32581 + Interview Questions in Mathematics Page 177 InterviewSolution

8801.	For the equation, x+3y=5, x in terms of y can be written as____ and y in terms of x can be written as ______.
Answer» For the equation, $x + 3 y = 5$ , $x$ in terms of $y$ can be written as____ and $y$ in terms of $x$ can be written as ______.

Discussion

8802.	Select the option that contains the factor of 4x3+4x2−x−1
Answer» Select the option that contains the factor of $4 x^{3} + 4 x^{2} - x - 1$

Discussion

8803.	If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is(a) 4 : π(b) π : 4(c) π : 7(d) 7 : π
Answer» If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is (a) 4 : π (b) π : 4 (c) π : 7 (d) 7 : π

Discussion

8804.	In a three digit number, hundred's digit is two more than ten's digit is one-third of unit's digit. If unit's digit be z, then the number is?
Answer» In a three digit number, hundred's digit is two more than ten's digit is one-third of unit's digit. If unit's digit be z, then the number is?

Discussion

8805.	The distance between two successive screw threads is known as __ of the screw.
Answer» The distance between two successive screw threads is known as __ of the screw.

Discussion

8806.	It (2, –2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is ___________.
Answer» It (2, –2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is ___________.

Discussion

8807.	Obtain all the zeroes of the polynomial 3x4−12x3+5x2+16x−12, if two of its zeroes are 2√3 and −2√3.
Answer» Obtain all the zeroes of the polynomial $3 x^{4} - 12 x^{3} + 5 x^{2} + 16 x - 12,$ if two of its zeroes are $\frac{2}{\sqrt{3}} a n d \frac{- 2}{\sqrt{3}} .$

Discussion

8808.	Question 2 (v) Verify that each of the following is an AP and then write its next three terms. a, 2a + 1, 3a + 2, 4a + 3, . . . .
Answer» Question 2 (v) Verify that each of the following is an AP and then write its next three terms. a, 2a + 1, 3a + 2, 4a + 3, . . . .

Discussion

8809.	a3=18 a7=30 find s17
Answer» a3=18 a7=30 find s17

Discussion

8810.	Define the zero of a polynomial.
Answer» Define the zero of a polynomial.

Discussion

8811.	Show that △ABC with vertices A(-2, 0), B(0, 2), and C(2, 0) is similar to △DEF with vertices D(-4, 0), F(4, 0) and E(0, 4)
Answer» Show that $△ A B C$ with vertices A(-2, 0), B(0, 2), and C(2, 0) is similar to $△ D E F$ with vertices D(-4, 0), F(4, 0) and E(0, 4)

Discussion

8812.	If A(2,1,9),B(−4,1,−3),C(0,7,6) are the vertices of △ABC and the equation of the median through C is xa=y−7b=z−6−3, then \|a+b\| is equal to
Answer» If $A (2, 1, 9), B (- 4, 1, - 3), C (0, 7, 6)$ are the vertices of $△ A B C$ and the equation of the median through $C$ is $\frac{x}{a} = \frac{y - 7}{b} = \frac{z - 6}{- 3},$ then $\| a + b \|$ is equal to

Discussion

8813.

Following is the Trial Balance as on 31st March, 2018. Prepare Trading and Profit and Loss Account and Balance Sheet: Particulars Dr. (₹) Cr. (₹) Stock on 1st April, 2017 8,000 Sales 2,20,000 Purchases 1,26,000 Productive Wages 56,500 Salaries 16,000 Stores Consumed 6,050 Carriage 3,050 Rent 5,200 Insurance 1,320 Machinery 52,000 Building 67,000 Capital Less Drawings 1,45,600 Sundry Debtors 44,000 Sundry Creditors 20,000 Secured Loan 16,000 Furniture 3,350 General Expenses 2,600 Cash in Hand 1,930 Bad Debts 1,020 Bank 6,580 Input CGST 3,000 Input SGST 3,000 Output CGST 2,500 Output SGST 2,500 Total 4,06,600 4,06,600 Stock on 31st March, 2018, ₹20,600.You are to make adjustments in respect of the following:(a) Depreciate Machinery at 10% p.a.(b) Make a provision 5% for Doubtful Debts.(c) Provide discount on debtors 212%.(d) Rent includes Rent deposit of ₹400.(e) Insurance Prepaid ₹120.

Answer» Following is the Trial Balance as on 31st March, 2018. Prepare Trading and Profit and Loss Account and Balance Sheet:


Particulars	Dr. (₹)	Cr. (₹)
Stock on 1st April, 2017	8,000
Sales		2,20,000
Purchases	1,26,000
Productive Wages	56,500
Salaries	16,000
Stores Consumed	6,050
Carriage	3,050
Rent	5,200
Insurance	1,320
Machinery	52,000
Building	67,000
Capital Less Drawings		1,45,600
Sundry Debtors	44,000
Sundry Creditors		20,000
Secured Loan		16,000
Furniture	3,350
General Expenses	2,600
Cash in Hand	1,930
Bad Debts	1,020
Bank	6,580
Input CGST	3,000
Input SGST	3,000
Output CGST		2,500
Output SGST		2,500
Total	4,06,600	4,06,600

Stock on 31st March, 2018, ₹20,600.

You are to make adjustments in respect of the following:

(a) Depreciate Machinery at 10% p.a.

(b) Make a provision 5% for Doubtful Debts.

(c) Provide discount on debtors $2 \frac{1}{2}$ %.

(d) Rent includes Rent deposit of ₹400.

(e) Insurance Prepaid ₹120.

Discussion

8814.	If △ABC ~ △DEF such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of △ ABC and △DEF.
Answer» If $△$ ABC ~ $△$ DEF such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of $△$ ABC and $△$ DEF.

Discussion

8815.	A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Answer» A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Discussion

8816.	A rational number can be expressed as a terminating decimal if its denominator has factors
Answer» A rational number can be expressed as a terminating decimal if its denominator has factors

Discussion

8817.	Write the value of cosec2 (90° − θ) − tan2 θ.
Answer» Write the value of cosec² (90° − θ) − tan² θ.

Discussion

8818.	A, B and C were in partnership sharing profits and losses in the ratio of 4 : 2 : 1. It was provided that C's share in profit for a year would not be less then ₹ 7,500. Profit for the year ended 31st March, 2019 amounted to ₹ 31,500. You are required to show the appropriation among the partners. The profit and Loss Appropriation Account is not required.
Answer» A, B and C were in partnership sharing profits and losses in the ratio of 4 : 2 : 1. It was provided that C's share in profit for a year would not be less then ₹ 7,500. Profit for the year ended 31st March, 2019 amounted to ₹ 31,500. You are required to show the appropriation among the partners. The profit and Loss Appropriation Account is not required.

Discussion

8819.	Question 36Factorise:(i) a3−8b3−64c3−24abc(ii) 2√2a3+8b3−27c3+18√2abc
Answer» Question 36 Factorise: (i) $a^{3} - 8 b^{3} - 64 c^{3} - 24 a b c$ (ii) $2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$

Discussion

8820.	Verma and Sharma are partners in a firm sharing profits and losses in the ratio of 5 : 3. They admitted Ghosh as a new partner for 1/5th share of profits. Ghosh is to bring in ₹ 20,000 as capital and ₹ 4,000 as his share of goodwill premium. Give the necessary Journal entries:(a) When the amount of goodwill is retained in the business.(b) When the amount of goodwill is fully withdrawn.(c) When 50% of the amount of goodwill is withdrawn.(d) When goodwill is paid privately.
Answer» Verma and Sharma are partners in a firm sharing profits and losses in the ratio of 5 : 3. They admitted Ghosh as a new partner for 1/5th share of profits. Ghosh is to bring in ₹ 20,000 as capital and ₹ 4,000 as his share of goodwill premium. Give the necessary Journal entries: (a) When the amount of goodwill is retained in the business. (b) When the amount of goodwill is fully withdrawn. (c) When 50% of the amount of goodwill is withdrawn. (d) When goodwill is paid privately.

Discussion

8821.	Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of thesum of the first seven terms to the sum of thefirst eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is
Answer» Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of thesum of the first seven terms to the sum of thefirst eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

Discussion

8822.	How to divide two polynomials tell me the hardest way to do it
Answer» How to divide two polynomials tell me the hardest way to do it

Discussion

8823.	The distance between the points (cos q, sin q) and (sin q, – cos q) is ___.
Answer» The distance between the points ( $cos$ q, $sin$ q) and ( $sin$ q, – $cos$ q) is ___.

Discussion

8824.	One leg of a right angle triangle exceeds the other leg by 4 inches. Length of the hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.
Answer» One leg of a right angle triangle exceeds the other leg by 4 inches. Length of the hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

Discussion

8825.	(x-3)(x-7)(x-12)
Answer» (x-3)(x-7)(x-12)<0 solve for real x in equalities

Discussion

8826.	The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.
Answer» The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

Discussion

8827.	A motorist traveled 190 km in 5 hours. His average speed for first 100 kilometres was 50 km/h. What was his average speed for the second 90 kilometres?
Answer» A motorist traveled 190 km in 5 hours. His average speed for first 100 kilometres was 50 km/h. What was his average speed for the second 90 kilometres?

Discussion

8828.	If p and q are two prime number, then what is their LCM?
Answer» If p and q are two prime number, then what is their LCM?

Discussion

8829.	Question 5 Draw a triangle ABC with side BC=6 cm, AB=5 cm and∠ABC=60∘. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.
Answer» Question 5 Draw a triangle ABC with side $B C = 6 c m, A B = 5 c m a n d ∠ A B C = 60^{\circ}$ . Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle ABC.

Discussion

8830.	Which of the following is the correct value of (3 / 1+tan^2 θ) + 2 sin^2 θ + (1 / 1+cot^2 θ)?
Answer» Which of the following is the correct value of (3 / 1+tan^2 θ) + 2 sin^2 θ + (1 / 1+cot^2 θ)?

Discussion

8831.	The coordinates of the in centre of the triangle whose vertices are (0, 0), (4, 0) and (0, 3) are __________.
Answer» The coordinates of the in centre of the triangle whose vertices are (0, 0), (4, 0) and (0, 3) are __________.

Discussion

8832.	If sin 3θ = cos (θ − 6°), where (3θ) and (θ − 6°) are both acute angles, then the value of θ is(a) 18°(b) 24°(c) 36°(d) 30°
Answer» If sin 3θ = cos (θ − 6°), where (3θ) and (θ − 6°) are both acute angles, then the value of θ is (a) 18° (b) 24° (c) 36° (d) 30°

Discussion

8833.	Question 3A soft drink is available in two packs−(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm(ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? [Assume π=227]
Answer» Question 3 A soft drink is available in two packs− (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm (ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? $[A s s u m e π = \frac{22}{7}]$

8833.

Question 3A soft drink is available in two packs−(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm(ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? [Assume π=227]

Answer»

Question 3

A soft drink is available in two packs−

(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm

(ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

$[A s s u m e π = \frac{22}{7}]$

Discussion

8834.	Find the equation of normal to the circle x2+y2−5x+2y−48=0 which is parallel to the line 14x - 5y - 30 = 0
Answer» Find the equation of normal to the circle $x^{2} + y^{2} - 5 x + 2 y - 48 = 0$ which is parallel to the line 14x - 5y - 30 = 0

Discussion

8835.	Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.(i) n and Sn, if a = 5, d = 3 and an = 50.(ii) n and a, if an = 4, d = 2 and Sn = −14.(iii) d, if a = 3, n = 8 and Sn = 192.(iv) a, if an = 28, Sn = 144 and n= 9.(v) n and d, if a = 8, an = 62 and Sn = 210(vi) n and an, if a= 2, d = 8 and Sn = 90.(vii) k, if Sn=3n2+5n and ak=164.(viii) S22, if d=22 and a22=149
Answer» Let there be an A.P. with first term 'a', common difference 'd'. If a_n denotes in n^th term and S_n the sum of first n terms, find. (i) n and S_n, if a = 5, d = 3 and a_n = 50. (ii) n and a, if a_n = 4, d = 2 and S_n= −14. (iii) d, if a = 3, n = 8 and S_n = 192. (iv) a, if a_n = 28, S_n = 144 and n= 9. (v) n and d, if a = 8, a_n = 62 and S_n = 210 (vi) n and a_n, if a= 2, d = 8 and S_n = 90. (vii) $k, if S_{n} = 3 n^{2} + 5 n and a_{k} = 164$ . (viii) $S_{22}, if d = 22 and a_{22} = 149$

Discussion

8836.	Find the 9th term of the series : 1, 4, 16, 64, ......................
Answer» Find the 9th term of the series : 1, 4, 16, 64, ......................

8836.

Find the 9th term of the series : 1, 4, 16, 64, ......................

Answer»

Find the 9th term of the series :

1, 4, 16, 64, ......................

Discussion

8837.	A die has its six faces marked 0, 1, 1, 1, 6, 6. If two such dice are thrown together, then the probability of getting a total of 7 is _________.
Answer» A die has its six faces marked 0, 1, 1, 1, 6, 6. If two such dice are thrown together, then the probability of getting a total of 7 is _________.

Discussion

8838.	If the equation x2+2(k+2)x+9=0 has equal roots, then find the values of k.
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 = 0$ has equal roots, then find the values of k.

Discussion

8839.	I want modal question papers of 80 marks on the topics - Real numbers, Polynomials, Linear Equations, Quadratic Equations, Triangles, Trigonometry, Circles and Statistics for revision as I have Half Yearly Exam on Friday. Please send it as soon as possible.
Answer» I want modal question papers of 80 marks on the topics - Real numbers, Polynomials, Linear Equations, Quadratic Equations, Triangles, Trigonometry, Circles and Statistics for revision as I have Half Yearly Exam on Friday. Please send it as soon as possible.

Discussion

8840.	In the figure, the ∠ABC=30°. If CB=18 m , then AB = and AC = .
Answer» In the figure, the $∠ A B C = 30 °$ . If $C B = 18 m$ , then AB = and AC = .

Discussion

8841.	Which of the following are similar?
Answer» Which of the following are similar?

Discussion

8842.	A man goes 12 m due south and then 35 m due west. How far is he from the starting point ?
Answer» A man goes 12 m due south and then 35 m due west. How far is he from the starting point ?

Discussion

8843.	Slope of the tangent to y=(x+2)(x+3) at point where curve intersects the y−axis is
Answer» Slope of the tangent to $y = (x + 2) (x + 3)$ at point where curve intersects the $y -$ axis is

Discussion

8844.	If m and n are the zeroes of the polynomial f(x)=ax*2+bx+c then evaluate 1. 1/m+1/n 2. M/n+n/m
Answer» If m and n are the zeroes of the polynomial f(x)=ax*2+bx+c then evaluate 1. 1/m+1/n 2. M/n+n/m

Discussion

8845.	47. Two circles passing through A(1, 2), B(2, 1) touch the line 4x + 8y-7 = 0 at C and D Such that ACED is a parallelogram. Then coordinates of E
Answer» 47. Two circles passing through A(1, 2), B(2, 1) touch the line 4x + 8y-7 = 0 at C and D Such that ACED is a parallelogram. Then coordinates of E

Discussion

8846.	How many radii can a circle have?
Answer» How many radii can a circle have?

Discussion

8847.	{ If }α and }β are the zeroes of the polynomial }f(x)=ax^2+bx+c, where }a,b and }c are non-negative, }}{ then find the value of }\vertα-β\vert.
Answer» { If }α and }β are the zeroes of the polynomial }f(x)=ax^2+bx+c, where }a,b and }c are non-negative, }}{ then find the value of }\vertα-β\vert.

Discussion

8848.	60,16,20,36,72,?,288
Answer» 60,16,20,36,72,?,288

Discussion

8849.	The construction of triangle ΔA′C′B similar to triangle ΔACB is shown in the figure below. Choose the correct option:
Answer» The construction of triangle $Δ A^{'} C^{'} B$ similar to triangle $Δ A C B$ is shown in the figure below. Choose the correct option:

Discussion

8850.	In the given figure, if A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR ( π = 3.14)
Answer» In the given figure, if A is the centre of the circle. $∠$ PAR = 30^°, AP = 7.5, find the area of the segment PQR ( $π$ = 3.14)

Discussion

Explore topic-wise InterviewSolutions in .

For the equation, x+3y=5, x in terms of y can be written as____ and y in terms of x can be written as ______.

Select the option that contains the factor of 4x3+4x2−x−1

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is(a) 4 : π(b) π : 4(c) π : 7(d) 7 : π

In a three digit number, hundred's digit is two more than ten's digit is one-third of unit's digit. If unit's digit be z, then the number is?

The distance between two successive screw threads is known as __ of the screw.

It (2, –2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is ___________.

Obtain all the zeroes of the polynomial 3x4−12x3+5x2+16x−12, if two of its zeroes are 2√3 and −2√3.

Question 2 (v) Verify that each of the following is an AP and then write its next three terms. a, 2a + 1, 3a + 2, 4a + 3, . . . .

a3=18 a7=30 find s17

Define the zero of a polynomial.

Show that △ABC with vertices A(-2, 0), B(0, 2), and C(2, 0) is similar to △DEF with vertices D(-4, 0), F(4, 0) and E(0, 4)

If A(2,1,9),B(−4,1,−3),C(0,7,6) are the vertices of △ABC and the equation of the median through C is xa=y−7b=z−6−3, then |a+b| is equal to

If △ABC ~ △DEF such that AB = 1.2 cm and DE = 1.4 cm . Find the ratio of area of △ ABC and △DEF.

A rational number can be expressed as a terminating decimal if its denominator has factors

Write the value of cosec2 (90° − θ) − tan2 θ.

Question 36Factorise:(i) a3−8b3−64c3−24abc(ii) 2√2a3+8b3−27c3+18√2abc

Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of thesum of the first seven terms to the sum of thefirst eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

How to divide two polynomials tell me the hardest way to do it

The distance between the points (cos q, sin q) and (sin q, – cos q) is ___.

One leg of a right angle triangle exceeds the other leg by 4 inches. Length of the hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

(x-3)(x-7)(x-12)

The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

A motorist traveled 190 km in 5 hours. His average speed for first 100 kilometres was 50 km/h. What was his average speed for the second 90 kilometres?

If p and q are two prime number, then what is their LCM?

Question 5 Draw a triangle ABC with side BC=6 cm, AB=5 cm and∠ABC=60∘. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.

Which of the following is the correct value of (3 / 1+tan^2 θ) + 2 sin^2 θ + (1 / 1+cot^2 θ)?

The coordinates of the in centre of the triangle whose vertices are (0, 0), (4, 0) and (0, 3) are __________.

If sin 3θ = cos (θ − 6°), where (3θ) and (θ − 6°) are both acute angles, then the value of θ is(a) 18°(b) 24°(c) 36°(d) 30°

Question 3A soft drink is available in two packs−(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm(ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? [Assume π=227]

Find the equation of normal to the circle x2+y2−5x+2y−48=0 which is parallel to the line 14x - 5y - 30 = 0

Find the 9th term of the series : 1, 4, 16, 64, ......................

A die has its six faces marked 0, 1, 1, 1, 6, 6. If two such dice are thrown together, then the probability of getting a total of 7 is _________.

If the equation x2+2(k+2)x+9=0 has equal roots, then find the values of k.

I want modal question papers of 80 marks on the topics - Real numbers, Polynomials, Linear Equations, Quadratic Equations, Triangles, Trigonometry, Circles and Statistics for revision as I have Half Yearly Exam on Friday. Please send it as soon as possible.

In the figure, the ∠ABC=30°. If CB=18 m , then AB = and AC = .

Which of the following are similar?

A man goes 12 m due south and then 35 m due west. How far is he from the starting point ?

Slope of the tangent to y=(x+2)(x+3) at point where curve intersects the y−axis is

If m and n are the zeroes of the polynomial f(x)=ax*2+bx+c then evaluate 1. 1/m+1/n 2. M/n+n/m

47. Two circles passing through A(1, 2), B(2, 1) touch the line 4x + 8y-7 = 0 at C and D Such that ACED is a parallelogram. Then coordinates of E

How many radii can a circle have?

{ If }α and }β are the zeroes of the polynomial }f(x)=ax^2+bx+c, where }a,b and }c are non-negative, }}{ then find the value of }\vertα-β\vert.

60,16,20,36,72,?,288

The construction of triangle ΔA′C′B similar to triangle ΔACB is shown in the figure below. Choose the correct option:

In the given figure, if A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR ( π = 3.14)

For the equation, x+3y=5, x in terms of y can be written as and y in terms of x can be written as __.