24740 + Interview Questions in Mathematics

1.	Prove that two different circles cannot intersect each other at more than two points.
Answer» Prove that two different circles cannot intersect each other at more than two points.

Discussion

2.	ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Answer» ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.

Discussion

3.	The volume of a sphere of radius 21 cm is
Answer» The volume of a sphere of radius 21 cm is

Discussion

4.	If logab+logba=log(a+b), then :
Answer» If $l o g \frac{a}{b} + l o g \frac{b}{a} = l o g (a + b)$ , then :

Discussion

5.	What are real numbers?
Answer» What are real numbers?

Discussion

6.	How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
Answer» How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?

Discussion

7.	A cylindrical bucket open at the top has base radius 35 cm and height 49 cm, its total surface area is
Answer» A cylindrical bucket open at the top has base radius 35 cm and height 49 cm, its total surface area is

Discussion

8.	Assertion : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Reason : The opposite angles of a parallelogram are equal. Which of the following is correct?
Answer» Assertion : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Reason : The opposite angles of a parallelogram are equal. Which of the following is correct?

Discussion

9.	Find the area of the 1.5 m wide pathway (green) if length is twice the breadth. Breadth is equal to 6 m..
Answer» Find the area of the 1.5 m wide pathway (green) if length is twice the breadth. Breadth is equal to 6 m..

9.

Find the area of the 1.5 m wide pathway (green) if length is twice the breadth. Breadth is equal to 6 m..

Answer»

Find the area of the 1.5 m wide pathway (green) if length is twice the breadth. Breadth is equal to 6 m..

Discussion

10.	What is tanθ in △ABC, if θ is increased by 30∘?
Answer» What is $t a n θ$ in $△ A B C$ , if $θ$ is increased by $30^{\circ}$ ?

Discussion

11.	In △ ABC, tan(B+C2)= _______.
Answer» In $△ A B C$ , $t a n (\frac{B + C}{2}) =$ _______.

Discussion

12.	ABCD is a square. E, F, G and H are points on AB, BC, CD and DA respectively, such that AE = BF = CG = DH. Prove that EFGH is a square.
Answer» ABCD is a square. E, F, G and H are points on AB, BC, CD and DA respectively, such that AE = BF = CG = DH. Prove that EFGH is a square.

Discussion

13.	If x=1 and y=6 is a solution of the equation 8x−ay+a2=0, find the values of a.
Answer» $I f x = 1 a n d y = 6 is a solution of the equation 8 x - a y + a^{2} = 0, find the values of a.$

Discussion

14.	Find the value of a, so that the point (3, a) lies on the line represented by 2x-3y = 5
Answer» Find the value of a, so that the point (3, a) lies on the line represented by 2x-3y = 5

Discussion

15.	Find the curved surface area of a cone,if its slant height is 60 cm and the radius of its base is 21 cm.
Answer» Find the curved surface area of a cone,if its slant height is 60 cm and the radius of its base is 21 cm.

Discussion

16.	A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6m. For how many days will the water of this tank last?
Answer» A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring $20 m \times 15 m \times 6 m .$ For how many days will the water of this tank last?

Discussion

17.	If a is any vector then (a×^i)2+(a×^j)2+(a×^k)2 =
Answer» If a is any vector then $(a \times^i)^{2} + (a \times^j)^{2} + (a \times^k)^{2}$ =

Discussion

18.	The diameter of one sphere is 21 cm, and the diameter of another sphere is 14 cm, the ratios of their curved surface areas is
Answer» The diameter of one sphere is 21 cm, and the diameter of another sphere is 14 cm, the ratios of their curved surface areas is

Discussion

19.	If log√8x=103, find the value of x
Answer» If $l o g_{\sqrt{8}} x = \frac{10}{3}$ , find the value of x

Discussion

20.	The sum of 12abx, 2a2bx, 8abx and 8a2bx is
Answer» The sum of $12 a b x$ , $2 a^{2} b x$ , $8 a b x$ and $8 a^{2} b x$ is

Discussion

21.	Write 545 = 2502 in logarithmic form
Answer» Write 5⁴5 = 2502 in logarithmic form

Discussion

22.	If the zeroes of the polynomials p(x)=2x−4 and q(x)=5x−15 are multipled, we get a zero of the polynomial r(x)=ax2+bx+10. Which of the following relations is true?
Answer» If the zeroes of the polynomials $p (x) = 2 x - 4$ and $q (x) = 5 x - 15$ are multipled, we get a zero of the polynomial $r (x) = a x^{2} + b x + 10$ . Which of the following relations is true?

Discussion

23.	If 3√3(3√x−13√x)=2,then3√x+13√x= ___.
Answer» If $\sqrt[3]{3 (\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}})} = 2, t h e n \sqrt[3]{x} + \frac{1}{\sqrt[3]{x}} =$ ___.

Discussion

24.	The mean weight of a group of seven boys is 56 kgs. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy. [4 MARKS]
Answer» The mean weight of a group of seven boys is 56 kgs. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy. [4 MARKS]

Discussion

25.	factorise (x^4 +4)
Answer» factorise (x^4 +4)

Discussion

26.	True or false. Give reasons A rational number is a quotient of any two integers.
Answer» True or false. Give reasons A rational number is a quotient of any two integers.

26.

True or false. Give reasons A rational number is a quotient of any two integers.

Answer»

True or false. Give reasons

A rational number is a quotient of any two integers.

Discussion

27.	Evaluate (2+3+4)2 using identities
Answer» Evaluate $(2 + 3 + 4)^{2}$ using identities

Discussion

28.	To construct a parallelogram___
Answer» To construct a parallelogram___

Discussion

29.	How to construct incircle of triangle.
Answer» How to construct incircle of triangle.

Discussion

30.	Is difference of two irrational numbers always an irrational number?
Answer» Is difference of two irrational numbers always an irrational number?

Discussion

31.	Choose the correct answer in the following question: The mid-value of a class interval is 42 and the class size is 10. The lower and upper limits are (a) 37−47 (b) 37.5−47.5 (c) 36.5−47.5 (d) 36.5−46.5
Answer» Choose the correct answer in the following question: The mid-value of a class interval is $42$ and the class size is $10$ . The lower and upper limits are (a) $37 - 47$ (b) $37.5 - 47.5$ (c) $36.5 - 47.5$ (d) $36.5 - 46.5$

Discussion

32.	Calculate the mode of the following sizes of shoes sold by a shop on a particular day. 5,9,8,6,9,4,3,9,1,6,3,9,7,1,2,5,9
Answer» Calculate the mode of the following sizes of shoes sold by a shop on a particular day. 5,9,8,6,9,4,3,9,1,6,3,9,7,1,2,5,9

Discussion

33.	In aΔABC,it is given that ∠A:∠B:∠C=3:2:1and ∠ACD=90∘.If BC is produced to E then ∠ECD=? (a) 60∘(b) 50∘(c) 40∘(d) 25∘
Answer» $I n a Δ A B C, it is given that ∠ A : ∠ B : ∠ C = 3 : 2 : 1 a n d ∠ A C D = 90^{\circ} . If BC is produced to E then ∠ E C D = ?$ $(a) 60^{\circ} (b) 50^{\circ} (c) 40^{\circ} (d) 25^{\circ}$

33.

In aΔABC,it is given that ∠A:∠B:∠C=3:2:1and ∠ACD=90∘.If BC is produced to E then ∠ECD=? (a) 60∘(b) 50∘(c) 40∘(d) 25∘

Answer»

$I n a Δ A B C, it is given that ∠ A : ∠ B : ∠ C = 3 : 2 : 1 a n d ∠ A C D = 90^{\circ} . If BC is produced to E then ∠ E C D = ?$

$(a) 60^{\circ} (b) 50^{\circ} (c) 40^{\circ} (d) 25^{\circ}$

Discussion

34.	1) Solve graphically the following equations : x+2y=4 , 3x -2y =4 . take 2cm = 1 unit on eachaxis. Write down the area of the triangle formed by the lines and the x- axis. 2) on graph paper take 2 cm to represent one unit on both the axes draw the lines: x+3= 0, y-2=0, 2x+3y=12. Write down the coordinates of the vertices of the triangle formed by the lines
Answer» 1) Solve graphically the following equations : x+2y=4 , 3x -2y =4 . take 2cm = 1 unit on eachaxis. Write down the area of the triangle formed by the lines and the x- axis. 2) on graph paper take 2 cm to represent one unit on both the axes draw the lines: x+3= 0, y-2=0, 2x+3y=12. Write down the coordinates of the vertices of the triangle formed by the lines

34.

1) Solve graphically the following equations : x+2y=4 , 3x -2y =4 . take 2cm = 1 unit on eachaxis. Write down the area of the triangle formed by the lines and the x- axis. 2) on graph paper take 2 cm to represent one unit on both the axes draw the lines: x+3= 0, y-2=0, 2x+3y=12. Write down the coordinates of the vertices of the triangle formed by the lines

Answer»

1) Solve graphically the following equations :

x+2y=4 , 3x -2y =4 . take 2cm = 1 unit on eachaxis. Write down the area of the triangle formed by the lines and the x- axis.

2) on graph paper take 2 cm to represent one unit on both the axes draw the lines:

x+3= 0, y-2=0, 2x+3y=12. Write down the coordinates of the vertices of the triangle formed by the lines

Discussion

35.	The mean of n observations is x (bar). If each observation is multiplied by k, then find the mean of new observations.
Answer» The mean of n observations is x (bar). If each observation is multiplied by k, then find the mean of new observations.

Discussion

36.	Choose the correct option for the underlined phrases. The company had hired someone smarter than the current manager.
Answer» Choose the correct option for the underlined phrases. The company had hired someone smarter than the current manager.

36.

Choose the correct option for the underlined phrases. The company had hired someone smarter than the current manager.

Answer»

Choose the correct option for the underlined phrases.

The company had hired someone smarter than the current manager.

Discussion

37.	Express y interms of x 3x-2y+12=0
Answer» Express y interms of x 3x-2y+12=0

Discussion

38.	The angles of a triangle are arranged in ascending order . if the difference between consecutive angles is 10 then all the angles will be
Answer» The angles of a triangle are arranged in ascending order . if the difference between consecutive angles is 10 then all the angles will be

Discussion

39.	Given that x and y are in inverse proportion, and y1 y2 are values of y corresponding to the values x1x2 of x respectively. Which of the following is correct?
Answer» Given that x and y are in inverse proportion, and $y_{1}$ $y_{2}$ are values of $y$ corresponding to the values $x_{1}$ $x_{2}$ of $x$ respectively. Which of the following is correct?

Discussion

40.	The number of values of x∈[0,nπ],n∈I that satisfy log\|sinx\|(1+cosx)=2 is
Answer» The number of values of $x \in [0, n π], n \in I$ that satisfy $l o g_{\| s i n x \|} (1 + c o s x) = 2$ is

Discussion

41.	Volume of a cuboid is 12cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is
Answer» Volume of a cuboid is 12 $c m^{3} .$ The volume $(i n c m^{3})$ of a cuboid whose sides are double of the above cuboid is

Discussion

42.	The mean weight of a class of 24 students is 48 kg. If the weight of the teacher be included, then the mean weight increases by 500 g. Find the weight of the teacher.
Answer» The mean weight of a class of 24 students is 48 kg. If the weight of the teacher be included, then the mean weight increases by 500 g. Find the weight of the teacher.

Discussion

43.	What is the area of the shaded region in the figure, if it is given that the side of square ABCD is 90 m and the side of square PQRS is 100 m?
Answer» What is the area of the shaded region in the figure, if it is given that the side of square ABCD is 90 m and the side of square PQRS is 100 m?

Discussion

44.	if secAand cosecA are roots of x^2-px+q then choose the correct option a)p^2+q^2=2q b)p^2+q^2=2p c)p^2-q^2=2q d)p^2-q^2=2p
Answer» if secAand cosecA are roots of x^2-px+q then choose the correct option a)p^2+q^2=2q b)p^2+q^2=2p c)p^2-q^2=2q d)p^2-q^2=2p

44.

if secAand cosecA are roots of x^2-px+q then choose the correct option a)p^2+q^2=2q b)p^2+q^2=2p c)p^2-q^2=2q d)p^2-q^2=2p

Answer»

if secAand cosecA are roots of x^2-px+q then choose the correct option

a)p^2+q^2=2q

b)p^2+q^2=2p

c)p^2-q^2=2q

d)p^2-q^2=2p

Discussion

45.	If y = 4x is rewritten in the form ax + by + c = 0, which of these options represents the values of a, b and c respectively?
Answer» If y = 4x is rewritten in the form ax + by + c = 0, which of these options represents the values of a, b and c respectively?

Discussion

46.	Evaluate the following using suitable identities: (i)(99)3 (ii) (102)3 (iii) (998)3
Answer» Evaluate the following using suitable identities: (i) $(99)^{3}$ (ii) $(102)^{3}$ (iii) $(998)^{3}$

Discussion

47.	Question 66 Fill in the blanks to make the statements true. The number of diagonals in a hexagon is ___.
Answer» Question 66 Fill in the blanks to make the statements true. The number of diagonals in a hexagon is ___.

Discussion

48.	Find the unique solution for the pair of linear equations: x + 2y = 5 and 7x + 3y = 13.
Answer» Find the unique solution for the pair of linear equations: x + 2y = 5 and 7x + 3y = 13.

Discussion

49.	Which of the following is a factor of (x+y)3−(x3+y3)? (a) x2+y2+2xy (b) x2+y2−xy (c) xy2 (d) 3xy
Answer» Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ? (a) $x^{2} + y^{2} + 2 x y$ (b) $x^{2} + y^{2} - x y$ (c) $x y^{2}$ (d) $3 x y$

49.

Which of the following is a factor of (x+y)3−(x3+y3)? (a) x2+y2+2xy (b) x2+y2−xy (c) xy2 (d) 3xy

Answer»

Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

(a) $x^{2} + y^{2} + 2 x y$

(b) $x^{2} + y^{2} - x y$

(c) $x y^{2}$

(d) $3 x y$

Discussion

50.	Given ∠POR=3x and ∠QOR=2x+100. If POQ is a striaght line, then the value of x is:
Answer» Given $∠ P O R = 3 x a n d ∠ Q O R = 2 x + 10^{0}$ . If POQ is a striaght line, then the value of x is:

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Prove that two different circles cannot intersect each other at more than two points.

ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.

The volume of a sphere of radius 21 cm is

If logab+logba=log(a+b), then :

What are real numbers?

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?

A cylindrical bucket open at the top has base radius 35 cm and height 49 cm, its total surface area is

Assertion : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Reason : The opposite angles of a parallelogram are equal. Which of the following is correct?

Find the area of the 1.5 m wide pathway (green) if length is twice the breadth. Breadth is equal to 6 m..

What is tanθ in △ABC, if θ is increased by 30∘?

In △ ABC, tan(B+C2)= _______.

ABCD is a square. E, F, G and H are points on AB, BC, CD and DA respectively, such that AE = BF = CG = DH. Prove that EFGH is a square.

If x=1 and y=6 is a solution of the equation 8x−ay+a2=0, find the values of a.

Find the value of a, so that the point (3, a) lies on the line represented by 2x-3y = 5

Find the curved surface area of a cone,if its slant height is 60 cm and the radius of its base is 21 cm.

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6m. For how many days will the water of this tank last?

If a is any vector then (a×^i)2+(a×^j)2+(a×^k)2 =

The diameter of one sphere is 21 cm, and the diameter of another sphere is 14 cm, the ratios of their curved surface areas is

If log√8x=103, find the value of x

The sum of 12abx, 2a2bx, 8abx and 8a2bx is

Write 545 = 2502 in logarithmic form

If the zeroes of the polynomials p(x)=2x−4 and q(x)=5x−15 are multipled, we get a zero of the polynomial r(x)=ax2+bx+10. Which of the following relations is true?

If 3√3(3√x−13√x)=2,then3√x+13√x= ___.

The mean weight of a group of seven boys is 56 kgs. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy. [4 MARKS]

factorise (x^4 +4)

True or false. Give reasons A rational number is a quotient of any two integers.

Evaluate (2+3+4)2 using identities

To construct a parallelogram___

How to construct incircle of triangle.

Is difference of two irrational numbers always an irrational number?

Choose the correct answer in the following question: The mid-value of a class interval is 42 and the class size is 10. The lower and upper limits are (a) 37−47 (b) 37.5−47.5 (c) 36.5−47.5 (d) 36.5−46.5

Calculate the mode of the following sizes of shoes sold by a shop on a particular day. 5,9,8,6,9,4,3,9,1,6,3,9,7,1,2,5,9

In aΔABC,it is given that ∠A:∠B:∠C=3:2:1and ∠ACD=90∘.If BC is produced to E then ∠ECD=? (a) 60∘(b) 50∘(c) 40∘(d) 25∘

The mean of n observations is x (bar). If each observation is multiplied by k, then find the mean of new observations.

Choose the correct option for the underlined phrases. The company had hired someone smarter than the current manager.

Express y interms of x 3x-2y+12=0

The angles of a triangle are arranged in ascending order . if the difference between consecutive angles is 10 then all the angles will be

Given that x and y are in inverse proportion, and y1 y2 are values of y corresponding to the values x1x2 of x respectively. Which of the following is correct?

The number of values of x∈[0,nπ],n∈I that satisfy log|sinx|(1+cosx)=2 is

Volume of a cuboid is 12cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is

The mean weight of a class of 24 students is 48 kg. If the weight of the teacher be included, then the mean weight increases by 500 g. Find the weight of the teacher.

What is the area of the shaded region in the figure, if it is given that the side of square ABCD is 90 m and the side of square PQRS is 100 m?

if secAand cosecA are roots of x^2-px+q then choose the correct option a)p^2+q^2=2q b)p^2+q^2=2p c)p^2-q^2=2q d)p^2-q^2=2p

If y = 4x is rewritten in the form ax + by + c = 0, which of these options represents the values of a, b and c respectively?

Evaluate the following using suitable identities: (i)(99)3 (ii) (102)3 (iii) (998)3

Question 66 Fill in the blanks to make the statements true. The number of diagonals in a hexagon is ___.

Find the unique solution for the pair of linear equations: x + 2y = 5 and 7x + 3y = 13.

Which of the following is a factor of (x+y)3−(x3+y3)? (a) x2+y2+2xy (b) x2+y2−xy (c) xy2 (d) 3xy

Given ∠POR=3x and ∠QOR=2x+100. If POQ is a striaght line, then the value of x is: