24740 + Interview Questions in Mathematics Page 96 InterviewSolution

4751.	Question 88 (xv) Factorise the following expression. y2+8zx−2xy−4yz
Answer» Question 88 (xv) Factorise the following expression. $y^{2} + 8 z x - 2 x y - 4 y z$

Discussion

4752.	The length of shorter diagonal of parallelogram constructed on 5→a−6→b and 4→a−3→b where \|→a\|=4 and \|→b\|=3 and →a and →b are anti parallel is
Answer» The length of shorter diagonal of parallelogram constructed on $5 \to a - 6 \to b$ and $4 \to a - 3 \to b$ where $\| \to a \| = 4$ and $\| \to b \| = 3$ and $\to a$ and $\to b$ are anti parallel is

Discussion

4753.	Zero is even or odd. Why and Explain it.
Answer» Zero is even or odd. Why and Explain it.

Discussion

4754.	10. Let the point p (5, 9, 3) lies on the top of Qutub Minar, Delhi. Find the image of the point on the linex – 1/2 = y – 2/3 = z – 3/4 .
Answer» 10. Let the point p (5, 9, 3) lies on the top of Qutub Minar, Delhi. Find the image of the point on the linex – 1/2 = y – 2/3 = z – 3/4 .

Discussion

4755.

From the following Balance Sheet, prepare Cash Flow Statement: Particulars ulars Note No. 31st March, 2019 (₹) 31st March, 2018 (₹) I. EQUITY AND LIABILITIES 1. Shareholders' Funds (a) Share Capital 2,50,000 2,00,000 (b) Reserves and Surplus, 1 90,600 80,500 2. Current Liabilities (a) Short-term Borrowings: Bank Loan ... 70,000 (b) Trade Payables 1,35,200 1,50,000 (c) Short-term Provisions: Provision for Tax 35,000 30,000 Total Total Expenses 5,10,800 5,30,500 II. ASSETS 1. Non-Current Assets Fixed Assets: (i) Tangible Assets 2 3,59,000 3,50,000 (ii) Intangible Assets: Goodwill 5,000 ... 2. Current Assets (a) Inventories 74,000 1,00,000 (b) Trade Receivables 64,200 80,000 (c) Cash and Cash Equivalents 8,600 500 Total 5,10,800 5,30,500 Notes to Accounts Particulars 31st March, 2019 (₹) 31st March, 2018 (₹) I. Reserves and Surplus General Reserve 60,000 50,000 Surplus, i.e., Balance in Statement of Profit and Loss 30,600 30,500 90,600 80,500 2. Tangible Assets Land and Building 1,90,000 2,00,000 Plant and Machinery 1,69,000 1,50,000 3,59,000 3,50,000 Additional Information:1. Proposed Dividend for the year ended 31st March, 2019 was ₹ 25,000 and for the year ended 31st March, 2018 was ₹ 14,000.2. Interim Dividend paid during the year was ₹ 9,000.3. Income Tax paid during the year was ₹ 28,000.4. Machinery was purchased during the year ₹ 33,000.5. Depreciation to be charged on machinery ₹ 14,000 and building ₹ 10,000.

Answer»

From the following Balance Sheet, prepare Cash Flow Statement:

Particulars ulars	Note No.	31st March, 2019 (₹)	31st March, 2018 (₹)
I. EQUITY AND LIABILITIES
1. Shareholders' Funds
(a) Share Capital		2,50,000	2,00,000
(b) Reserves and Surplus,	1	90,600	80,500
2. Current Liabilities
(a) Short-term Borrowings: Bank Loan		...	70,000
(b) Trade Payables		1,35,200	1,50,000
(c) Short-term Provisions: Provision for Tax		35,000	30,000
Total Total Expenses		5,10,800	5,30,500
II. ASSETS
1. Non-Current Assets
Fixed Assets:
(i) Tangible Assets	2	3,59,000	3,50,000
(ii) Intangible Assets: Goodwill		5,000	...
2. Current Assets
(a) Inventories		74,000	1,00,000
(b) Trade Receivables		64,200	80,000
(c) Cash and Cash Equivalents		8,600	500
Total		5,10,800	5,30,500

Notes to Accounts

Particulars	31st March, 2019 (₹)	31st March, 2018 (₹)
I. Reserves and Surplus
General Reserve	60,000	50,000
Surplus, i.e., Balance in Statement of Profit and Loss	30,600	30,500
	90,600	80,500
2. Tangible Assets
Land and Building	1,90,000	2,00,000
Plant and Machinery	1,69,000	1,50,000
	3,59,000	3,50,000

Additional Information:

1. Proposed Dividend for the year ended 31st March, 2019 was ₹ 25,000 and for the year ended 31st March, 2018 was ₹ 14,000.

2. Interim Dividend paid during the year was ₹ 9,000.

3. Income Tax paid during the year was ₹ 28,000.

4. Machinery was purchased during the year ₹ 33,000.

5. Depreciation to be charged on machinery ₹ 14,000 and building ₹ 10,000.

Discussion

4756.	Three bus-stops situated at A, B and C in the following figure are operated by handicapped person. These three bus − stops are equidistant from each other. OB is the bisector of ∠ABC and OC is the bisector of ∠ACB.(i) Find ∠BOC.(ii) Do you think employment provided to handicapped persons is important for the development of the society? Express your views with relevant points.
Answer» Three bus-stops situated at A, B and C in the following figure are operated by handicapped person. These three bus − stops are equidistant from each other. OB is the bisector of ∠ABC and OC is the bisector of ∠ACB. (i) Find ∠BOC. (ii) Do you think employment provided to handicapped persons is important for the development of the society? Express your views with relevant points.

Discussion

4757.	Set up an equation and solve it to find the unknown number:Alex thinks of a number. If he adds 19 to it and divides the sum by 5, he will get 8.
Answer» Set up an equation and solve it to find the unknown number: Alex thinks of a number. If he adds 19 to it and divides the sum by 5, he will get 8.

Discussion

4758.	Question 1Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
Answer» Question 1 Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Discussion

4759.	If the measures of two of the angles of a triangle are 25 degrees and 60 degrees, then the third angle is _____.
Answer» If the measures of two of the angles of a triangle are 25 degrees and 60 degrees, then the third angle is _____.

Discussion

4760.	Question 3Show how √5 can be represented on the number line.
Answer» Question 3 Show how $\sqrt{5}$ can be represented on the number line.

Discussion

4761.	Heights in cm of 12 students are given as:154, 158, 155, 160, 165, 145, 148, 150, 147, 151, 166, 152Make a frequency table taking 145-150 as first class interval.
Answer» Heights in cm of 12 students are given as: 154, 158, 155, 160, 165, 145, 148, 150, 147, 151, 166, 152 Make a frequency table taking 145-150 as first class interval.

Discussion

4762.	22a3+162b3+c3-12abc
Answer» $2 \sqrt{2} a^{3} + 16 \sqrt{2} b^{3} + c^{3} - 12 a b c$

Discussion

4763.	In a city, 30% are females, 40% are males and the remaining are children. What percent are children?
Answer» In a city, 30% are females, 40% are males and the remaining are children. What percent are children?

Discussion

4764.	What are differences between state function and state variable?
Answer» What are differences between state function and state variable?

Discussion

4765.	Question 1 (iii) State whether the following statement is true or false. Justify your answer. Every real number is an irrational number.
Answer» Question 1 (iii) State whether the following statement is true or false. Justify your answer. Every real number is an irrational number.

4765.

Question 1 (iii) State whether the following statement is true or false. Justify your answer. Every real number is an irrational number.

Answer»

Question 1 (iii)
State whether the following statement is true or false. Justify your answer.

Every real number is an irrational number.

Discussion

4766.	In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If ∠ABC=25∘, calculate ∠CED.
Answer» In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If $∠ A B C = 25^{\circ}$ , calculate $∠ C E D$ .

4766.

In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If ∠ABC=25∘, calculate ∠CED.

Answer»

In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If $∠ A B C = 25^{\circ}$ , calculate $∠ C E D$ .

Discussion

4767.	Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.Section ASection BMarksFrequencyMarksFrequency0−1550−15315−301215−301630−452830−452545−603045−602760−753560−754075−901375−9010Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?
Answer» Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them. $\begin{matrix} Section A & Section B Marks & Frequency & Marks & Frequency 0 - 15 & 5 & 0 - 15 & 3 15 - 30 & 12 & 15 - 30 & 16 30 - 45 & 28 & 30 - 45 & 25 45 - 60 & 30 & 45 - 60 & 27 60 - 75 & 35 & 60 - 75 & 40 75 - 90 & 13 & 75 - 90 & 10 \end{matrix}$ Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?

Discussion

4768.	12.How was the formula for finding area of a sphere derived?
Answer» 12.How was the formula for finding area of a sphere derived?

Discussion

4769.	A hemispherical tank is emptied by a pipe at the rate of 5 litres per minute. How long will it take to half-empty the tank if its diameter is 112 m.
Answer» A hemispherical tank is emptied by a pipe at the rate of $5$ litres per minute. How long will it take to half-empty the tank if its diameter is $1 \frac{1}{2} m$ .

Discussion

4770.	Find the length of a chord that is at a distance of 4 cm from the centre of a circle of radius 6 cm.
Answer» Find the length of a chord that is at a distance of 4 cm from the centre of a circle of radius 6 cm.

Discussion

4771.	M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.
Answer» M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.

Discussion

4772.	What is the region shaded in purple known as?
Answer» What is the region shaded in purple known as?

Discussion

4773.	During construction of each case/type of problem in Triangle Construction 2-
Answer» During construction of each case/type of problem in Triangle Construction 2-

Discussion

4774.	If x+y=5 and xy=6, then find x^3+y^3
Answer» If x+y=5 and xy=6, then find x^3+y^3

Discussion

4775.	A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the
Answer» A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the

Discussion

4776.	The path of a train A is given by the equation 3x + 4y - 12 = 0 and the path of another train B is given by the equation 6x + 8y - 48 = 0. Represent this situation graphically.
Answer» The path of a train A is given by the equation 3x + 4y - 12 = 0 and the path of another train B is given by the equation 6x + 8y - 48 = 0. Represent this situation graphically.

Discussion

4777.	A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14).
Answer» A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14).

Discussion

4778.	The classes in a frequency distribution range from 110 to 170 with class interval being 10. What is the Mid value of this Class Distribution?
Answer» The classes in a frequency distribution range from 110 to 170 with class interval being 10. What is the Mid value of this Class Distribution?

4778.

The classes in a frequency distribution range from 110 to 170 with class interval being 10. What is the Mid value of this Class Distribution?

Answer»

The classes in a frequency distribution range from 110 to 170 with class interval being 10.

What is the Mid value of this Class Distribution?

Discussion

4779.	If each number of mean, median or mode is increased 17% then how much mean median or mode is increased
Answer» If each number of mean, median or mode is increased 17% then how much mean median or mode is increased

Discussion

4780.	Find the distance from the point (1,2,3) to the line (x+1)/1 = (y-1)/2 = z/1 measured parallel to the plane x+y+2z+1=0
Answer» Find the distance from the point (1,2,3) to the line (x+1)/1 = (y-1)/2 = z/1 measured parallel to the plane x+y+2z+1=0

Discussion

4781.	27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere. Find the radius of the big sphere formed.
Answer» 27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere. Find the radius of the big sphere formed.

Discussion

4782.	39. angle ABG = angle DCH angle GBC = angle HCB GD and AH are line segments. Show that AE+AB/2(ED+DC) = 1/2
Answer» 39. angle ABG = angle DCH angle GBC = angle HCB GD and AH are line segments. Show that AE+AB/2(ED+DC) = 1/2

Discussion

4783.	If kx cube +9x square +4x - 10 divided by x+3 leaves remainder 5.find the value of k
Answer» If kx cube +9x square +4x - 10 divided by x+3 leaves remainder 5.find the value of k

Discussion

4784.	In the figure below, G is the centroid of ΔABC. Prove that the triangles AGB, AGC, BGC have the same area.
Answer» In the figure below, G is the centroid of ΔABC. Prove that the triangles AGB, AGC, BGC have the same area.

4784.

In the figure below, G is the centroid of ΔABC. Prove that the triangles AGB, AGC, BGC have the same area.

Answer»

In the figure below, G is the centroid of ΔABC.

Prove that the triangles AGB, AGC, BGC have the same area.

Discussion

4785.	Question 94A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.
Answer» Question 94 A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.

4785.

Question 94A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.

Answer»

Question 94

A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.

Discussion

4786.	3x3 − x2 − 3x + 1
Answer» 3x³ − x² − 3x + 1

Discussion

4787.	If interest on ₹x for 2 years at R% per annum is ₹80, the interest on ₹2x for one year at R% per annum is(a) ₹160(b) ₹40(c) ₹80(d) ₹120
Answer» If interest on ₹x for 2 years at R% per annum is ₹80, the interest on ₹2x for one year at R% per annum is (a) ₹160 (b) ₹40 (c) ₹80 (d) ₹120

Discussion

4788.	If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
Answer» If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Discussion

4789.	If the point (3, 5) lies on the graph of the equation 3y = ax + 9, find the value of a.
Answer» If the point (3, 5) lies on the graph of the equation 3y = ax + 9, find the value of a.

Discussion

4790.	Question 118Solve the following question:Find the length of each side of a cube, if its volume is 512 cm3
Answer» Question 118 Solve the following question: Find the length of each side of a cube, if its volume is $512 c m^{3}$

4790.

Question 118Solve the following question:Find the length of each side of a cube, if its volume is 512 cm3

Answer»

Question 118

Solve the following question:

Find the length of each side of a cube, if its volume is $512 c m^{3}$

Discussion

4791.	Let a→, b→, c→ be three non-coplanar vectors such that a→ b→ c→=24 and a→×b→=6. Then the height the parallelopiped formed by a→, b→, c→ with a→ and b→ as two adjacent edges of the base, is ____________.
Answer» Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors such that $[\vec{a} \vec{b} \vec{c}] = 24 and \|\vec{a} \times \vec{b}\| = 6 .$ Then the height the parallelopiped formed by $\vec{a}, \vec{b}, \vec{c} with \vec{a} and \vec{b}$ as two adjacent edges of the base, is ____________.

Discussion

4792.	Find the value of x in the given figure if ∠AOB=70∘ and AB=CD.
Answer» Find the value of $x$ in the given figure if $∠ A O B = 70^{\circ}$ and $A B = C D .$

Discussion

4793.	A chord 8 cm long is 3 cm away from the centre of the circle A. Calculate the length of a chord that is 4 cm away from the centre of circle A.
Answer» A chord 8 cm long is 3 cm away from the centre of the circle A. Calculate the length of a chord that is 4 cm away from the centre of circle A.

Discussion

4794.	find the domain of f(x) = squae root x square - 25x + 144
Answer» find the domain of f(x) = squae root x square - 25x + 144

Discussion

4795.	POQ is a line . Ray OR is perpendicular to line PQ . OS is another Ray lying between rays OP and OR . Prove that angle ROS = 1/2(angle QOS - angle POS).
Answer» POQ is a line . Ray OR is perpendicular to line PQ . OS is another Ray lying between rays OP and OR . Prove that angle ROS = 1/2(angle QOS - angle POS).

Discussion

4796.	are the coordinates of vertex of quadratic polynomial are the real zeroes of quadratic polynomial ?
Answer» are the coordinates of vertex of quadratic polynomial are the real zeroes of quadratic polynomial ?

Discussion

4797.	What is the degree of a constant polynomial
Answer» What is the degree of a constant polynomial

Discussion

4798.	\|− \|− 7\| − 3\| is equal to(a) − 7 (b) 7 (c) 10 (d) − 10
Answer» \|− \|− 7\| − 3\| is equal to (a) − 7 (b) 7 (c) 10 (d) − 10

Discussion

4799.	Find the zeroes of the polynomial: 6x3−5x2−3x+2=0
Answer» Find the zeroes of the polynomial: $6 x^{3} - 5 x^{2} - 3 x + 2 = 0$

Discussion

4800.	By using data in example (6), and taking classes 30-40, 40-50... prepare equal to or more than type cumulative frequency table and answer the following questions based on it. (i) How many students have scored marks 70 or more than 70 ?(ii) How many students have scored marks 30 or more than 30 ?
Answer» By using data in example (6), and taking classes 30-40, 40-50... prepare equal to or more than type cumulative frequency table and answer the following questions based on it. (i) How many students have scored marks 70 or more than 70 ? (ii) How many students have scored marks 30 or more than 30 ?

Discussion

Explore topic-wise InterviewSolutions in .

Question 88 (xv) Factorise the following expression. y2+8zx−2xy−4yz

The length of shorter diagonal of parallelogram constructed on 5→a−6→b and 4→a−3→b where |→a|=4 and |→b|=3 and →a and →b are anti parallel is

Zero is even or odd. Why and Explain it.

10. Let the point p (5, 9, 3) lies on the top of Qutub Minar, Delhi. Find the image of the point on the linex – 1/2 = y – 2/3 = z – 3/4 .

Set up an equation and solve it to find the unknown number:Alex thinks of a number. If he adds 19 to it and divides the sum by 5, he will get 8.

Question 1Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

If the measures of two of the angles of a triangle are 25 degrees and 60 degrees, then the third angle is _____.

Question 3Show how √5 can be represented on the number line.

Heights in cm of 12 students are given as:154, 158, 155, 160, 165, 145, 148, 150, 147, 151, 166, 152Make a frequency table taking 145-150 as first class interval.

22a3+162b3+c3-12abc

In a city, 30% are females, 40% are males and the remaining are children. What percent are children?

What are differences between state function and state variable?

Question 1 (iii) State whether the following statement is true or false. Justify your answer. Every real number is an irrational number.

In the adjoining figure, O is the centre of a circle. Chord CD is parallel to diameter AB. If ∠ABC=25∘, calculate ∠CED.

12.How was the formula for finding area of a sphere derived?

A hemispherical tank is emptied by a pipe at the rate of 5 litres per minute. How long will it take to half-empty the tank if its diameter is 112 m.

Find the length of a chord that is at a distance of 4 cm from the centre of a circle of radius 6 cm.

M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.

What is the region shaded in purple known as?

During construction of each case/type of problem in Triangle Construction 2-

If x+y=5 and xy=6, then find x^3+y^3

A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the

The path of a train A is given by the equation 3x + 4y - 12 = 0 and the path of another train B is given by the equation 6x + 8y - 48 = 0. Represent this situation graphically.

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14).

The classes in a frequency distribution range from 110 to 170 with class interval being 10. What is the Mid value of this Class Distribution?

If each number of mean, median or mode is increased 17% then how much mean median or mode is increased

Find the distance from the point (1,2,3) to the line (x+1)/1 = (y-1)/2 = z/1 measured parallel to the plane x+y+2z+1=0

27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere. Find the radius of the big sphere formed.

39. angle ABG = angle DCH angle GBC = angle HCB GD and AH are line segments. Show that AE+AB/2(ED+DC) = 1/2

If kx cube +9x square +4x - 10 divided by x+3 leaves remainder 5.find the value of k

In the figure below, G is the centroid of ΔABC. Prove that the triangles AGB, AGC, BGC have the same area.

Question 94A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.

3x3 − x2 − 3x + 1

If interest on ₹x for 2 years at R% per annum is ₹80, the interest on ₹2x for one year at R% per annum is(a) ₹160(b) ₹40(c) ₹80(d) ₹120

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

If the point (3, 5) lies on the graph of the equation 3y = ax + 9, find the value of a.

Question 118Solve the following question:Find the length of each side of a cube, if its volume is 512 cm3

Let a→, b→, c→ be three non-coplanar vectors such that a→ b→ c→=24 and a→×b→=6. Then the height the parallelopiped formed by a→, b→, c→ with a→ and b→ as two adjacent edges of the base, is ____________.

Find the value of x in the given figure if ∠AOB=70∘ and AB=CD.

A chord 8 cm long is 3 cm away from the centre of the circle A. Calculate the length of a chord that is 4 cm away from the centre of circle A.

find the domain of f(x) = squae root x square - 25x + 144

POQ is a line . Ray OR is perpendicular to line PQ . OS is another Ray lying between rays OP and OR . Prove that angle ROS = 1/2(angle QOS - angle POS).

are the coordinates of vertex of quadratic polynomial are the real zeroes of quadratic polynomial ?

What is the degree of a constant polynomial

|− |− 7| − 3| is equal to(a) − 7 (b) 7 (c) 10 (d) − 10

Find the zeroes of the polynomial: 6x3−5x2−3x+2=0

By using data in example (6), and taking classes 30-40, 40-50... prepare equal to or more than type cumulative frequency table and answer the following questions based on it. (i) How many students have scored marks 70 or more than 70 ?(ii) How many students have scored marks 30 or more than 30 ?