32581 + Interview Questions in Mathematics

1.	If the first term of an AP is 4 and the common difference is -4, find the next term.
Answer» If the first term of an AP is 4 and the common difference is -4, find the next term.

Discussion

2.	Solve : 99x+101y=499 101x+99y= 501 (With steps)
Answer» Solve : 99x+101y=499 101x+99y= 501 (With steps)

2.

Solve : 99x+101y=499 101x+99y= 501 (With steps)

Answer»

Solve :

99x+101y=499

101x+99y= 501

(With steps)

Discussion

3.	Show that one and only one out of n, n+1, n+4 is divisible by 3 where n is any positive integer.
Answer» Show that one and only one out of n, n+1, n+4 is divisible by 3 where n is any positive integer.

Discussion

4.	Eight times a two digit number is equal to three times the number obtained by reversing the order of the digits. If the difference between the digits of the number is 5, find the number
Answer» Eight times a two digit number is equal to three times the number obtained by reversing the order of the digits. If the difference between the digits of the number is 5, find the number

Discussion

5.	a number is atwo digit number which is three times more than 4 times the sum of the digits . if 18 is added to the number , the digits gets opposite. represent geometrically.
Answer» a number is atwo digit number which is three times more than 4 times the sum of the digits . if 18 is added to the number , the digits gets opposite. represent geometrically.

Discussion

6.	How many number of solutions does pair of equations y=0 and y=-5 has ???
Answer» How many number of solutions does pair of equations y=0 and y=-5 has ???

Discussion

7.	P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.
Answer» P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.

Discussion

8.	If a^2+b^2+c^2-ab-bc-ca =0,prove that a=b=c.
Answer» If a^2+b^2+c^2-ab-bc-ca =0,prove that a=b=c.

Discussion

9.	Consider A = (x+y+z3012) = (−azx+z−y). The value of a is ___
Answer» Consider A = $(\begin{matrix} x + y + z & 3 0 & 12 \end{matrix})$ = $(\begin{matrix} - a & z x + z & - y \end{matrix})$ . The value of a is ___

Discussion

10.	Question 8 A hallow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 18 space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate is Thinking process If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles. (A) 142296 (B) 142396 (C) 142496 (D) 142596
Answer» Question 8 A hallow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate is Thinking process If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles. (A) 142296 (B) 142396 (C) 142496 (D) 142596

Discussion

11.	In the following question, two equations are given. Solve both the equations and mark the corresponding answer, if: a) x is greater than y b) x is less than y c) x is greater than or equal than y d) x is less than or equal to y e) x = y or a definite relationship between x & y cannot be established I.x2 - 19x + 84 = 0 II. y2 - 25y + 156 = 0
Answer» In the following question, two equations are given. Solve both the equations and mark the corresponding answer, if: a) x is greater than y b) x is less than y c) x is greater than or equal than y d) x is less than or equal to y e) x = y or a definite relationship between x & y cannot be established I.x $^{2}$ - 19x + 84 = 0 II. y $^{2}$ - 25y + 156 = 0

11.

In the following question, two equations are given. Solve both the equations and mark the corresponding answer, if: a) x is greater than y b) x is less than y c) x is greater than or equal than y d) x is less than or equal to y e) x = y or a definite relationship between x & y cannot be established I.x2 - 19x + 84 = 0 II. y2 - 25y + 156 = 0

Answer»

In the following question, two equations are given. Solve both the equations and mark the corresponding answer, if:

a) x is greater than y

b) x is less than y

c) x is greater than or equal than y

d) x is less than or equal to y

e) x = y or a definite relationship between x & y cannot be established

I.x $^{2}$ - 19x + 84 = 0

II. y $^{2}$ - 25y + 156 = 0

Discussion

12.	a) Solve the following equation and give your answer correct to 3 significant figures: 5x2−3x−4=0 b) Without solving the following quadratic equation, find the value of p for which the roots are equal: px2−4x+3=0 [6 MARKS]
Answer» a) Solve the following equation and give your answer correct to 3 significant figures: $5 x^{2} - 3 x - 4 = 0$ b) Without solving the following quadratic equation, find the value of p for which the roots are equal: $p x^{2} - 4 x + 3 = 0$ [6 MARKS]

Discussion

13.	Find the angle of inclination of the straight line whose slope is 1√3
Answer» Find the angle of inclination of the straight line whose slope is $\frac{1}{\sqrt{3}}$

Discussion

14.	What is/are the condition(s) for (a2−4)xd−2+bx+c=0 to be a quadratic equation in x?
Answer» What is/are the condition(s) for $(a^{2} - 4) x^{d - 2} + b x + c = 0$ to be a quadratic equation in $x$ ?

Discussion

15.	In figure below, ΔABC is right-angled at B and tan A = 4/3. If AC = 15 cm, then the length of AB is :
Answer» In figure below, ΔABC is right-angled at B and tan A = ⁴/₃. If AC = 15 cm, then the length of AB is :

15.

In figure below, ΔABC is right-angled at B and tan A = 4/3. If AC = 15 cm, then the length of AB is :

Answer»

In figure below, ΔABC is right-angled at B and tan A = ⁴/₃. If AC = 15 cm, then the length of AB is :

Discussion

16.	The sum of areas of two squares is 468m2. If the difference of their perimeters is 24m, then the sides of the two squares are:
Answer» The sum of areas of two squares is 468m². If the difference of their perimeters is 24m, then the sides of the two squares are:

Discussion

17.	The median for the data is IQ60−7070−8080−9090−100100−110110−120120−130No. of pupils2351614137
Answer» The median for the data is $\begin{matrix} I Q & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 N o . o f p u p i l s & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

17.

The median for the data is IQ60−7070−8080−9090−100100−110110−120120−130No. of pupils2351614137

Answer»

The median for the data is

$\begin{matrix} I Q & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 N o . o f p u p i l s & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

Discussion

18.	A hollow cube has volume equal to 216 cm3. Find the surface area of the largest sphere which can be enclosed in it is
Answer» A hollow cube has volume equal to 216 cm $^{3}$ . Find the surface area of the largest sphere which can be enclosed in it is

Discussion

19.	What is the probability of obtaining the sum of interior angles of a triangle as 180∘?
Answer» What is the probability of obtaining the sum of interior angles of a triangle as $180^{\circ}$ ?

Discussion

20.	State the fundamental theorem of arithmetic
Answer» State the fundamental theorem of arithmetic

Discussion

21.	Find the value of x for which the points A(x, 2), B(-3, -4) and C(7, -5) are collinear.
Answer» Find the value of x for which the points A(x, 2), B(-3, -4) and C(7, -5) are collinear.

Discussion

22.	A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g? (Given:Pure gold is 24-carat).
Answer» A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g? (Given:Pure gold is 24-carat).

22.

A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g? (Given:Pure gold is 24-carat).

Answer»

A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g?

(Given:Pure gold is 24-carat).

Discussion

23.	A number consists of two digits.When it is divided by the sum of its digits,the quotient is 6 with no remainder.When the number is diminished by 9, the digits are reversed.Find the number.
Answer» A number consists of two digits.When it is divided by the sum of its digits,the quotient is 6 with no remainder.When the number is diminished by 9, the digits are reversed.Find the number.

Discussion

24.	The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the volume of cylinder.
Answer» The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 $c m^{2}$ , find the volume of cylinder.

Discussion

25.	Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60∘and 30∘, respectively. Then the distances of the point from the poles are respectively.
Answer» Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ , respectively. Then the distances of the point from the poles are respectively.

Discussion

26.	Any two digit number can be represented as ___x + y, where x and y are the digits of the number.
Answer» Any two digit number can be represented as ___x + y, where x and y are the digits of the number.

Discussion

27.	If the point C(k,4) divides the join of A(2, 6) and B(5, 1) in the ratio 2:3 then find the value of k.
Answer» If the point C(k,4) divides the join of A(2, 6) and B(5, 1) in the ratio 2:3 then find the value of k.

Discussion

28.	Explain Pythagoras theorem.
Answer» Explain Pythagoras theorem.

Discussion

29.	The complete set of values of k, for which the quadratic equation x2−kx+k+2=0 has equal roots, consists of
Answer» The complete set of values of k, for which the quadratic equation $x^{2} - k x + k + 2 = 0$ has equal roots, consists of

Discussion

30.	Factorise : (3x−2y)2+3(3x−2y)−10
Answer» Factorise : $(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$

30.

Factorise : (3x−2y)2+3(3x−2y)−10

Answer»

Factorise :

$(3 x - 2 y)^{2} + 3 (3 x - 2 y) - 10$

Discussion

31.	There is a hollow cylinder as shown in figure having an inner and outer radius as 7 cm and 14 cm respectively and height is 28 cm. A man wants to paint it completely inside out. The area which he needs to paint is equal to:
Answer» There is a hollow cylinder as shown in figure having an inner and outer radius as 7 cm and 14 cm respectively and height is 28 cm. A man wants to paint it completely inside out. The area which he needs to paint is equal to:

Discussion

32.	Calculate the other sides of a triangle whose shortest side is 6cm and which is similar to a triangle whose sides are 4cm,7cm,8cm
Answer» Calculate the other sides of a triangle whose shortest side is 6cm and which is similar to a triangle whose sides are 4cm,7cm,8cm

Discussion

33.	The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is (a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1
Answer» The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is (a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

33.

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is (a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

Answer»

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is

(a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

Discussion

34.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula: 3x2−2√6x+2=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $3 x^{2} - 2 \sqrt{6} x + 2 = 0$

Discussion

35.	Question 176 By what number should (−8)−3 be multiplied so that the product may be equal to (−6)−3 ?
Answer» Question 176 By what number should $(- 8)^{- 3}$ be multiplied so that the product may be equal to $(- 6)^{- 3}$ ?

35.

Question 176 By what number should (−8)−3 be multiplied so that the product may be equal to (−6)−3 ?

Answer»

Question 176

By what number should $(- 8)^{- 3}$ be multiplied so that the product may be equal to $(- 6)^{- 3}$ ?

Discussion

36.	What can be said about the profit of a company, which sells tablets, from the following data? MonthJanuaryFebruaryMarchAprilMayNo. of tablets solds11009816451234990
Answer» What can be said about the profit of a company, which sells tablets, from the following data? $\begin{matrix} M o n t h & J a n u a r y & F e b r u a r y & M a r c h & A p r i l & M a y N o . o f t a b l e t s s o l d s & 1100 & 981 & 645 & 1234 & 990 \end{matrix}$

Discussion

37.	A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60∘. If the angle of elevation is 30∘ from a point at a distance 'y' metres from the bank, then the height of the tree = ___ m.
Answer» A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is $60^{\circ}$ . If the angle of elevation is $30^{\circ}$ from a point at a distance 'y' metres from the bank, then the height of the tree = ___ m.

Discussion

38.	Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket ?
Answer» Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket ?

Discussion

39.	Find the least number that is divisible by all the numbers between 1 and 10( both inclusive)
Answer» Find the least number that is divisible by all the numbers between 1 and 10( both inclusive)

Discussion

40.	Find d2ydx2 for y=cos−1x.
Answer» Find $\frac{d^{2} y}{d x^{2}}$ for $y = c o s^{- 1} x$ .

Discussion

41.	3/x -1/y = -9 , 2/x +3/y = 5 . By substituting method
Answer» 3/x -1/y = -9 , 2/x +3/y = 5 . By substituting method

Discussion

42.	An electric cable costs RS 200. If the cable was 5 metres longer and each metre of cable costs RS 2 less, the cost of the table would have remain unchanged. Find the length of the cable.
Answer» An electric cable costs RS 200. If the cable was 5 metres longer and each metre of cable costs RS 2 less, the cost of the table would have remain unchanged. Find the length of the cable.

Discussion

43.	Find the degree of the polynomial x4−5x2+4x2−x−2
Answer» Find the degree of the polynomial $x^{4} - 5 x^{2} + \frac{4}{x^{2}} - x - 2$

Discussion

44.	A tent 10 m high is tied with a taut rope from the ground to the top of the tent making an angle of elevation of 30∘ with the ground. The length of the rope is ___ m
Answer» A tent 10 m high is tied with a taut rope from the ground to the top of the tent making an angle of elevation of $30^{\circ}$ with the ground. The length of the rope is ___ m

Discussion

45.	Find the value of k for which the system of equation X+2y-3=0 and 5x+my+7=0 has no solution
Answer» Find the value of k for which the system of equation X+2y-3=0 and 5x+my+7=0 has no solution

Discussion

46.	A computer manufacturing company ABC sells a computer to a distributor P for ₹ 44000 including sales tax. The rate of sales tax is 10 % , find the sale price of the computer for the distributor P.
Answer» A computer manufacturing company ABC sells a computer to a distributor P for ₹ 44000 including sales tax. The rate of sales tax is 10 % , find the sale price of the computer for the distributor P.

Discussion

47.	Solve by method of elimination by equating coefficients: 10y = 7x - 4 12 x+ 18y = 1
Answer» Solve by method of elimination by equating coefficients: 10y = 7x - 4 12 x+ 18y = 1

47.

Solve by method of elimination by equating coefficients: 10y = 7x - 4 12 x+ 18y = 1

Answer»

Solve by method of elimination by equating coefficients:

10y = 7x - 4

12 x+ 18y = 1

Discussion

48.	81. The greatest number of four digits which when divided by 3, 5, 7, 9 leaves the remainders 1, 3, 5, 7 respectively is
Answer» 81. The greatest number of four digits which when divided by 3, 5, 7, 9 leaves the remainders 1, 3, 5, 7 respectively is

Discussion

49.	Find three number in A.P. whose sum is 24 and whose product is 440
Answer» Find three number in A.P. whose sum is 24 and whose product is 440

Discussion

50.	If θis a positive acute angle such that sec θ = cosec 60o,find the value of 2 cos2 θ − 1
Answer» If $θ$ is a positive acute angle such that sec $θ = c o s e c 60^{o}$ ,find the value of 2 $c o s^{2} θ - 1$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the first term of an AP is 4 and the common difference is -4, find the next term.

Solve : 99x+101y=499 101x+99y= 501 (With steps)

Show that one and only one out of n, n+1, n+4 is divisible by 3 where n is any positive integer.

Eight times a two digit number is equal to three times the number obtained by reversing the order of the digits. If the difference between the digits of the number is 5, find the number

a number is atwo digit number which is three times more than 4 times the sum of the digits . if 18 is added to the number , the digits gets opposite. represent geometrically.

How many number of solutions does pair of equations y=0 and y=-5 has ???

P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.

If a^2+b^2+c^2-ab-bc-ca =0,prove that a=b=c.

Consider A = (x+y+z3012) = (−azx+z−y). The value of a is ___

a) Solve the following equation and give your answer correct to 3 significant figures: 5x2−3x−4=0 b) Without solving the following quadratic equation, find the value of p for which the roots are equal: px2−4x+3=0 [6 MARKS]

Find the angle of inclination of the straight line whose slope is 1√3

What is/are the condition(s) for (a2−4)xd−2+bx+c=0 to be a quadratic equation in x?

In figure below, ΔABC is right-angled at B and tan A = 4/3. If AC = 15 cm, then the length of AB is :

The sum of areas of two squares is 468m2. If the difference of their perimeters is 24m, then the sides of the two squares are:

The median for the data is IQ60−7070−8080−9090−100100−110110−120120−130No. of pupils2351614137

A hollow cube has volume equal to 216 cm3. Find the surface area of the largest sphere which can be enclosed in it is

What is the probability of obtaining the sum of interior angles of a triangle as 180∘?

State the fundamental theorem of arithmetic

Find the value of x for which the points A(x, 2), B(-3, -4) and C(7, -5) are collinear.

A jeweller has bars of 18-carat gold and 12-carat gold.How much of each must be melted together to obtain a bar of 16-carat gold,weighing 120 g? (Given:Pure gold is 24-carat).

A number consists of two digits.When it is divided by the sum of its digits,the quotient is 6 with no remainder.When the number is diminished by 9, the digits are reversed.Find the number.

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the volume of cylinder.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60∘and 30∘, respectively. Then the distances of the point from the poles are respectively.

Any two digit number can be represented as ___x + y, where x and y are the digits of the number.

If the point C(k,4) divides the join of A(2, 6) and B(5, 1) in the ratio 2:3 then find the value of k.

Explain Pythagoras theorem.

The complete set of values of k, for which the quadratic equation x2−kx+k+2=0 has equal roots, consists of

Factorise : (3x−2y)2+3(3x−2y)−10

There is a hollow cylinder as shown in figure having an inner and outer radius as 7 cm and 14 cm respectively and height is 28 cm. A man wants to paint it completely inside out. The area which he needs to paint is equal to:

Calculate the other sides of a triangle whose shortest side is 6cm and which is similar to a triangle whose sides are 4cm,7cm,8cm

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is (a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

Find the roots of each of the following equations, if they exist, by applying the quadratic formula: 3x2−2√6x+2=0

Question 176 By what number should (−8)−3 be multiplied so that the product may be equal to (−6)−3 ?

What can be said about the profit of a company, which sells tablets, from the following data? MonthJanuaryFebruaryMarchAprilMayNo. of tablets solds11009816451234990

A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60∘. If the angle of elevation is 30∘ from a point at a distance 'y' metres from the bank, then the height of the tree = ___ m.

Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket ?

Find the least number that is divisible by all the numbers between 1 and 10( both inclusive)

Find d2ydx2 for y=cos−1x.

3/x -1/y = -9 , 2/x +3/y = 5 . By substituting method

An electric cable costs RS 200. If the cable was 5 metres longer and each metre of cable costs RS 2 less, the cost of the table would have remain unchanged. Find the length of the cable.

Find the degree of the polynomial x4−5x2+4x2−x−2

A tent 10 m high is tied with a taut rope from the ground to the top of the tent making an angle of elevation of 30∘ with the ground. The length of the rope is ___ m

Find the value of k for which the system of equation X+2y-3=0 and 5x+my+7=0 has no solution

A computer manufacturing company ABC sells a computer to a distributor P for ₹ 44000 including sales tax. The rate of sales tax is 10 % , find the sale price of the computer for the distributor P.

Solve by method of elimination by equating coefficients: 10y = 7x - 4 12 x+ 18y = 1

81. The greatest number of four digits which when divided by 3, 5, 7, 9 leaves the remainders 1, 3, 5, 7 respectively is

Find three number in A.P. whose sum is 24 and whose product is 440

If θis a positive acute angle such that sec θ = cosec 60o,find the value of 2 cos2 θ − 1