drawings; (vi) The fixed capitals of Maneesh and Girish are Rs 1,00,000 and Rs 80,000 respectively. Their annual drawings were Rs 16,000 and Rs 14,000 respectively. The net profit for the year ending March 31, 2006 amounted to Rs 40,000; Prepare firm's profit and toss appropriation account.

27.

The Partnership agreement between Maneesh and Girish provides that (i) Profits will be shared equally; (ii) Maneesh will be allowed a salary of Rs 400 pm; (iii) Girish who manages the sales department will be allowed a commission equal to 10% of the net profits, after allowing Maneesh's salary; (iv) 7% interest will be allowed on partner's fixed capital; (v) 5% interest will be charged on partner's annual drawings; (vi) The fixed capitals of Maneesh and Girish are Rs 1,00,000 and Rs 80,000 respectively. Their annual drawings were Rs 16,000 and Rs 14,000 respectively. The net profit for the year ending March 31, 2006 amounted to Rs 40,000; Prepare firm's profit and toss appropriation account.

Answer»

The Partnership agreement between Maneesh and Girish provides that

(i) Profits will be shared equally;

(ii) Maneesh will be allowed a salary of Rs 400 pm;

(iii) Girish who manages the sales department will be allowed a commission equal to 10% of the net profits, after allowing Maneesh's salary;

(iv) 7% interest will be allowed on partner's fixed capital;

(v) 5% interest will be charged on partner's annual drawings;

(vi) The fixed capitals of Maneesh and Girish are Rs 1,00,000 and Rs 80,000 respectively. Their annual drawings were Rs 16,000 and Rs 14,000 respectively. The net profit for the year ending March 31, 2006 amounted to Rs 40,000;

Prepare firm's profit and toss appropriation account.

Discussion

28.	∫π40(πx−4x2) In(1 + tan x)dx = ___
Answer» $\int_{0}^{\frac{π}{4}} (π x - 4 x^{2})$ In(1 + tan x)dx = ___

Discussion

29.	Show that,is an increasing function of x throughout its domain.
Answer» Show that, is an increasing function of x throughout its domain.

Discussion

30.	what is chinaclay?? is there any other category ??
Answer» what is chinaclay?? is there any other category ??

Discussion

31.	If current I_1= 3A sin(ω)T and I_2= 4A cos (ω)T, then I_3 is
Answer» If current I_1= 3A sin(ω)T and I_2= 4A cos (ω)T, then I_3 is

Discussion

32.	If sum of the squares of zeros of the quadratic polynomial f(x)=xsquare -8x+k is 40 find the value of K
Answer» If sum of the squares of zeros of the quadratic polynomial f(x)=xsquare -8x+k is 40 find the value of K

Discussion

33.	The position (x) of a particle moving along x-axis varies with time (t) as x = (t 2 – 6t + 3) m, where time t is in second. The particle turns around at
Answer» The position (x) of a particle moving along x-axis varies with time (t) as x = (t 2 – 6t + 3) m, where time t is in second. The particle turns around at

Discussion

34.	If the angles A,B and C of a triangle are in arithmetic progression and if a,b and c denote the lengths of the sides opposite to A,B and C respectively, then the value of the expression acsin2C+casin2A is:
Answer» If the angles $A, B$ and $C$ of a triangle are in arithmetic progression and if $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively, then the value of the expression $\frac{a}{c} sin 2 C + \frac{c}{a} sin 2 A$ is:

Discussion

35.	If the middle term of 1x+x sin x10 is equal to 778, then the value of x is(a) 2nπ+π6(b) nπ+π6(c) nπ+-1nπ6(d) nπ+-1nπ3
Answer» If the middle term of ${(\frac{1}{x} + x \sin x)}^{10}$ is equal to $7 \frac{7}{8},$ then the value of x is (a) $2 n π + \frac{π}{6}$ (b) $n π + \frac{π}{6}$ (c) $n π + {(- 1)}^{n} \frac{π}{6}$ (d) $n π + {(- 1)}^{n} \frac{π}{3}$

Discussion

36.	if (5,0) and (-5,0) are coordinates of vertices of an eqilateral triangle then find the coordiantes of third vertice
Answer» if (5,0) and (-5,0) are coordinates of vertices of an eqilateral triangle then find the coordiantes of third vertice

Discussion

37.	A covered box of volume 72 cm3 and the base sides in a ratio of 1:2 is to be made. The length of all sides so that the total surface area is the least possible is
Answer» A covered box of volume $72 {cm}^{3}$ and the base sides in a ratio of $1 : 2$ is to be made. The length of all sides so that the total surface area is the least possible is

Discussion

38.	Find the number of solutions of \|x-1\|+\|x-2\|+\|x-3\|=10
Answer» Find the number of solutions of \|x-1\|+\|x-2\|+\|x-3\|=10

Discussion

39.	A plane P contains the line x+2y+3z+1=0=x−y−z−6, and is perpendicular to the plane −2x+y+z+8=0. Then which of the following points lies on P ?
Answer» A plane $P$ contains the line $x + 2 y + 3 z + 1 = 0 = x - y - z - 6,$ and is perpendicular to the plane $- 2 x + y + z + 8 = 0.$ Then which of the following points lies on $P ?$

Discussion

40.	tan 5° tan 25° tan 30° tan 65° tan 85° = ?(a) 1(b) 3(c) 13(d) 12
Answer» tan 5° tan 25° tan 30° tan 65° tan 85° = ? (a) 1 (b) $\sqrt{3}$ (c) $\frac{1}{\sqrt{3}}$ (d) $\frac{1}{2}$

Discussion

41.	The length of the perpendicular drawn from the point (2,1,4) to the plane containing the lines →r=(^i+^j)+λ(^i+2^j−^k) and →r=(^i+^j)+μ(−^i+^j−2^k) is :
Answer» The length of the perpendicular drawn from the point $(2, 1, 4)$ to the plane containing the lines $\to r = (^i +^j) + λ (^i + 2^j -^k)$ and $\to r = (^i +^j) + μ (-^i +^j - 2^k)$ is :

Discussion

42.	formula to find rydberg cons†an t is its value 2.18×10^{-18} also?
Answer» formula to find rydberg cons†an t is its value 2.18×10^{-18} also?

Discussion

43.	(t +1) (x+logx)
Answer» (t +1) (x+logx)

Discussion

44.	If x=1/3-√5 ,then the value of (√x+1/√x) is
Answer» If x=1/3-√5 ,then the value of (√x+1/√x) is

Discussion

45.	34.Prove 1+cos theta=2costheta/2
Answer» 34.Prove 1+cos theta=2costheta/2

Discussion

46.	If →a,→b,→c be three non-coplanar uni-modular vectors each inclined with other at an angle of 60∘, then volume of the tetrahedron whose edges are →a,→b and →c is
Answer» If $\to a, \to b, \to c$ be three non-coplanar uni-modular vectors each inclined with other at an angle of $60^{\circ}$ , then volume of the tetrahedron whose edges are $\to a, \to b$ and $\to c$ is

Discussion

47.	Prove that two lines perpendicular to the same line are parallel to each other.
Answer» Prove that two lines perpendicular to the same line are parallel to each other.

Discussion

48.	Evaluate ∫3x+4x2+x−12dx(where C is constant of integration)
Answer» Evaluate $\int \frac{3 x + 4}{x^{2} + x - 12} d x$ (where $C$ is constant of integration)

Discussion

49.	If a curve passes through the origin and the slope of the tangent to it at any point (x,y) is x2−4x+y+8x−2, then this curve also passes through the point :
Answer» If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^{2} - 4 x + y + 8}{x - 2}$ , then this curve also passes through the point :

Discussion

50.	1.centre (0,2) and radius 2
Answer» 1.centre (0,2) and radius 2

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

There are total 18 balls in a bag. Out of them, 6 are red in colour, 4 are green in colour and 8 are blue in colour. If Vishal picks three balls randomly from the bag, then what is the probability that all the three balls are not of the same colour?

What's the equation of a tangent on the parabolay2=5x at the point (5, 5)

20.Graph of x+integral value of x

If limx→1(2x+22x+23x+⋯+2nx)=126 (n∈N), then the value of n is equal to

A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is 332, then n is equal to ___.

limx→0 x2cosx1-cosx is(a) 2 (b) 32 (c) -32 (d) 1

Let x0 be the point of Local maxima of f(x)=→a⋅(→b×→c), where →a=x^i−2^j+3^k,→b=−2^i+x^j−^k and →c=7^i−2^j+x^k. Then the value of →a⋅→b+→b⋅→c+→c⋅→a at x=x0 is

The range of f(x)=x2−81x−9 is

If g(x) = 2f(x) + x + log (f(x)) then d(g(x))d(f(x))_________

ABC is a right angle triangle at B and BC=10. If 100 points L1,L2,L3,…,L100 on AB are such that AB is divided into 101 equal parts and L1M1,L2M2,…,L100M100 are line segments parallel to BC and points M1,M2,M3,…,M100 are on AC, then the sum of L1M1,L2M2,…,L100M100 is

The area of the quadrilateral formed by the lines 4x−3y−a=0,3x−4y+a=0, 4x−3y−3a=0 and 3x−4y+2a=0 is

Equation of curve through point(1,0) which satisfies the differential equation (1+y2)dx−xydy=0, is

If a + ib =,prove that a2 + b2 =

If I1=∫102x2 dx, I2=∫102x3dx, I3=∫212x2dx and I4=∫212x3 dx then

The lengths and bearing of a traverse PQRS are: Segment Length(m) Bearing PQ 40 80∘ QR 50 10∘ RS 30 210∘ The length of line segment SP (in m, round off to two decimal places), is44.79

Show that the linesandareperpendicular to each other.

Given that and . What can you conclude about the vectors ?

An aeroplane flying at a height of 9000 m vertically above from the ground, passes another aeroplane when the angles of elevation of the two aeroplanes from a point on the ground are 60∘ and 30∘ respectively. Then the vertical distance between the aeroplanes at that instant is

An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is [CEE 1993; IIT Screening]

If, in a right angled triangle ABC, the hypotenuse AB = p, then AB . AC + BC . BA + CA . CB =

The equation of chord to the parabola y2=4x whose sum of ordinates and product of abscissas of the endpoints of the chord is 4 and 9 respectively, is :

The eccentricity of a hyperbola passing through the points (3, 0),(3√2,2) will be

22.The interval on which f(x)=2x3+9x2+12x-1 is decreasing in interval

If 20C1+(22)20C2+(32)20C3+.....+(202)20C20=A(2β), then the ordered pair (A,β) is equal to:

Number of 2 digit even numbers that can be formed using the digits 1, 2, 3, 4, 5, if the digits can be repeated is

∫π40(πx−4x2) In(1 + tan x)dx = ___

Show that,is an increasing function of x throughout its domain.

what is chinaclay?? is there any other category ??

If current I_1= 3A sin(ω)T and I_2= 4A cos (ω)T, then I_3 is

If sum of the squares of zeros of the quadratic polynomial f(x)=xsquare -8x+k is 40 find the value of K

The position (x) of a particle moving along x-axis varies with time (t) as x = (t 2 – 6t + 3) m, where time t is in second. The particle turns around at

If the angles A,B and C of a triangle are in arithmetic progression and if a,b and c denote the lengths of the sides opposite to A,B and C respectively, then the value of the expression acsin2C+casin2A is:

If the middle term of 1x+x sin x10 is equal to 778, then the value of x is(a) 2nπ+π6(b) nπ+π6(c) nπ+-1nπ6(d) nπ+-1nπ3

if (5,0) and (-5,0) are coordinates of vertices of an eqilateral triangle then find the coordiantes of third vertice

A covered box of volume 72 cm3 and the base sides in a ratio of 1:2 is to be made. The length of all sides so that the total surface area is the least possible is

Find the number of solutions of |x-1|+|x-2|+|x-3|=10

A plane P contains the line x+2y+3z+1=0=x−y−z−6, and is perpendicular to the plane −2x+y+z+8=0. Then which of the following points lies on P ?

tan 5° tan 25° tan 30° tan 65° tan 85° = ?(a) 1(b) 3(c) 13(d) 12

The length of the perpendicular drawn from the point (2,1,4) to the plane containing the lines →r=(^i+^j)+λ(^i+2^j−^k) and →r=(^i+^j)+μ(−^i+^j−2^k) is :

formula to find rydberg cons†an t is its value 2.18×10^{-18} also?

(t +1) (x+logx)

If x=1/3-√5 ,then the value of (√x+1/√x) is

34.Prove 1+cos theta=2costheta/2

If →a,→b,→c be three non-coplanar uni-modular vectors each inclined with other at an angle of 60∘, then volume of the tetrahedron whose edges are →a,→b and →c is

Prove that two lines perpendicular to the same line are parallel to each other.

Evaluate ∫3x+4x2+x−12dx(where C is constant of integration)

If a curve passes through the origin and the slope of the tangent to it at any point (x,y) is x2−4x+y+8x−2, then this curve also passes through the point :

1.centre (0,2) and radius 2