32581 + Interview Questions in Mathematics Page 132 InterviewSolution

6551.	PQ is a chord of length 16 cm of a circle of radius 10 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP [CBSE 2013C]
Answer» PQ is a chord of length 16 cm of a circle of radius 10 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP [CBSE 2013C]

Discussion

6552.	If diameter of a circle is increased by 40%, then its area increase by(a) 96%(b) 40%(c) 80%(d) 48%
Answer» If diameter of a circle is increased by 40%, then its area increase by (a) 96% (b) 40% (c) 80% (d) 48%

Discussion

6553.	a triangle ABC right angled at C and D is the mid point of BC. prove that AB^2 =4AD^2 -3AC^2.
Answer» a triangle ABC right angled at C and D is the mid point of BC. prove that AB^2 =4AD^2 -3AC^2.

Discussion

6554.	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 (see the given figure).
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 (see the given figure).

6554.

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 (see the given figure).

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 (see the given figure).

Discussion

6555.	Number of common factors of 360 and 18144 are
Answer» Number of common factors of 360 and 18144 are

Discussion

6556.	There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?
Answer» There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?

6556.

There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?

Answer»

There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?

Discussion

6557.	Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Answer» Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Discussion

6558.	Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it.
Answer» Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it.

Discussion

6559.	2. Enumerate the indirect taxes which have been subsumed in the goods and services tax (GST) in Indi(a) Also, comment on the revenue implications of the GST introduced in India since July 2017.
Answer» 2. Enumerate the indirect taxes which have been subsumed in the goods and services tax (GST) in Indi(a) Also, comment on the revenue implications of the GST introduced in India since July 2017.

Discussion

6560.	What is the volume of the figure given below?
Answer» What is the volume of the figure given below?

6560.

What is the volume of the figure given below?

Answer»

What is the volume of the figure given below?

Discussion

6561.	Solve the equation: 10cos(×)= 15sin(×)+9
Answer» Solve the equation: 10cos(×)= 15sin(×)+9

Discussion

6562.	zeroes of x^2 + 5^1/2
Answer» zeroes of x^2 + 5^1/2

Discussion

6563.	A model of a ship is made to a scale of 1: 400. If the length of the model is 8 m, calculate the length of the ship.
Answer» A model of a ship is made to a scale of 1: 400. If the length of the model is 8 m, calculate the length of the ship.

Discussion

6564.	Short-Answer QuestionsSolve: 3x2+10x-83=0 [CBSE 2014]
Answer» Short-Answer Questions Solve: $\sqrt{3} x^{2} + 10 x - 8 \sqrt{3} = 0$ [CBSE 2014]

Discussion

6565.	The product of three numbers in AP is 224 and the largest number is 7 times the smallest. Find the numbers.
Answer» The product of three numbers in AP is 224 and the largest number is 7 times the smallest. Find the numbers.

Discussion

6566.	The median of a frequency distribution is found graphically with help of (a)a histogram (b) a frequency curve (c) a frequency polygon (d) ogives
Answer» The median of a frequency distribution is found graphically with help of (a)a histogram (b) a frequency curve (c) a frequency polygon (d) ogives

6566.

The median of a frequency distribution is found graphically with help of (a)a histogram (b) a frequency curve (c) a frequency polygon (d) ogives

Answer»

The median of a frequency distribution is found graphically with help of

(a)a histogram (b) a frequency curve (c) a frequency polygon (d) ogives

Discussion

6567.	The angle ∠XZY is degrees, where P is the center of the given circle.
Answer» The angle ∠XZY is degrees, where P is the center of the given circle.

Discussion

6568.	The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
Answer» The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Discussion

6569.	If two positive integers p and q are written as p=a2b3 and q=a3b; a and b are prime numbers, then verify: LCM(p,q)*HCF(p,q)=pq
Answer» If two positive integers p and q are written as p=a²b³and q=a³b; a and b are prime numbers, then verify: LCM(p,q)*HCF(p,q)=pq

Discussion

6570.	If p times the pth term is equal to q times the qth term. Then show that (p+q)th term is equal to zero
Answer» If p times the pth term is equal to q times the qth term. Then show that (p+q)th term is equal to zero

Discussion

6571.	Find the sum of first 40 positive integers divisible by 6.
Answer» Find the sum of first 40 positive integers divisible by 6.

Discussion

6572.	The sum of two numbers is 8 and the sum of their reciprocals is 815. Find the numbers.
Answer» The sum of two numbers is 8 and the sum of their reciprocals is $\frac{8}{15}$ . Find the numbers.

Discussion

6573.	Which of the following are quadratic surds?
Answer» Which of the following are quadratic surds?

Discussion

6574.	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.Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54
Answer» 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. $\begin{matrix} Daily pocket allowance (in Rs) & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 & 19 - 21 & 21 - 23 & 23 - 25 Number of workers & 7 & 6 & 9 & 13 & f & 5 & 4 \end{matrix}$

6574.

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.Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54

Answer»

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

6575.	Find the value of k for which each of the following system of equations have no solution :2x + ky = 115x − 7y = 5
Answer» Find the value of k for which each of the following system of equations have no solution : 2x + ky = 11 5x − 7y = 5

Discussion

6576.	Find the value of ‘m’ for which the given value of the variable is a solution of the equation x2+2ax+m=0; x+a=0
Answer» Find the value of ‘m’ for which the given value of the variable is a solution of the equation $x^{2} + 2 a x + m = 0$ ; $x + a = 0$

Discussion

6577.	Question 9If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be6:π.
Answer» Question 9 If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be $6 : π$ .

Discussion

6578.	If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Answer» If x = a sin θ and y = b cos θ, what is the value of b²x² + a²y²?

Discussion

6579.	If the length of the sides BC, CA and AB of a △ABC are a, b and c respectively and AD is the bisector of ∠A then find the length of BD and DC.
Answer» If the length of the sides BC, CA and AB of a △ABC are a, b and c respectively and AD is the bisector of ∠A then find the length of BD and DC.

Discussion

6580.	A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from 45∘ to 30∘. Find the speed of the boat. [Tan 45∘=1, Tan 30∘ = 0.57]
Answer» A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from $45^{\circ}$ to $30^{\circ}$ . Find the speed of the boat. $[T a n 45^{\circ} = 1, T a n 30^{\circ} = 0.57]$

Discussion

6581.	Find the LCF.(i) 12, 15(ii) 6, 8, 10(iii) 18, 32(iv) 10, 15, 20(v) 45, 86(vi) 15, 30, 90(vii) 105, 195(viii) 12, 15, 45(ix) 63, 81(x) 18, 36, 27
Answer» Find the LCF. (i) 12, 15 (ii) 6, 8, 10 (iii) 18, 32 (iv) 10, 15, 20 (v) 45, 86 (vi) 15, 30, 90 (vii) 105, 195 (viii) 12, 15, 45 (ix) 63, 81 (x) 18, 36, 27

Discussion

6582.	ABCD is a parallelogram in which P is the midpoint of DC and Q is point on AC such that CQ=1/4 AC . If produced PQ meets at BC at R then prove that R is the midpoint of BC.
Answer» ABCD is a parallelogram in which P is the midpoint of DC and Q is point on AC such that CQ=1/4 AC . If produced PQ meets at BC at R then prove that R is the midpoint of BC.

Discussion

6583.	If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2.
Answer» If $(x^{2} - y^{2}) = 18$ and $(x - y) = 3$ , find the value of $16 x^{2} y^{2}$ .

Discussion

6584.	The value of tan6tan42tan66*tan78 is
Answer» The value of tan6tan42tan66*tan78 is

Discussion

6585.	From the figure, determine the value of sin2θ + cos2θ1
Answer» From the figure, determine the value of $s i n^{2} θ$ + $c o s^{2} θ$ 1

Discussion

6586.	If the sum of the zeros of the polynomial f(x) = 2x3 − 3kx2 + 4x − 5 is 6, then the value of k is(a) 2(b) 4(c) −2(d) −4
Answer» If the sum of the zeros of the polynomial f(x) = 2x³ − 3kx² + 4x − 5 is 6, then the value of k is (a) 2 (b) 4 (c) −2 (d) −4

Discussion

6587.	Factors of x6−y6 is:
Answer» Factors of $x^{6} - y^{6}$ is:

Discussion

6588.	A man has some hens and cows. If the number of heads be 48 and the number of feetbe 140, how many cows are there?
Answer» A man has some hens and cows. If the number of heads be $48$ and the number of feet be $140$ , how many cows are there?

Discussion

6589.	If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2+y2+z2=r2
Answer» If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : $x^{2} + y^{2} + z^{2} = r^{2}$

6589.

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2+y2+z2=r2

Answer»

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that :

$x^{2} + y^{2} + z^{2} = r^{2}$

Discussion

6590.	Find the value of 1−tan2 30∘1+tan2 30∘.
Answer» Find the value of $\frac{1 - t a n^{2} 30^{\circ}}{1 + t a n^{2} 30^{\circ}} .$

Discussion

6591.	If the points A(x, 2), B(−3, −4) and C(7, −5) are collinear then the value of x is [CBSE 2014](a) −63 (b) 63 (c) 60 (d) −60
Answer» If the points A(x, 2), B(−3, −4) and C(7, −5) are collinear then the value of x is [CBSE 2014] (a) −63 (b) 63 (c) 60 (d) −60

Discussion

6592.	The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5\sqrt5 cm. Its surface area
Answer» The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5\sqrt5 cm. Its surface area

Discussion

6593.	The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11 hours more than earlier.Find the speed of the stream and speed of the boat.
Answer» The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11 hours more than earlier. Find the speed of the stream and speed of the boat.

Discussion

6594.	There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?
Answer» There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Discussion

6595.	A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 30° and 60°. Find the height of the tower.
Answer» A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 30° and 60°. Find the height of the tower.

Discussion

6596.

Prepare Trading and Profit and Loss Account and Balance Sheet from the following balances relating to the year ended 31st March, 2018: ₹ ₹ Capital 1,00,000 Wages 50,000 Creditors 12,000 Bank 10,000 Returns Outward 5,000 Repairs 500 Sales 1,64,000 Stock on 1st April, 2017 20,000 Bills Payable 5,000 Rent 4,000 Plant and Machinery 40,000 Manufacturing Expenses 8,000 Sundry Debtors 24,000 Trade Expenses 7,000 Drawing 10,000 Bad Debts 2,000 Purchases 1,05,000 Carriage 1,500 Returns Inward 3,000 Fuel and Power 1,000 Additional Information:(i) Closing Stock was valued at ₹ 14,500.(ii) Depreciate Plant and Machinery by ₹ 4,000.(iii) Write off Bad Debts ₹ 5,000.(iv) A sum of ₹ 400 is due for repairs.

Answer» Prepare Trading and Profit and Loss Account and Balance Sheet from the following balances relating to the year ended 31st March, 2018:

	₹		₹
Capital	1,00,000	Wages	50,000
Creditors	12,000	Bank	10,000
Returns Outward	5,000	Repairs	500
Sales	1,64,000	Stock on 1st April, 2017	20,000
Bills Payable	5,000	Rent	4,000
Plant and Machinery	40,000	Manufacturing Expenses	8,000
Sundry Debtors	24,000	Trade Expenses	7,000
Drawing	10,000	Bad Debts	2,000
Purchases	1,05,000	Carriage	1,500
Returns Inward	3,000	Fuel and Power	1,000

Additional Information:

(i) Closing Stock was valued at ₹ 14,500.

(ii) Depreciate Plant and Machinery by ₹ 4,000.

(iii) Write off Bad Debts ₹ 5,000.

(iv) A sum of ₹ 400 is due for repairs.

Discussion

6597.

On 31st March, 2018, W Ltd. had the following balances in its books: ₹ 9% Debentures 6,00,000 Debentures Redemption Reserve 50,000 Surplus,i.e., Balance in Statement of Profit and Loss 3,00,000 On that date, the company decided to transfer ₹ 1,00,000 to Debentures Redemption Reserve. It also decided to redeem debentures of ₹ 3,00,000 on 30th June, 2018.Pass necessary Journal entries in the books of the company.

Answer»

On 31st March, 2018, W Ltd. had the following balances in its books:	₹
9% Debentures	6,00,000
Debentures Redemption Reserve	50,000
Surplus,i.e., Balance in Statement of Profit and Loss	3,00,000

On that date, the company decided to transfer ₹ 1,00,000 to Debentures Redemption Reserve. It also decided to redeem debentures of ₹ 3,00,000 on 30th June, 2018.

Pass necessary Journal entries in the books of the company.

Discussion

6598.	For any positive integer , n3−n is always divisible by ___?
Answer» For any positive integer , $n^{3} - n$ is always divisible by ___?

Discussion

6599.	Prepare an Accounting Equation on the basis of the following transactions:(i) Started business with cash ₹ 70,000.(ii) Credit purchase of goods ₹ 18,000.(iii) Payment made to creditors in full settlement ₹ 17,500.(iv) Purchase of machinery for cash ₹ 20,000.(v) Depreciation on machinery ₹ 2,000.
Answer» Prepare an Accounting Equation on the basis of the following transactions: (i) Started business with cash ₹ 70,000. (ii) Credit purchase of goods ₹ 18,000. (iii) Payment made to creditors in full settlement ₹ 17,500. (iv) Purchase of machinery for cash ₹ 20,000. (v) Depreciation on machinery ₹ 2,000.

Discussion

6600.	Why does the writer refer to the 'early to bed...' principle?
Answer» Why does the writer refer to the 'early to bed...' principle?

Discussion

Explore topic-wise InterviewSolutions in .

PQ is a chord of length 16 cm of a circle of radius 10 cm. The tangent at P and Q intersect at a point T as shown in the figure. Find the length of TP [CBSE 2013C]

If diameter of a circle is increased by 40%, then its area increase by(a) 96%(b) 40%(c) 80%(d) 48%

a triangle ABC right angled at C and D is the mid point of BC. prove that AB^2 =4AD^2 -3AC^2.

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 (see the given figure).

Number of common factors of 360 and 18144 are

There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?

Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it.

2. Enumerate the indirect taxes which have been subsumed in the goods and services tax (GST) in Indi(a) Also, comment on the revenue implications of the GST introduced in India since July 2017.

What is the volume of the figure given below?

Solve the equation: 10cos(×)= 15sin(×)+9

zeroes of x^2 + 5^1/2

A model of a ship is made to a scale of 1: 400. If the length of the model is 8 m, calculate the length of the ship.

Short-Answer QuestionsSolve: 3x2+10x-83=0 [CBSE 2014]

The product of three numbers in AP is 224 and the largest number is 7 times the smallest. Find the numbers.

The median of a frequency distribution is found graphically with help of (a)a histogram (b) a frequency curve (c) a frequency polygon (d) ogives

The angle ∠XZY is degrees, where P is the center of the given circle.

The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

If two positive integers p and q are written as p=a2b3 and q=a3b; a and b are prime numbers, then verify: LCM(p,q)*HCF(p,q)=pq

If p times the pth term is equal to q times the qth term. Then show that (p+q)th term is equal to zero

Find the sum of first 40 positive integers divisible by 6.

The sum of two numbers is 8 and the sum of their reciprocals is 815. Find the numbers.

Which of the following are quadratic surds?

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.Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54

Find the value of k for which each of the following system of equations have no solution :2x + ky = 115x − 7y = 5

Find the value of ‘m’ for which the given value of the variable is a solution of the equation x2+2ax+m=0; x+a=0

Question 9If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be6:π.

If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?

If the length of the sides BC, CA and AB of a △ABC are a, b and c respectively and AD is the bisector of ∠A then find the length of BD and DC.

A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from 45∘ to 30∘. Find the speed of the boat. [Tan 45∘=1, Tan 30∘ = 0.57]

Find the LCF.(i) 12, 15(ii) 6, 8, 10(iii) 18, 32(iv) 10, 15, 20(v) 45, 86(vi) 15, 30, 90(vii) 105, 195(viii) 12, 15, 45(ix) 63, 81(x) 18, 36, 27

ABCD is a parallelogram in which P is the midpoint of DC and Q is point on AC such that CQ=1/4 AC . If produced PQ meets at BC at R then prove that R is the midpoint of BC.

If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2.

The value of tan6*tan42*tan66*tan78 is

From the figure, determine the value of sin2θ + cos2θ1

If the sum of the zeros of the polynomial f(x) = 2x3 − 3kx2 + 4x − 5 is 6, then the value of k is(a) 2(b) 4(c) −2(d) −4

Factors of x6−y6 is:

A man has some hens and cows. If the number of heads be 48 and the number of feetbe 140, how many cows are there?

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2+y2+z2=r2

Find the value of 1−tan2 30∘1+tan2 30∘.

If the points A(x, 2), B(−3, −4) and C(7, −5) are collinear then the value of x is [CBSE 2014](a) −63 (b) 63 (c) 60 (d) −60

The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5\sqrt5 cm. Its surface area

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11 hours more than earlier.Find the speed of the stream and speed of the boat.

There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 30° and 60°. Find the height of the tower.

For any positive integer , n3−n is always divisible by ___?

Why does the writer refer to the 'early to bed...' principle?

The value of tan6tan42tan66*tan78 is