19743 + Interview Questions in Mathematics Page 226 InterviewSolution

11251.	36. A round balloon of radius 'r' subtends an angle "α " at the eye of the observer while the angle of elevation of its centre is “β ". Prove that the height of the centre of the balloon is rsinα .cosecβ /2
Answer» 36. A round balloon of radius 'r' subtends an angle "α " at the eye of the observer while the angle of elevation of its centre is “β ". Prove that the height of the centre of the balloon is rsinα .cosecβ /2

Discussion

11252.	Express the following in powers of 10.(a) 6,54,320 (b) 76,40,321
Answer» Express the following in powers of 10. (a) 6,54,320 (b) 76,40,321

11252.

Express the following in powers of 10.(a) 6,54,320 (b) 76,40,321

Answer»

Express the following in powers of 10.

(a) 6,54,320

(b) 76,40,321

Discussion

11253.	A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.
Answer» A two digit number is $3$ more than $4$ times the sum of its digits. If $18$ is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

Discussion

11254.	Question 40 Fill in the blanks to make the statement true. Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ............. of the term.
Answer» Question 40 Fill in the blanks to make the statement true. Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ............. of the term.

11254.

Question 40 Fill in the blanks to make the statement true. Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ............. of the term.

Answer»

Question 40

Fill in the blanks to make the statement true.

Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ............. of the term.

Discussion

11255.	Question 114Solve the following question:What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?
Answer» Question 114 Solve the following question: What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?

11255.

Question 114Solve the following question:What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?

Answer»

Question 114

Solve the following question:

What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?

Discussion

11256.	2+3×15−1÷2+(5+1)÷3=
Answer» $2 + 3 \times 15 - 1 \div 2 + (5 + 1) \div 3 =$

Discussion

11257.	Name of the following polygons. (a) 8 sided polygon (b) 7 sided polygon
Answer» Name of the following polygons. (a) 8 sided polygon (b) 7 sided polygon

11257.

Name of the following polygons. (a) 8 sided polygon (b) 7 sided polygon

Answer»

Name of the following polygons.

(a) 8 sided polygon

(b) 7 sided polygon

Discussion

11258.	Simplify and express each of the following in exponential form:(1) [(52)3 × 54] ÷ 57(2) (30 + 20) × 50
Answer» Simplify and express each of the following in exponential form: (1) [(5²)³ × 5⁴] ÷ 5^7 (2)(3⁰ + 2⁰) × 5⁰

Discussion

11259.	In the fig. below, if AB∥CD,∠APQ=50∘ and ∠PRD=127∘, find x and y.
Answer» In the fig. below, if $A B ∥ C D, ∠ A P Q = 50^{\circ}$ and $∠ P R D = 127^{\circ}$ , find x and y.

11259.

In the fig. below, if AB∥CD,∠APQ=50∘ and ∠PRD=127∘, find x and y.

Answer»

In the fig. below, if $A B ∥ C D, ∠ A P Q = 50^{\circ}$ and

$∠ P R D = 127^{\circ}$ ,

find x and y.

Discussion

11260.	(i) Identify the terms and their factors in the followingexpressions Show the terms and factors by tree diagrams.(a) x − 3 (b) 1 + x + x2 (c)y − y3(d) (e) − ab + 2b2 − 3a2(ii) Identify terms and factors in the expressions given below:(a) − 4x + 5 (b) − 4x + 5y (c) 5y+ 3y2(d) (e) pq + q (f) 1.2 ab − 2.4 b + 3.6 a (g) (h) 0.1p2 + 0.2 q2
Answer» (i) Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams. (a) x − 3 (b) 1 + x + x² (c) y − y³ (d) (e) − ab + 2b² − 3a² (ii) Identify terms and factors in the expressions given below: (a) − 4x + 5 (b) − 4x + 5y (c) 5y + 3y² (d) (e) pq + q (f) 1.2 ab − 2.4 b + 3.6 a (g) (h) 0.1p² + 0.2 q²

11260.

(i) Identify the terms and their factors in the followingexpressions Show the terms and factors by tree diagrams.(a) x − 3 (b) 1 + x + x2 (c)y − y3(d) (e) − ab + 2b2 − 3a2(ii) Identify terms and factors in the expressions given below:(a) − 4x + 5 (b) − 4x + 5y (c) 5y+ 3y2(d) (e) pq + q (f) 1.2 ab − 2.4 b + 3.6 a (g) (h) 0.1p2 + 0.2 q2

Answer»

(i) Identify the terms and their factors in the following
expressions

Show the terms and factors by tree diagrams.

(a) x − 3 (b) 1 + x + x² (c)
y − y³

(d)

(e) − ab + 2b² − 3a²

(ii) Identify terms and factors in the expressions given below:

(a) − 4x + 5 (b) − 4x + 5y (c) 5y
+ 3y²

(d)

(e) pq + q

(f) 1.2 ab − 2.4 b + 3.6 a (g)

(h) 0.1p² + 0.2 q²

Discussion

11261.	Find factor(s) of 216 which is divisible by both 3 and 8?
Answer» Find factor(s) of $216$ which is divisible by both $3$ and $8 ?$

Discussion

11262.	If line a is parallel to b, line p is parallel to line DF and line q is perpendicular to both parallel lines a & b.What is the value of x in the figure given below ?
Answer» If line $a$ is parallel to $b$ , line $p$ is parallel to line $D F$ and line $q$ is perpendicular to both parallel lines $a & b$ . What is the value of $x$ in the figure given below ?

Discussion

11263.	Observe the following graph and answer the question.(1) State the type of the graph.(2) How much is the savings of Vaishali in the month of April?(3) How much is the total savings of Saroj in the months March and April?(4) How much more is the total savings of Savita than the total savings of Megha?(5) Whose savings in the month of April is the least?
Answer» Observe the following graph and answer the question. (1) State the type of the graph. (2) How much is the savings of Vaishali in the month of April? (3) How much is the total savings of Saroj in the months March and April? (4) How much more is the total savings of Savita than the total savings of Megha? (5) Whose savings in the month of April is the least?

Discussion

11264.	29. A pair of dice is thrown independently 3 times.The prob of getting a score of 9 exactly twice is
Answer» 29. A pair of dice is thrown independently 3 times.The prob of getting a score of 9 exactly twice is

Discussion

11265.	2550÷[510-{270-(20-80+7)}]
Answer» 2550÷[510-{270-(20-80+7)}]

Discussion

11266.	A bar graph
Answer» A bar graph

Discussion

11267.	Which of the following cannot be the denominator of a finite fraction?
Answer» Which of the following cannot be the denominator of a finite fraction?

Discussion

11268.

Use the given algebraic expression to complete the table of number patterns. S. No Expression Terms 1st 2nd 3rd 4th 5th … 10th … 100th … (i) 2n − 1 1 3 5 7 9 - 19 - - - (ii) 3n + 2 2 5 8 11 - - - - - - (iii) 4n + 1 5 9 13 17 - - - - - - (iv) 7n + 20 27 34 41 48 - - - - - - (v) n2 + 1 2 5 10 17 - - - - 10, 001 -

Answer»

Use the given algebraic
expression to complete the table of number patterns.

S. No	Expression	Terms
S. No	Expression	1^st	2^nd	3^rd	4^th	5^th	…	10^th	…	100^th	…
(i)	2n − 1	1	3	5	7	9	-	19	-	-	-
(ii)	3n + 2	2	5	8	11	-	-	-	-	-	-
(iii)	4n + 1	5	9	13	17	-	-	-	-	-	-
(iv)	7n + 20	27	34	41	48	-	-	-	-	-	-
(v)	n² + 1	2	5	10	17	-	-	-	-	10, 001	-

Discussion

11269.	Question 101 (i)Here is a keyboard for a harmonium.Find the ratio of white key to black keys on the keyboard.
Answer» Question 101 (i) Here is a keyboard for a harmonium. Find the ratio of white key to black keys on the keyboard.

11269.

Question 101 (i)Here is a keyboard for a harmonium.Find the ratio of white key to black keys on the keyboard.

Answer»

Question 101 (i)

Here is a keyboard for a harmonium.

Find the ratio of white key to black keys on the keyboard.

Discussion

11270.	An angle at one corner of an envelope is given below.If the envelope is in the shape of a parallelogram, find the value of ∠ADC.
Answer» An angle at one corner of an envelope is given below. If the envelope is in the shape of a parallelogram, find the value of ∠ADC.

Discussion

11271.	In the given figure if line AB is parallel to line CD then which of the following are true?
Answer» In the given figure if line AB is parallel to line CD then which of the following are true?

11271.

In the given figure if line AB is parallel to line CD then which of the following are true?

Answer»

In the given figure if line AB is parallel to line CD then which of the following are true?

Discussion

11272.	15 Find the value of a and b :5+23/7+43=a-b3
Answer» 15 Find the value of a and b :5+23/7+43=a-b3

Discussion

11273.	Which disease does all the images correspond to?
Answer» Which disease does all the images correspond to?

Discussion

11274.	The corresponding bar graph for the following data is shown in the figure given below:Find the value of the mean for this data.
Answer» The corresponding bar graph for the following data is shown in the figure given below: Find the value of the mean for this data.

Discussion

11275.	What fraction of the cubes are not yellow?
Answer» What fraction of the cubes are not yellow?

11275.

What fraction of the cubes are not yellow?

Answer»

What fraction of the cubes are not yellow?

Discussion

11276.	Expand the following in base 5 system. (1) 32(5) (2) 124(5) (3) 432(5) (4) 3021(5)
Answer» Expand the following in base 5 system. (1) 32₍₅₎ (2) 124₍₅₎ (3) 432₍₅₎ (4) 3021₍₅₎

11276.

Expand the following in base 5 system. (1) 32(5) (2) 124(5) (3) 432(5) (4) 3021(5)

Answer»

Expand the following in base 5 system.

(1) 32₍₅₎

(2) 124₍₅₎

(3) 432₍₅₎

(4) 3021₍₅₎

Discussion

11277.	Using lawsof exponents, simplify and write the answer in exponential form:(i) 32× 34 ×38 (ii) 615 ÷610 (iii) a3 ×a2(iv) 7x× 72 (v) (vi) 25× 55(vii) a4× b4 (viii) (34)3 (ix) (x) 8t÷ 82
Answer» Using laws of exponents, simplify and write the answer in exponential form: (i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a² (iv) 7^x× 7² (v) (vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (3⁴)³ (ix) (x) 8^t ÷ 8²

11277.

Using lawsof exponents, simplify and write the answer in exponential form:(i) 32× 34 ×38 (ii) 615 ÷610 (iii) a3 ×a2(iv) 7x× 72 (v) (vi) 25× 55(vii) a4× b4 (viii) (34)3 (ix) (x) 8t÷ 82

Answer»

Using laws
of exponents, simplify and write the answer in exponential form:

(i) 3²
× 3⁴ ×
3⁸ (ii) 6¹⁵ ÷
6¹⁰ (iii) a³ ×
a²

(iv) 7^x× 7² (v) (vi) 2⁵
× 5⁵

(vii) a⁴
× b⁴ (viii) (3⁴)³

(ix) (x) 8^t
÷ 8²

Discussion

11278.	5x+4≥24 can be simplified into:
Answer» $5 x + 4 \geq 24 can be simplified into :$

Discussion

11279.	Find the probability of getting the same number when a die is thrown twice.
Answer» Find the probability of getting the same number when a die is thrown twice.

Discussion

11280.	In the figure given below, there are ___ transversals. ___
Answer» In the figure given below, there are ___ transversals. ___

11280.

In the figure given below, there are _ transversals. _

Answer»

In the figure given below, there are ___ transversals.

___

Discussion

11281.	Find the next term in the sequence 25, 30, 35, ...40
Answer» Find the next term in the sequence 25, 30, 35, ... 40

Discussion

11282.	Factorise the following:(i) 9x2–12x+3(ii) 9x2–12x+4
Answer» Factorise the following: $(i) 9 x^{2} - 12 x + 3$ $(i i) 9 x^{2} - 12 x + 4$

Discussion

11283.	If 27 of 21 bananas are spoilt, then how many are left?
Answer» If $\frac{2}{7}$ of 21 bananas are spoilt, then how many are left?

Discussion

11284.	A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .
Answer» A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .

Discussion

11285.	ABC is a right angled triangle right angled at A. AD is the altitude through A. E is a point on AC such that AE=CD and F is a point on AB such that AF=BD. Prove that BE=CF.
Answer» ABC is a right angled triangle right angled at A. AD is the altitude through A. E is a point on AC such that AE=CD and F is a point on AB such that AF=BD. Prove that BE=CF.

Discussion

11286.	Question 69(iv) Given below are heights of 15 boys of a class measured in centimetres: 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154. Find the median height of the boys.
Answer» Question 69(iv) Given below are heights of 15 boys of a class measured in centimetres: 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154. Find the median height of the boys.

Discussion

11287.	On subtracting − 7 from − 14, we get(a) − 12 (b) − 7 (c) −14 (d) 21
Answer» On subtracting − 7 from − 14, we get (a) − 12 (b) − 7 (c) −14 (d) 21

Discussion

11288.	What is 148 divided by 214 in its simplest form?
Answer» What is $\frac{14}{8}$ divided by $\frac{21}{4}$ in its simplest form?

Discussion

11289.	The combined equation of three sides of a triangle is (x^2 - y^2)(2x +3y-6)=0. If (secθ,1) is an Interior point of the triangle then find the value of θ.
Answer» The combined equation of three sides of a triangle is (x^2 - y^2)(2x +3y-6)=0. If (secθ,1) is an Interior point of the triangle then find the value of θ.

Discussion

11290.	Question 40 State whether the statement given is True or False. A trinomial has exactly three terms.
Answer» Question 40 State whether the statement given is True or False. A trinomial has exactly three terms.

11290.

Question 40 State whether the statement given is True or False. A trinomial has exactly three terms.

Answer»

Question 40

State whether the statement given is True or False.

A trinomial has exactly three terms.

Discussion

11291.	Net for the following solid is:
Answer» Net for the following solid is:

11291.

Net for the following solid is:

Answer»

Net for the following solid is:

Discussion

11292.	x varies inversely as y, when x=15 then y=10, if x=20 then y=?
Answer» $x$ varies inversely as $y$ , when $x = 15$ then $y = 10$ , if $x = 20$ then $y = ?$

Discussion

11293.	The correct equation for x and y is15, 12, 9, x, y
Answer» The correct equation for x and y is 15, 12, 9, x, y

Discussion

11294.	Both Arjun and Rahul went for jogging and stopped at a place where kids were playing on a slide as shown below:Two slides which are directed in the two opposite directions are combined by a vertical stairs in the midway between the two sliders. The lengths of both the slides are same.Two kids Mia and Anu reached down after sliding down. How much distance has Mia to walk from A to reach Anu who is at B if AC = 5 m and width of the stairs = 1 m?
Answer» Both Arjun and Rahul went for jogging and stopped at a place where kids were playing on a slide as shown below: Two slides which are directed in the two opposite directions are combined by a vertical stairs in the midway between the two sliders. The lengths of both the slides are same. Two kids Mia and Anu reached down after sliding down. How much distance has Mia to walk from A to reach Anu who is at B if AC = 5 m and width of the stairs = 1 m?

11294.

Both Arjun and Rahul went for jogging and stopped at a place where kids were playing on a slide as shown below:Two slides which are directed in the two opposite directions are combined by a vertical stairs in the midway between the two sliders. The lengths of both the slides are same.Two kids Mia and Anu reached down after sliding down. How much distance has Mia to walk from A to reach Anu who is at B if AC = 5 m and width of the stairs = 1 m?

Answer»

Both Arjun and Rahul went for jogging and stopped at a place where kids were playing on a slide as shown below:

Two slides which are directed in the two opposite directions are combined by a vertical stairs in the midway between the two sliders. The lengths of both the slides are same.

Two kids Mia and Anu reached down after sliding down. How much distance has Mia to walk from A to reach Anu who is at B if AC = 5 m and width of the stairs = 1 m?

Discussion

11295.

When we meet people, we notice their faces more than anything else. The box below contains words which describe the features of a face. Work in pairs and list them under the appropriate headings, then add more words of your own. twinkling shifty discoloured short oval pear-shaped large close-cropped broken long protruding gapped thick pointed wide fair thin pale swarthy staring square round untidy close-set neat wavy upturned Shape of face Complexion Eyes Hair Nose Lips Teeth

Answer»

When we meet people, we notice their faces more than anything else. The box below contains words which describe the features of a face. Work in pairs and list them under the appropriate headings, then add more words of your own.

twinkling	shifty	discoloured	short	oval
pear-shaped	large	close-cropped	broken	long
protruding	gapped	thick	pointed	wide
fair	thin	pale	swarthy	staring
square	round	untidy	close-set	neat
wavy	upturned

Shape of face	Complexion	Eyes	Hair	Nose	Lips	Teeth

Discussion

11296.	If A and B are two events such that P A∪B=23 and PA∪B=59, then PA+PB = ______________.
Answer» If A and B are two events such that P $(A \cup B) = \frac{2}{3} and P (A \cup B) = \frac{5}{9}, then P (A) + P (B)$ = ______________.

Discussion

11297.	Question 46 Answer True/False. 2x - 5 > 11 is an equation.
Answer» Question 46 Answer True/False. 2x - 5 > 11 is an equation.

11297.

Question 46 Answer True/False. 2x - 5 > 11 is an equation.

Answer»

Question 46

Answer True/False.

2x - 5 > 11 is an equation.

Discussion

11298.	The angle of rotation needed to obtain a second trinomino from the first one in the given figure is _____.
Answer» The angle of rotation needed to obtain a second trinomino from the first one in the given figure is _____.

Discussion

11299.

Two poles of height 10 cm and 20 cm stand on a plane ground. If the distance between their feet is 24 cm. Find the distance between their tops (in cm). 26

Answer»

Two poles of height 10 cm and 20 cm stand on a plane ground. If the distance between their feet is 24 cm. Find the distance between their tops (in cm).

26

Discussion

11300.

Question 112(i) In the given figure, show that AB || CD

Answer»

Question 112(i)

In the given figure, show that
AB || CD

Discussion

Explore topic-wise InterviewSolutions in .

36. A round balloon of radius 'r' subtends an angle "α " at the eye of the observer while the angle of elevation of its centre is “β ". Prove that the height of the centre of the balloon is rsinα .cosecβ /2

Express the following in powers of 10.(a) 6,54,320 (b) 76,40,321

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

Question 40 Fill in the blanks to make the statement true. Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ............. of the term.

Question 114Solve the following question:What will be the number of unit squares on each side of a square graph paper, if the total number of unit squares is 256?

2+3×15−1÷2+(5+1)÷3=

Name of the following polygons. (a) 8 sided polygon (b) 7 sided polygon

Simplify and express each of the following in exponential form:(1) [(52)3 × 54] ÷ 57(2) (30 + 20) × 50

In the fig. below, if AB∥CD,∠APQ=50∘ and ∠PRD=127∘, find x and y. ​

Find factor(s) of 216 which is divisible by both 3 and 8?

If line a is parallel to b, line p is parallel to line DF and line q is perpendicular to both parallel lines a &amp; b.What is the value of x in the figure given below ?

29. A pair of dice is thrown independently 3 times.The prob of getting a score of 9 exactly twice is

2550÷[510-{270-(20-80+7)}]

A bar graph

Which of the following cannot be the denominator of a finite fraction?

Question 101 (i)Here is a keyboard for a harmonium.Find the ratio of white key to black keys on the keyboard.

An angle at one corner of an envelope is given below.If the envelope is in the shape of a parallelogram, find the value of ∠ADC.

In the given figure if line AB is parallel to line CD then which of the following are true?

15 Find the value of a and b :5+23/7+43=a-b3

Which disease does all the images correspond to?

The corresponding bar graph for the following data is shown in the figure given below:Find the value of the mean for this data.

What fraction of the cubes are not yellow?

Expand the following in base 5 system. (1) 32(5) (2) 124(5) (3) 432(5) (4) 3021(5)

Using lawsof exponents, simplify and write the answer in exponential form:(i) 32× 34 ×38 (ii) 615 ÷610 (iii) a3 ×a2(iv) 7x× 72 (v) (vi) 25× 55(vii) a4× b4 (viii) (34)3 (ix) (x) 8t÷ 82

5x+4≥24 can be simplified into:

Find the probability of getting the same number when a die is thrown twice.

In the figure given below, there are ___ transversals. ___

Find the next term in the sequence 25, 30, 35, ...40

Factorise the following:(i) 9x2–12x+3(ii) 9x2–12x+4

If 27 of 21 bananas are spoilt, then how many are left?

A Goldsmith can choose between three metals A, B and C. The probability that he chooses C is .

ABC is a right angled triangle right angled at A. AD is the altitude through A. E is a point on AC such that AE=CD and F is a point on AB such that AF=BD. Prove that BE=CF.

Question 69(iv) Given below are heights of 15 boys of a class measured in centimetres: 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154. Find the median height of the boys.

On subtracting − 7 from − 14, we get(a) − 12 (b) − 7 (c) −14 (d) 21

What is 148 divided by 214 in its simplest form?

The combined equation of three sides of a triangle is (x^2 - y^2)(2x +3y-6)=0. If (secθ,1) is an Interior point of the triangle then find the value of θ.

Question 40 State whether the statement given is True or False. A trinomial has exactly three terms.

Net for the following solid is:

x varies inversely as y, when x=15 then y=10, if x=20 then y=?

The correct equation for x and y is15, 12, 9, x, y

If A and B are two events such that P A∪B=23 and PA∪B=59, then PA+PB = ______________.

Question 46 Answer True/False. 2x - 5 &gt; 11 is an equation.

The angle of rotation needed to obtain a second trinomino from the first one in the given figure is _____.

Two poles of height 10 cm and 20 cm stand on a plane ground. If the distance between their feet is 24 cm. Find the distance between their tops (in cm). 26

Question 112(i) In the given figure, show that AB || CD

In the fig. below, if AB∥CD,∠APQ=50∘ and ∠PRD=127∘, find x and y.

If line a is parallel to b, line p is parallel to line DF and line q is perpendicular to both parallel lines a & b.What is the value of x in the figure given below ?

In the figure given below, there are _ transversals. _

Question 46 Answer True/False. 2x - 5 > 11 is an equation.