32581 + Interview Questions in Mathematics Page 153 InterviewSolution

7601.	A gulab jamun, contains sugar syrup up to about 30% of its volume.Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm
Answer» A gulab jamun, contains sugar syrup up to about 30% of its volume.Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm

Discussion

7602.	The product of 3 consecutive numbers, when the first number is even is divisible by ___
Answer» The product of 3 consecutive numbers, when the first number is even is divisible by ___

Discussion

7603.	In a triangle ABC, the incircle (centre O) touches BC. CA and AB at points P, Q and R respectively, Calculate : ∠QOR=2∠QPR given that ∠A=60o
Answer» In a triangle ABC, the incircle (centre O) touches BC. CA and AB at points P, Q and R respectively, Calculate : $∠ Q O R = 2 ∠ Q P R$ given that $∠ A = 60^{o}$

7603.

In a triangle ABC, the incircle (centre O) touches BC. CA and AB at points P, Q and R respectively, Calculate : ∠QOR=2∠QPR given that ∠A=60o

Answer»

In a triangle ABC, the incircle (centre O) touches BC. CA and AB at points P, Q and R respectively, Calculate :

$∠ Q O R = 2 ∠ Q P R$
given that $∠ A = 60^{o}$

Discussion

7604.	AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.
Answer» AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.

Discussion

7605.	Which term of the A. P. 3, 10, 17, ......... will be 84 more than its 13th term ?
Answer» Which term of the A. P. 3, 10, 17, ......... will be 84 more than its $13^{t h}$ term ?

Discussion

7606.	A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17 innings
Answer» A Batsman makes a score of 87 runs in the 17^th inning and thus increases his average by 3. Find his average after 17 innings

Discussion

7607.	The value of limx→2 3x/2-33x-9 is ___________________.
Answer» The value of $\lim_{x \to 2} \frac{3^{x / 2} - 3}{3^{x} - 9} is___________________.$

Discussion

7608.	If a and d are the first term and the common difference of an AP, Sn denotes the sum of n terms of an AP. If Sn=Pn+Qn2, what are a and d in terms of P and Q?
Answer» If $a$ and $d$ are the first term and the common difference of an AP, $S_{n}$ denotes the sum of $n$ terms of an AP. If $S_{n} = P n + Q n^{2}$ , what are $a$ and $d$ in terms of $P$ and $Q$ ?

Discussion

7609.	There are two boxes, each containing slips numbered 1 to 5. One slip is drawn from each box and their numbers added. What are the possible sums? Compute the probability of each sum.
Answer» There are two boxes, each containing slips numbered 1 to 5. One slip is drawn from each box and their numbers added. What are the possible sums? Compute the probability of each sum.

Discussion

7610.	Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x3 + 7x2 – 24x – 45, g(x) = x – 3
Answer» Using factor theorem, show that g(x) is a factor of p(x), when p(x) = 2x³ + 7x² – 24x – 45, g(x) = x – 3

Discussion

7611.	The number of integral point(s) in the domain of f(x)=sin−1[x5]+cos−1{x} is(where [.] denotes greatest integer function and {.} denotes fractional part function)
Answer» The number of integral point(s) in the domain of $f (x) = {sin}^{- 1} [\frac{x}{5}] + {cos}^{- 1} {x}$ is (where $[.]$ denotes greatest integer function and ${.}$ denotes fractional part function)

Discussion

7612.	Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers. [CBSE 2010]
Answer» Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers. [CBSE 2010]

Discussion

7613.	You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.
Answer» You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

7613.

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Answer»

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Discussion

7614.	Q- proove that root3-root7 is an irrational number.Q-show that there is no positive integer n for which root n-1+root n+1is rational
Answer» Q- proove that root3-root7 is an irrational number. Q-show that there is no positive integer n for which root n-1+root n+1is rational

Discussion

7615.	In the given right triangle, the value of sinθ is .
Answer» In the given right triangle, the value of $sin θ$ is .

Discussion

7616.	O is the centre of the circle and AB is a chord. AC is the bisector of ∠OAB,∠OAB=56∘. Find ∠OBE.
Answer» O is the centre of the circle and AB is a chord. AC is the bisector of $∠ O A B, ∠ O A B = 56^{\circ}$ . Find $∠ O B E$ .

7616.

O is the centre of the circle and AB is a chord. AC is the bisector of ∠OAB,∠OAB=56∘. Find ∠OBE.

Answer»

O is the centre of the circle and AB is a chord. AC is the bisector of $∠ O A B, ∠ O A B = 56^{\circ}$ . Find $∠ O B E$ .

Discussion

7617.	18. The sides of a right angled triangle are in AP. Show that they are in the ratio 3 : 4 : 5.
Answer» 18. The sides of a right angled triangle are in AP. Show that they are in the ratio 3 : 4 : 5.

Discussion

7618.	Question 36Complete the crossword Fig. 5.2 with the help of the clues:
Answer» Question 36 Complete the crossword Fig. 5.2 with the help of the clues:

Discussion

7619.	In an AP, the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference. [CBSE 2011]
Answer» In an AP, the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference. [CBSE 2011]

Discussion

7620.	You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.
Answer» You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.

Discussion

7621.	The graph of the polynomial f(x) = ax2 + bx + c is as shown in Fig. 2.20. Write the value of b2 − 4ac and the number of real zeros of f(x).
Answer» The graph of the polynomial f(x) = ax² + bx + c is as shown in Fig. 2.20. Write the value of b² − 4ac and the number of real zeros of f(x).

Discussion

7622.	Out of 100 students sitting in an examination, 40 students got more than 60 marks out of 100. So, percent of students got more than 60 marks.
Answer» Out of 100 students sitting in an examination, 40 students got more than 60 marks out of 100. So, percent of students got more than 60 marks.

Discussion

7623.

Journalise the following transactions, post them into Ledger and prepare a Trial Balance: 2019 (₹) 2019 (₹) April 1 Mohan commenced business with cash 1,00,000 April 20 Received cash from Gopal 3,950 April 3 Bought goods 5,000 Discount Allowed 50 April 4 Sold goods to Gopal 4,000 April 25 Paid wages 700 April 10 Bought goods from Ram 8,000 April 27 Paid to Ram in full settlement 7,700 April 15 Paid trade expenses 2,000 April 30 Paid rent 1,500

Answer» Journalise the following transactions, post them into Ledger and prepare a Trial Balance:


2019		(₹)	2019		(₹)
April 1	Mohan commenced business with cash	1,00,000	April 20	Received cash from Gopal	3,950
April 3	Bought goods	5,000		Discount Allowed	50
April 4	Sold goods to Gopal	4,000	April 25	Paid wages	700
April 10	Bought goods from Ram	8,000	April 27	Paid to Ram in full settlement	7,700
April 15	Paid trade expenses	2,000	April 30	Paid rent	1,500

Discussion

7624.	23. A square has opp. Angular coordinates (1,-1),(3,4) then other coordinates will be?
Answer» 23. A square has opp. Angular coordinates (1,-1),(3,4) then other coordinates will be?

Discussion

7625.	If a and b are two odd positive integers such that a is greater than b then prove that one of the two numbers (a + b ) /2 and (a-b) / 2 is odd and the other is even
Answer» If a and b are two odd positive integers such that a is greater than b then prove that one of the two numbers (a + b ) /2 and (a-b) / 2 is odd and the other is even

Discussion

7626.	Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.
Answer» Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

Discussion

7627.	A solid is in the shape of a cone surmounted on a hemisphere,the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm.Find the volume of the solid. (Use π= 3.14)
Answer» A solid is in the shape of a cone surmounted on a hemisphere,the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm.Find the volume of the solid. $(U s e π = 3.14)$

Discussion

7628.	Calculate the product:13×114=
Answer» $Calculate the product:$ $\frac{1}{3} \times 1 \frac{1}{4}$ =

Discussion

7629.	1 Tg = how many pg
Answer» 1 Tg = how many pg

Discussion

7630.

Find the mode of the following frequency distribution: [CBSE 2014] Marks 10−20 20−30 30−40 40−50 50−60 Frequency 12 35 45 25 13

Answer» Find the mode of the following frequency distribution: [CBSE 2014]

Marks	10−20	20−30	30−40	40−50	50−60
Frequency	12	35	45	25	13

Discussion

7631.	{ 133. In the figure, }PQ=QR=RS=SP=}{SQ=6cm and }}{PT=RT=14cm. The length ST is :
Answer» { 133. In the figure, }PQ=QR=RS=SP=}{SQ=6cm and }}{PT=RT=14cm. The length ST is :

Discussion

7632.	Question 9 Which of the following equation has two distinct real roots? (a) 2x2−3√2x+94=0 (b) x2+x−5=0 (c) x2+3x+2√2=0 (d) 5x2−3x+1=0
Answer» Question 9 Which of the following equation has two distinct real roots? (a) $2 x^{2} - 3 \sqrt{2} x + \frac{9}{4} = 0$ (b) $x^{2} + x - 5 = 0$ (c) $x^{2} + 3 x + 2 \sqrt{2} = 0$ (d) $5 x^{2} - 3 x + 1 = 0$

Discussion

7633.	ΔABC is an equilateral triangle of side 2a units. Find each of its altitudes.
Answer» $Δ A B C$ is an equilateral triangle of side 2a units. Find each of its altitudes.

Discussion

7634.	Question 11Find the ratio in which the point P(34,512)divides the line segment joining the points A(12,32) and B(2, -5).
Answer» Question 11 Find the ratio in which the point $P (\frac{3}{4}, \frac{5}{12})$ divides the line segment joining the points $A (\frac{1}{2}, \frac{3}{2})$ and B(2, -5).

Discussion

7635.	Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Answer» Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Discussion

7636.	Write the value of tan2θ-sec2θcot2θ-cosec2θ.
Answer» Write the value of $\frac{\tan^{2} θ - \sec^{2} θ}{\cot^{2} θ - {cosec}^{2} θ}$ .

Discussion

7637.	If tan(theta)=a/b then find value of cos2theta
Answer» If tan(theta)=a/b then find value of cos2theta

Discussion

7638.	Solve each of the following quadratic equations: x2+6x−(a2+2a−8)=0
Answer» Solve each of the following quadratic equations: $x^{2} + 6 x - (a^{2} + 2 a - 8) = 0$

Discussion

7639.	If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, the circumference (in cm) of the circle is:
Answer» If the difference between the circumference and the radius of a circle is 37 cm, then using π = ²²/₇, the circumference (in cm) of the circle is:

Discussion

7640.	A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree.
Answer» A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^{\circ}$ with it. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree.

Discussion

7641.	A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.
Answer» A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.

Discussion

7642.	On a graph paper, plot the following points A (5, 4), B (2, 4), C (-2, 4), D (-4, 4), E (0, 4), F (3, 4)?
Answer» On a graph paper, plot the following points A (5, 4), B (2, 4), C (-2, 4), D (-4, 4), E (0, 4), F (3, 4)?

Discussion

7643.	Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 repectively.
Answer» Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 repectively.

Discussion

7644.	Question 07.Apoorv throws two dice once and computers the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36 ? why ?
Answer» Question 07. Apoorv throws two dice once and computers the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36 ? why ?

Discussion

7645.	If the radius of the base of a right circular cone is increased by 15%, then the volume of the cone will increase by ______.
Answer» If the radius of the base of a right circular cone is increased by 15%, then the volume of the cone will increase by ______.

Discussion

7646.	Find the volume (in cm3 ) of :
Answer» Find the volume (in $c m^{3}$ ) of :

7646.

Find the volume (in cm3 ) of :

Answer»

Find the volume (in $c m^{3}$ ) of :

Discussion

7647.	7. Find 6 rational numbers between 3 and 4.
Answer» 7. Find 6 rational numbers between 3 and 4.

Discussion

7648.	Find the point of intersection of a line passing through (5,3) & (3,5) by a line x−y=2.
Answer» Find the point of intersection of a line passing through $(5, 3) & (3, 5)$ by a line $x - y = 2$ .

Discussion

7649.	A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.
Answer» A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.

Discussion

7650.

Plan out and find the area of the field from the data given from the Surveyor’s field book Metre to E To D 100 To C 75 To B 50 350 300 250 150 50 150 to F 100 to G From A

Answer»

Plan out and find the area of the field from the data given from the Surveyor’s field book

Metre to E

To D 100

To C 75

To B 50

350

300

250

150

50

150 to F

100 to G

From A

Discussion

Explore topic-wise InterviewSolutions in .

A gulab jamun, contains sugar syrup up to about 30% of its volume.Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm

The product of 3 consecutive numbers, when the first number is even is divisible by ___

In a triangle ABC, the incircle (centre O) touches BC. CA and AB at points P, Q and R respectively, Calculate : ∠QOR=2∠QPR given that ∠A=60o

AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.

Which term of the A. P. 3, 10, 17, ......... will be 84 more than its 13th term ?

A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17 innings

The value of limx→2 3x/2-33x-9 is ___________________.

If a and d are the first term and the common difference of an AP, Sn denotes the sum of n terms of an AP. If Sn=Pn+Qn2, what are a and d in terms of P and Q?

There are two boxes, each containing slips numbered 1 to 5. One slip is drawn from each box and their numbers added. What are the possible sums? Compute the probability of each sum.

Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x3 + 7x2 – 24x – 45, g(x) = x – 3

The number of integral point(s) in the domain of f(x)=sin−1[x5]+cos−1{x} is(where [.] denotes greatest integer function and {.} denotes fractional part function)

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers. [CBSE 2010]

You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents from a point E which are inclined at an angle of 60° to each other. Refer the figure and select the option which would lead us to the required construction.

Q- proove that root3-root7 is an irrational number.Q-show that there is no positive integer n for which root n-1+root n+1is rational

In the given right triangle, the value of sinθ is .

O is the centre of the circle and AB is a chord. AC is the bisector of ∠OAB,∠OAB=56∘. Find ∠OBE.

18. The sides of a right angled triangle are in AP. Show that they are in the ratio 3 : 4 : 5.

Question 36Complete the crossword Fig. 5.2 with the help of the clues:

In an AP, the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference. [CBSE 2011]

You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.

The graph of the polynomial f(x) = ax2 + bx + c is as shown in Fig. 2.20. Write the value of b2 − 4ac and the number of real zeros of f(x).

Out of 100 students sitting in an examination, 40 students got more than 60 marks out of 100. So, percent of students got more than 60 marks.

23. A square has opp. Angular coordinates (1,-1),(3,4) then other coordinates will be?

If a and b are two odd positive integers such that a is greater than b then prove that one of the two numbers (a + b ) /2 and (a-b) / 2 is odd and the other is even

Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

A solid is in the shape of a cone surmounted on a hemisphere,the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm.Find the volume of the solid. (Use π= 3.14)

Calculate the product:13×114=

1 Tg = how many pg

Find the mode of the following frequency distribution: [CBSE 2014] Marks 10−20 20−30 30−40 40−50 50−60 Frequency 12 35 45 25 13

{ 133. In the figure, }PQ=QR=RS=SP=}{SQ=6cm and }}{PT=RT=14cm. The length ST is :

Question 9 Which of the following equation has two distinct real roots? (a) 2x2−3√2x+94=0 (b) x2+x−5=0​​​​​​​ (c) x2+3x+2√2=0​​​​​​​ (d) 5x2−3x+1=0​​​​​​​

ΔABC is an equilateral triangle of side 2a units. Find each of its altitudes.

Question 11Find the ratio in which the point P(34,512)divides the line segment joining the points A(12,32) and B(2, -5).

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Write the value of tan2θ-sec2θcot2θ-cosec2θ.

If tan(theta)=a/b then find value of cos2theta

Solve each of the following quadratic equations: x2+6x−(a2+2a−8)=0

If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, the circumference (in cm) of the circle is:

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30∘ with it. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree.

A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.

On a graph paper, plot the following points A (5, 4), B (2, 4), C (-2, 4), D (-4, 4), E (0, 4), F (3, 4)?

Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 repectively.

Question 07.Apoorv throws two dice once and computers the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36 ? why ?

If the radius of the base of a right circular cone is increased by 15%, then the volume of the cone will increase by ______.

Find the volume (in cm3 ) of :

7. Find 6 rational numbers between 3 and 4.

Find the point of intersection of a line passing through (5,3) &amp; (3,5) by a line x−y=2.

A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.

Plan out and find the area of the field from the data given from the Surveyor’s field book Metre to E To D 100 To C 75 To B 50 350 300 250 150 50 150 to F 100 to G From A

Question 9 Which of the following equation has two distinct real roots? (a) 2x2−3√2x+94=0 (b) x2+x−5=0 (c) x2+3x+2√2=0 (d) 5x2−3x+1=0

Find the point of intersection of a line passing through (5,3) & (3,5) by a line x−y=2.