24740 + Interview Questions in Mathematics

1.

Draw circles of the given radii and draw chords of the given lengths. Sl. No. Radius (cm) Length of chord (cm) 1. 2. 2.5 4.0 3.0 3.5

Answer»

Draw circles of the given radii and draw chords of the given lengths.

Sl. No.

Radius (cm)

Length of chord (cm)

1.

2.

2.5

4.0

3.0

3.5

Discussion

2.	ABCD is parallelogram. The angle bisectors of ∠A and ∠D intersect at O. Find the measures of ∠AOD.
Answer» ABCD is parallelogram. The angle bisectors of ∠A and ∠D intersect at O. Find the measures of ∠AOD.

Discussion

3.	Find area of an isosceles triangle whose perimeter is 50m and the unequal side is 10m.
Answer» Find area of an isosceles triangle whose perimeter is 50m and the unequal side is 10m.

Discussion

4.

Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Conc. of SO2 0.00-0.04 0.04-0.08 0.08-0.12 0.12-0.16 0.16-0.20 0.20-0.24 No. days: 4 8 9 2 4 3 Find the probability of concentration of sulphur dioxide in the interval0.12-0.16 on any of these days.

Answer» Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.

Conc. of SO₂	0.00-0.04	0.04-0.08	0.08-0.12	0.12-0.16	0.16-0.20	0.20-0.24
No. days:	4	8	9	2	4	3

Find the probability of concentration of sulphur dioxide in the interval

0.12-0.16 on any of these days.

Discussion

5.	If (a – b)2 + (b – c)2 + (c – a)2 = 0, then __________.
Answer» If (a – b)² + (b – c)² + (c – a)²= 0, then __________.

Discussion

6.	Which of the following is a rational number? (a) √2 (b) √23 (c) √225 (d) 0.1010010001....
Answer» Which of the following is a rational number? $(a) \sqrt{2}$ $(b) \sqrt{23}$ $(c) \sqrt{225}$ $(d) 0.1010010001....$

6.

Which of the following is a rational number? (a) √2 (b) √23 (c) √225 (d) 0.1010010001....

Answer»

Which of the following is a rational number?

$(a) \sqrt{2}$

$(b) \sqrt{23}$

$(c) \sqrt{225}$

$(d) 0.1010010001....$

Discussion

7.	Question 34State whether the given statement is True or False.If the arms of an angle on the paper are decreased, the angle decreases.
Answer» Question 34 State whether the given statement is True or False. If the arms of an angle on the paper are decreased, the angle decreases.

7.

Question 34State whether the given statement is True or False.If the arms of an angle on the paper are decreased, the angle decreases.

Answer»

Question 34

State whether the given statement is True or False.

If the arms of an angle on the paper are decreased, the angle decreases.

Discussion

8.

From the following information of a Not-for-Profit Organisation, show the 'Sports Materials' item in the Income and Expenditure Account for the year ended 31st March, 2019 and Balance Sheets as at 31st March, 2018 and 31st March, 2019: Particulars 31st March, 2018 ₹ 31st March, 2019 ₹ Stocks of Sports Materials 6,200 4,800 Creditors for Sports Materials 9,800 7,200 Advance to Suppliers for Sports Materials 11,000 19,000 Payment to suppliers for Sports Materials during the year was ₹ 1,02,000. There were no cash purchases made.

Answer» From the following information of a Not-for-Profit Organisation, show the 'Sports Materials' item in the Income and Expenditure Account for the year ended 31st March, 2019 and Balance Sheets as at 31st March, 2018 and 31st March, 2019:

Particulars	31st March, 2018 ₹	31st March, 2019 ₹
Stocks of Sports Materials	6,200	4,800
Creditors for Sports Materials	9,800	7,200
Advance to Suppliers for Sports Materials	11,000	19,000

Payment to suppliers for Sports Materials during the year was ₹ 1,02,000. There were no cash purchases made.

Discussion

9.	ABCD is a rectangle whose three vertices are B (4,0), C (4,3) and D (0, 3). The length of one of its diagonals is [CBSE 2014](a) 5(b) 4(c) 3(d) 25
Answer» ABCD is a rectangle whose three vertices are B (4,0), C (4,3) and D (0, 3). The length of one of its diagonals is [CBSE 2014] (a) 5 (b) 4 (c) 3 (d) 25

Discussion

10.	Why is Delta T=-4/9 Delta O
Answer» Why is Delta T=-4/9 Delta O

Discussion

11.	Represent root 19 on the number line by Pythagorean triplet.
Answer» Represent root 19 on the number line by Pythagorean triplet.

Discussion

12.	If a triangle is isosceles, then prove that two angle bisectors drawn from vertices at the base to the sides are of equal length.
Answer» If a triangle is isosceles, then prove that two angle bisectors drawn from vertices at the base to the sides are of equal length.

Discussion

13.	Which one of these linear equations is written in slope-intercept form?
Answer» Which one of these linear equations is written in slope-intercept form?

Discussion

14.	Which are the properties of congruent triangles?
Answer» Which are the properties of congruent triangles?

Discussion

15.	Degree of the polynomial f(x) = 4x4 + 0x3 + 0x5 + 5x + 7 is(a) 4(b) 5(c) 3(d) 7
Answer» Degree of the polynomial f(x) = 4x⁴ + 0x³+ 0x⁵ + 5x + 7 is (a) 4 (b) 5 (c) 3 (d) 7

Discussion

16.	Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.
Answer» Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.

Discussion

17.	If three sides of one triangle are equal to the three sides of another triangle, then, the two triangles are congruent by __ congruence condition.
Answer» If three sides of one triangle are equal to the three sides of another triangle, then, the two triangles are congruent by __ congruence condition.

Discussion

18.	Question 18Square of 9x−7xy isa) 81x2+49x2y2b) 81x2−49x2y2c) 81x2+49x2y2−126x2yd) 81x2+49x2y2−63x2y
Answer» Question 18 Square of $9 x - 7 x y$ is a) $81 x^{2} + 49 x^{2} y^{2}$ b) $81 x^{2} - 49 x^{2} y^{2}$ c) $81 x^{2} + 49 x^{2} y^{2} - 126 x^{2} y$ d) $81 x^{2} + 49 x^{2} y^{2} - 63 x^{2} y$

Discussion

19.	Prove that: (i) a+b+ca−1b−1+b−1c−1+c−1a−1=abc (ii) (a−1+b−1)−1=aba+b
Answer» Prove that: (i) $\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c$ (ii) $(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

19.

Prove that: (i) a+b+ca−1b−1+b−1c−1+c−1a−1=abc (ii) (a−1+b−1)−1=aba+b

Answer»

Prove that:

(i) $\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c$

(ii) $(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

Discussion

20.	If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
Answer» If x = 0 and x = −1 are the roots of the polynomial f(x) =2x³ − 3x²+ ax + b, find the value of a and b.

Discussion

21.	If the vertex of the parabola y = x2 – 16x + k lies on x-axis, then k = __________.
Answer» If the vertex of the parabola y = x² – 16x + k lies on x-axis, then k = __________.

Discussion

22.	The set builder representation of the set B = {29, 31, 37, 41, 43, 47}, is ______ .
Answer» The set builder representation of the set B = {29, 31, 37, 41, 43, 47}, is ______ .

Discussion

23.	Evaluate the following limits lim x tending to 1 (x+1)^4-2^4/(2x+1)^5-3^5
Answer» Evaluate the following limits lim x tending to 1 (x+1)^4-2^4/(2x+1)^5-3^5

Discussion

24.	By inspection, 4 (x - y)3 + 6 (x - y)2 gives
Answer» By inspection, 4 (x - y)³ + 6 (x - y)² gives

Discussion

25.

On a page of a telephone directory, there are 200 telephone numbers. The frequency distribution of the digits at their units place is given below: Unit digit 0 1 2 3 4 5 6 7 8 9 Frequency 22 26 22 22 20 10 14 28 16 20 Without looking at the page, a number is chosen at random from the page. What is the probability that the digit at the unit's place of the number chosen is greater than 6?

Answer» On a page of a telephone directory, there are 200 telephone numbers. The frequency distribution of the digits at their units place is given below:

Unit digit	0	1	2	3	4	5	6	7	8	9
Frequency	22	26	22	22	20	10	14	28	16	20

Without looking at the page, a number is chosen at random from the page. What is the probability that the digit at the unit's place of the number chosen is greater than 6?

Discussion

26.	Question 2(vi)Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following products: (2a2+9)(2a2+5)
Answer» Question 2(vi) Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products: $(2 a^{2} + 9) (2 a^{2} + 5)$

Discussion

27.	How to find rational numbers between two rational numbers
Answer» How to find rational numbers between two rational numbers

Discussion

28.	Solve for x: 3(9x)<8(3x)+3
Answer» Solve for $x$ : $3 (9^{x}) < 8 (3^{x}) + 3$

28.

Solve for x: 3(9x)<8(3x)+3

Answer»

Solve for $x$ :

$3 (9^{x}) < 8 (3^{x}) + 3$

Discussion

29.	In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.
Answer» In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.

Discussion

30.	The solution set of the inequality (log10x)4−13(log10x)2+36>0 is
Answer» The solution set of the inequality $({log}_{10} x)^{4} - 13 ({log}_{10} x)^{2} + 36 > 0$ is

Discussion

31.	In a cricket match, a batsman hit a boundary 6 times (out of 30 balls). Find the probability that next ball he plays is not a boundary.
Answer» In a cricket match, a batsman hit a boundary 6 times (out of 30 balls). Find the probability that next ball he plays is not a boundary.

Discussion

32.	Two figures are congruent if they have
Answer» Two figures are congruent if they have

Discussion

33.	Question 7 A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. [Assume π=227]
Answer» Question 7 A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. $[A s s u m e π = \frac{22}{7}]$

Discussion

34.	Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of ∠NPM.
Answer» Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of $∠$ NPM.

Discussion

35.	Find the value of k, if (2, 3) lies on the line represented by the equation 2x=3y−k.
Answer» Find the value of $k$ , if (2, 3) lies on the line represented by the equation $2 x = 3 y - k .$

Discussion

36.	A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm.Their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm.If the cone is then removed,find the height to which water level will fall.
Answer» A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm.Their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm.If the cone is then removed,find the height to which water level will fall.

Discussion

37.	AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm. Find the distance of AB from the centre of the circle.
Answer» AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm. Find the distance of AB from the centre of the circle.

Discussion

38.	Factorise: (x4- 14x2y2 - 51y4).
Answer» Factorise: (x⁴- 14x²y² - 51y⁴).

Discussion

39.	A spherical steel ball of radius r is melted to make eight new identical balls. The radius of each new ball is _________.
Answer» A spherical steel ball of radius r is melted to make eight new identical balls. The radius of each new ball is _________.

Discussion

40.	In △ABC, if 3∠A=4∠B=6∠C, calculate A,B,C.
Answer» In $△ A B C$ , if $3 ∠ A = 4 ∠ B = 6 ∠ C$ , calculate $A, B, C$ .

Discussion

41.	The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation. [4 MARKS]
Answer» The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation. [4 MARKS]

Discussion

42.	The distance between the graph of the equations x = - 3 and x = 2 is
Answer» The distance between the graph of the equations x = - 3 and x = 2 is

Discussion

43.	The range of the data 3, 5, 7, 3, 11 is
Answer» The range of the data 3, 5, 7, 3, 11 is

Discussion

44.	Factorise:x2+33x+6
Answer» Factorise: $x^{2} + 3 \sqrt{3} x + 6$

Discussion

45.	If one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair will be:
Answer» If one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair will be:

Discussion

46.	Prove that any three points on a circle cannot be collinear.
Answer» Prove that any three points on a circle cannot be collinear.

Discussion

47.	Question 9A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.
Answer» Question 9 A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.

Discussion

48.

An equilateral triangle ABC is inscribed in a circle centered at O and of radius 12 cm, as shown below. OD is a radius such that it is perpendicular to BC and cuts BC at point E. Then the length of OE is

Answer»

An equilateral triangle ABC is inscribed in a circle centered at O and of radius 12 cm, as shown below. OD is a radius such that it is perpendicular to BC and cuts BC at point E. Then the length of OE is

Discussion

49.

Question 3The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54

Answer»

Question 3

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

$\begin{matrix} Daily pocket allowance (in Rs) & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 & 19 - 21 & 21 - 23 & 23 - 25 Number of workers & 7 & 6 & 9 & 13 & f & 5 & 4 \end{matrix}$

Discussion

50.	Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.
Answer» Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Draw circles of the given radii and draw chords of the given lengths. Sl. No. Radius (cm) Length of chord (cm) 1. 2. 2.5 4.0 3.0 3.5

ABCD is parallelogram. The angle bisectors of ∠A and ∠D intersect at O. Find the measures of ∠AOD.

Find area of an isosceles triangle whose perimeter is 50m and the unequal side is 10m.

If (a – b)2 + (b – c)2 + (c – a)2 = 0, then __________.

Which of the following is a rational number? (a) √2 (b) √23 (c) √225 (d) 0.1010010001....

Question 34State whether the given statement is True or False.If the arms of an angle on the paper are decreased, the angle decreases.

ABCD is a rectangle whose three vertices are B (4,0), C (4,3) and D (0, 3). The length of one of its diagonals is [CBSE 2014](a) 5(b) 4(c) 3(d) 25

Why is Delta T=-4/9 Delta O

Represent root 19 on the number line by Pythagorean triplet.

If a triangle is isosceles, then prove that two angle bisectors drawn from vertices at the base to the sides are of equal length.

Which one of these linear equations is written in slope-intercept form?

Which are the properties of congruent triangles?

Degree of the polynomial f(x) = 4x4 + 0x3 + 0x5 + 5x + 7 is(a) 4(b) 5(c) 3(d) 7

Two poles of height 10 m and 18 m stand on a plane ground. If the distance between the feet of the poles is 15 m, find the distance between the top of the poles.

If three sides of one triangle are equal to the three sides of another triangle, then, the two triangles are congruent by __ congruence condition.

Question 18Square of 9x−7xy isa) 81x2+49x2y2b) 81x2−49x2y2c) 81x2+49x2y2−126x2yd) 81x2+49x2y2−63x2y

Prove that: (i) a+b+ca−1b−1+b−1c−1+c−1a−1=abc (ii) (a−1+b−1)−1=aba+b

If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.

If the vertex of the parabola y = x2 – 16x + k lies on x-axis, then k = __________.

The set builder representation of the set B = {29, 31, 37, 41, 43, 47}, is ______ .

Evaluate the following limits lim x tending to 1 (x+1)^4-2^4/(2x+1)^5-3^5

By inspection, 4 (x - y)3 + 6 (x - y)2 gives

Question 2(vi)Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following products: (2a2+9)(2a2+5)

How to find rational numbers between two rational numbers

Solve for x: 3(9x)&lt;8(3x)+3

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is correct or not.

The solution set of the inequality (log10x)4−13(log10x)2+36&gt;0 is

In a cricket match, a batsman hit a boundary 6 times (out of 30 balls). Find the probability that next ball he plays is not a boundary.

Two figures are congruent if they have

Question 7 A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. [Assume π=227]

Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of ∠NPM.

Find the value of k, if (2, 3) lies on the line represented by the equation 2x=3y−k.

A right circular cone of diameter r cm and height 12 cm rests on the base of right circular cylinder of radius r cm.Their bases are in the same plane and the cylinder is filled with water up to a height of 12 cm.If the cone is then removed,find the height to which water level will fall.

AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm. Find the distance of AB from the centre of the circle.

Factorise: (x4- 14x2y2 - 51y4​​​​​​).

A spherical steel ball of radius r is melted to make eight new identical balls. The radius of each new ball is _________.

In △ABC, if 3∠A=4∠B=6∠C, calculate A,B,C.

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation. [4 MARKS]

The distance between the graph of the equations x = - 3 and x = 2 is

The range of the data 3, 5, 7, 3, 11 is

Factorise:x2+33x+6

If one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair will be:

Prove that any three points on a circle cannot be collinear.

Question 9A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.

An equilateral triangle ABC is inscribed in a circle centered at O and of radius 12 cm, as shown below. OD is a radius such that it is perpendicular to BC and cuts BC at point E. Then the length of OE is

Question 3The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54

Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Solve for x: 3(9x)<8(3x)+3

The solution set of the inequality (log10x)4−13(log10x)2+36>0 is

Factorise: (x4- 14x2y2 - 51y4).