24740 + Interview Questions in Mathematics Page 187 InterviewSolution

9301.	The sum of two times a number and three is equal to eleven times the number. Find the number.
Answer» The sum of two times a number and three is equal to eleven times the number. Find the number.

Discussion

9302.	Question 2 Determine the mean of the following distribution MarksNumber of studentsBelow 10 5Below 20 9Below 30 17Below 40 29Below 50 45Below 60 60Below 70 70Below 80 78Below 90 83Below 100 85
Answer» Question 2 Determine the mean of the following distribution $\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 5 B e l o w 20 & 9 B e l o w 30 & 17 B e l o w 40 & 29 B e l o w 50 & 45 B e l o w 60 & 60 B e l o w 70 & 70 B e l o w 80 & 78 B e l o w 90 & 83 B e l o w 100 & 85 \end{matrix}$

Discussion

9303.	Draw ΔABC as in the first problem. Draw a triangle of the same area with two of its sides 6 centimetres and 7 centimetres.
Answer» Draw ΔABC as in the first problem. Draw a triangle of the same area with two of its sides 6 centimetres and 7 centimetres.

Discussion

9304.	Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Answer» Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Discussion

9305.	Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find its shortest altitude.
Answer» Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find its shortest altitude.

Discussion

9306.	The surface area of a sphere of radius 14 cms is
Answer» The surface area of a sphere of radius 14 cms is

Discussion

9307.	What is the minimum number of multiplications involved in computing the matrix product PQR? matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column
Answer» What is the minimum number of multiplications involved in computing the matrix product PQR? matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column

Discussion

9308.	In the given figure, determine the value of x.
Answer» In the given figure, determine the value of x.

Discussion

9309.	Simplify:(i) (a +b + c)2 + (a − b + c)2(ii) (a +b + c)2 − (a − b + c)2(iii) (a +b + c)2 + (a − b + c)2 + (a +b − c)2(iv) (2x + p − c)2 − (2x − p + c)2(v) (x2 + y2 − z2) − (x2 − y2 + z2)2
Answer» Simplify: (i) (a +b + c)² + (a − b + c)² (ii) (a +b + c)² − (a − b + c)2 (iii) (a +b + c)²+ (a − b + c)² + (a +b − c)² (iv) (2x + p − c)²− (2x − p + c)² (v) (x² + y²− z²) − (x² − y² + z²)²

Discussion

9310.	Probe that sum of rational and irrational is an irrational number?
Answer» Probe that sum of rational and irrational is an irrational number?

Discussion

9311.	Find the length of the longest pole that can be placed in a room 12m long, 8m broad and 9m high.
Answer» Find the length of the longest pole that can be placed in a room 12m long, 8m broad and 9m high.

Discussion

9312.	In the given figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that ▢ABCD is cyclic.
Answer» In the given figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that ▢ABCD is cyclic.

Discussion

9313.	The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle is
Answer» The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle is

Discussion

9314.	Question 2 (iv) Are the following statements ‘True’ or False’? Justify your answer. iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Answer» Question 2 (iv) Are the following statements ‘True’ or False’? Justify your answer. iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Discussion

9315.	If natural number is from 1 to positive infinity. Then we say that natural numbers are within rational numbers, where we can express a number in the form of p/q where q≠0. But we also know 1/0= 'Infinity'. So we are having a controversy. Is 1/0 ="Infinity" is a rational no. or irrational no.?
Answer» If natural number is from 1 to positive infinity. Then we say that natural numbers are within rational numbers, where we can express a number in the form of p/q where q≠0. But we also know 1/0= 'Infinity'. So we are having a controversy. Is 1/0 ="Infinity" is a rational no. or irrational no.?

Discussion

9316.	Verifty the property x×(y+z)=x×y+x×z of rational numbers by takingx=−12,y=23 and z=−34
Answer» Verifty the property $x \times (y + z) = x \times y + x \times z$ of rational numbers by taking $x = \frac{- 1}{2}, y = \frac{2}{3}$ and $z = \frac{- 3}{4}$

Discussion

9317.	ABCD is a parallelogram with ∠ABC=90∘, then number of right angles in the parallelogram excluding ∠ABC is/are ____?
Answer» ABCD is a parallelogram with $∠$ ABC= $90^{\circ}$ , then number of right angles in the parallelogram excluding $∠$ ABC is/are ____?

Discussion

9318.	find all zeroes of x³ – 4x² – 5x +14 if two of its zeroes are (3–√2) and (3+√2).
Answer» find all zeroes of x³ – 4x² – 5x +14 if two of its zeroes are (3–√2) and (3+√2).

Discussion

9319.	If a and b are rational numbers, find 'a' and 'b' when√7−2√7+2=a√7+b
Answer» If a and b are rational numbers, find 'a' and 'b' when $\frac{\sqrt{7} - 2}{\sqrt{7} + 2} = a \sqrt{7} + b$

9319.

If a and b are rational numbers, find 'a' and 'b' when√7−2√7+2=a√7+b

Answer»

If a and b are rational numbers, find 'a' and 'b' when

$\frac{\sqrt{7} - 2}{\sqrt{7} + 2} = a \sqrt{7} + b$

Discussion

9320.

A retail trader did not keep his books on the double entry system. Following balances were obtained from his books: 1st April 2013 31st March 2014 ₹ ₹ Sundry Debtors 32,000 38,800 Sundry Creditors 20,300 24,600 Cash 6,000 – Stock 22,000 28,000 Office Equipments 8,000 8,000 Machinery 30,000 40,000 Following further details of the transactions for the year ended 31st March, 2014 are available from his incomplete records: ₹ Sales (including Cash Sales ₹ 62,000) 1,20,000 Purchases (including Cash Purchases ₹ 25,000) 72,000 Salaries 16,500 Drawings 8,500 Rent, Taxes & Insurance 7,100 Bad-Debts written off 2,400 You are required to prepare his Trading, P & L A/c and Balance Sheet after considering the following:1. ₹ 1,500 are outstanding for salaries.2. Insurance was unexpired to the extent of ₹ 800.3. Goods worth ₹ 2,000 were used by the proprietor for personal use.

Answer» A retail trader did not keep his books on the double entry system. Following balances were obtained from his books:

	1st April 2013	31st March 2014
	₹	₹
Sundry Debtors	32,000	38,800
Sundry Creditors	20,300	24,600
Cash	6,000	–
Stock	22,000	28,000
Office Equipments	8,000	8,000
Machinery	30,000	40,000

Following further details of the transactions for the year ended 31st March, 2014 are available from his incomplete records:

	₹
Sales (including Cash Sales ₹ 62,000)	1,20,000
Purchases (including Cash Purchases ₹ 25,000)	72,000
Salaries	16,500
Drawings	8,500
Rent, Taxes & Insurance	7,100
Bad-Debts written off	2,400

You are required to prepare his Trading, P & L A/c and Balance Sheet after considering the following:

1. ₹ 1,500 are outstanding for salaries.

2. Insurance was unexpired to the extent of ₹ 800.

3. Goods worth ₹ 2,000 were used by the proprietor for personal use.

Discussion

9321.	The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Find its area.
Answer» The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Find its area.

Discussion

9322.	t is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.
Answer» t is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Discussion

9323.	f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
Answer» f(x) = 4x⁴ − 3x³ − 2x² + x − 7, g(x) = x − 1

Discussion

9324.	Ram’s salary is equal to Mohan’s salary. Due to recession, the salaries of Ram and Mohan are made half. The final salary of Ram will be:
Answer» Ram’s salary is equal to Mohan’s salary. Due to recession, the salaries of Ram and Mohan are made half. The final salary of Ram will be:

Discussion

9325.	Integration of inverse of tan
Answer» Integration of inverse of tan

Discussion

9326.	If the diameters of the concentric circles are consecutive even numbers, what would be the area of the yellow region?
Answer» If the diameters of the concentric circles are consecutive even numbers, what would be the area of the yellow region?

Discussion

9327.	A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.
Answer» A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

9327.

A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

Answer»

A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

Discussion

9328.	In the given figure, a ∆ABC has been given in which AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC, a parallelogram DBCE of the same area as that of ∆ABC is constructed. Find the height DL of the parallelogram.
Answer» In the given figure, a ∆ABC has been given in which AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC, a parallelogram DBCE of the same area as that of ∆ABC is constructed. Find the height DL of the parallelogram.

Discussion

9329.	Match the following: a.Interior angles on the same side of the transversal(i)1–5,2–6,3–7 and 4–8b.Alternate exterior angles(ii)4–6,3–5c.Corresponding angles(iii)1–7,2–8d.Alternate interior angles(iv)3–6,4−5
Answer» Match the following: $\begin{matrix} a . I n t e r i o r a n g l e s o n t h e s a m e s i d e o f t h e t r a n s v e r s a l & (i) 1 - 5, 2 - 6, 3 - 7 a n d 4 - 8 b . A l t e r n a t e e x t e r i o r a n g l e s & (i i) 4 - 6, 3 - 5 c . C o r r e s p o n d i n g a n g l e s & (i i i) 1 - 7, 2 - 8 d . A l t e r n a t e i n t e r i o r a n g l e s & (i v) 3 - 6, 4 - 5 \end{matrix}$

9329.

Match the following: a.Interior angles on the same side of the transversal(i)1–5,2–6,3–7 and 4–8b.Alternate exterior angles(ii)4–6,3–5c.Corresponding angles(iii)1–7,2–8d.Alternate interior angles(iv)3–6,4−5

Answer»

Match the following:

$\begin{matrix} a . I n t e r i o r a n g l e s o n t h e s a m e s i d e o f t h e t r a n s v e r s a l & (i) 1 - 5, 2 - 6, 3 - 7 a n d 4 - 8 b . A l t e r n a t e e x t e r i o r a n g l e s & (i i) 4 - 6, 3 - 5 c . C o r r e s p o n d i n g a n g l e s & (i i i) 1 - 7, 2 - 8 d . A l t e r n a t e i n t e r i o r a n g l e s & (i v) 3 - 6, 4 - 5 \end{matrix}$

Discussion

9330.	The square root of a number when multiplied by square root of another number gives 8 as the answer. The numbers could possibly be :
Answer» The square root of a number when multiplied by square root of another number gives 8 as the answer. The numbers could possibly be :

Discussion

9331.	Is it possible for a circle to have two segments that cover equal region inside a circle?
Answer» Is it possible for a circle to have two segments that cover equal region inside a circle?

Discussion

9332.	If the lateral surface area of a cube is 1600 cm2, then its edge is:
Answer» If the lateral surface area of a cube is 1600 cm², then its edge is:

Discussion

9333.	12 men working 8 hours a day complete a work in 10 days. How long would 16 men working 7 12 hours a day take to complete the same work ?
Answer» 12 men working 8 hours a day complete a work in 10 days. How long would 16 men working 7 $\frac{1}{2}$ hours a day take to complete the same work ?

Discussion

9334.	Question 8If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Answer» Question 8 If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Discussion

9335.	If a, b, c are positive real numbers, then 3125a10b5c105 is equal to(a) 5a2bc2(b) 25ab2c(c) 5a3bc3(d) 125a2bc2
Answer» If a, b, c are positive real numbers, then $\sqrt[5]{3125 a^{10} b^{5} c^{10}}$ is equal to (a) 5a²bc² (b) 25ab²c (c) 5a³bc³ (d) 125a²bc²

Discussion

9336.	Find the value of 3√48−4√75+5√192
Answer» Find the value of $3 \sqrt{48} - 4 \sqrt{75} + 5 \sqrt{192}$

Discussion

9337.	Prove that V3+ V5is an irrational number.
Answer» Prove that V3+ V5 is an irrational number.

Discussion

9338.	If b is the base of the parallelogram, and h is the height of the parallelogram. What is the area of parallelogram?
Answer» If b is the base of the parallelogram, and h is the height of the parallelogram. What is the area of parallelogram?

Discussion

9339.	Question 7Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ΔABC as shown in figure. Show that BC=12QR.
Answer» Question 7 Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $Δ A B C$ as shown in figure. Show that $B C = \frac{1}{2} Q R$ .

Discussion

9340.	What is the ratio of the total surface area of a sphere to that of a hemisphere if they have the same radius?
Answer» What is the ratio of the total surface area of a sphere to that of a hemisphere if they have the same radius?

Discussion

9341.	The abscissa of the point (2, -3) is ________.
Answer» The abscissa of the point (2, -3) is ________.

Discussion

9342.	Simplify:- 4√12×7√6
Answer» Simplify:- ⁴√12×⁷√6

9342.

Simplify:- 4√12×7√6

Answer»

Simplify:-

⁴√12×⁷√6

Discussion

9343.	3. What are the five postulates Euclid ?
Answer» 3. What are the five postulates Euclid ?

Discussion

9344.	Which of the following statement is not correct regarding rational number?
Answer» Which of the following statement is not correct regarding rational number?

Discussion

9345.	If the radius of the base of a cylinder is doubled, keeping the height same, find the ratio of the volume of the new cylinder to that of the original cylinder.
Answer» If the radius of the base of a cylinder is doubled, keeping the height same, find the ratio of the volume of the new cylinder to that of the original cylinder.

Discussion

9346.	Question 5 (ii)In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:ar(ΔAXS)=12ar(PQRS)
Answer» Question 5 (ii) In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that: $a r (Δ A X S) = \frac{1}{2} a r (P Q R S)$

Discussion

9347.	two semicircular rings of linear mass densities 'lemda' and '3lemda' and of radius R each are joining to form a complete ring.the distance of the centre of the mass of complete ring from its geometrical centre is(in terms of R and pi)
Answer» two semicircular rings of linear mass densities 'lemda' and '3lemda' and of radius R each are joining to form a complete ring.the distance of the centre of the mass of complete ring from its geometrical centre is(in terms of R and pi)

Discussion

9348.	The average of long Jump taken by an athlete is 8.05 m. If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m, what will be his 4th jump distance?
Answer» The average of long Jump taken by an athlete is 8.05 m. If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m, what will be his 4th jump distance?

9348.

The average of long Jump taken by an athlete is 8.05 m. If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m, what will be his 4th jump distance?

Answer»

The average of long Jump taken by an athlete is 8.05 m.

If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m,

what will be his 4th jump distance?

Discussion

9349.	45 How many kg of CaCO3 is needed to produce 336 kg of CaO , if % yeild of the reaction gives is 60% . CaCO3 -> CaO + CO2
Answer» 45 How many kg of CaCO3 is needed to produce 336 kg of CaO , if % yeild of the reaction gives is 60% . CaCO3 -> CaO + CO2

Discussion

9350.	Prove that √3+√5 is irrational.
Answer» Prove that $\sqrt 3 + \sqrt 5$ is irrational.

Discussion

Explore topic-wise InterviewSolutions in .

The sum of two times a number and three is equal to eleven times the number. Find the number.

Question 2 Determine the mean of the following distribution MarksNumber of studentsBelow 10 5Below 20 9Below 30 17Below 40 29Below 50 45Below 60 60Below 70 70Below 80 78Below 90 83Below 100 85

Draw ΔABC as in the first problem. Draw a triangle of the same area with two of its sides 6 centimetres and 7 centimetres.

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find its shortest altitude.

The surface area of a sphere of radius 14 cms is

What is the minimum number of multiplications involved in computing the matrix product PQR? matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column

In the given figure, determine the value of x.

Simplify:(i) (a +b + c)2 + (a − b + c)2(ii) (a +b + c)2 − (a − b + c)2(iii) (a +b + c)2 + (a − b + c)2 + (a +b − c)2(iv) (2x + p − c)2 − (2x − p + c)2(v) (x2 + y2 − z2) − (x2 − y2 + z2)2

Probe that sum of rational and irrational is an irrational number?

Find the length of the longest pole that can be placed in a room 12m long, 8m broad and 9m high.

In the given figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that ▢ABCD is cyclic.

The radius of a circle which has a 6 cm long chord, 4 cm away from the centre of the circle is

Question 2 (iv) Are the following statements ‘True’ or False’? Justify your answer. iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

If natural number is from 1 to positive infinity. Then we say that natural numbers are within rational numbers, where we can express a number in the form of p/q where q≠0. But we also know 1/0= 'Infinity'. So we are having a controversy. Is 1/0 ="Infinity" is a rational no. or irrational no.?

Verifty the property x×(y+z)=x×y+x×z of rational numbers by takingx=−12,y=23 and z=−34

ABCD is a parallelogram with ∠ABC=90∘, then number of right angles in the parallelogram excluding ∠ABC is/are ____?

find all zeroes of x³ – 4x² – 5x +14 if two of its zeroes are (3–√2) and (3+√2).

If a and b are rational numbers, find 'a' and 'b' when√7−2√7+2=a√7+b

The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Find its area.

t is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1

Ram’s salary is equal to Mohan’s salary. Due to recession, the salaries of Ram and Mohan are made half. The final salary of Ram will be:

Integration of inverse of tan

If the diameters of the concentric circles are consecutive even numbers, what would be the area of the yellow region?

A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

In the given figure, a ∆ABC has been given in which AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC, a parallelogram DBCE of the same area as that of ∆ABC is constructed. Find the height DL of the parallelogram.

Match the following: a.Interior angles on the same side of the transversal(i)1–5,2–6,3–7 and 4–8b.Alternate exterior angles(ii)4–6,3–5c.Corresponding angles(iii)1–7,2–8d.Alternate interior angles(iv)3–6,4−5

The square root of a number when multiplied by square root of another number gives 8 as the answer. The numbers could possibly be :

Is it possible for a circle to have two segments that cover equal region inside a circle?

If the lateral surface area of a cube is 1600 cm2, then its edge is:

12 men working 8 hours a day complete a work in 10 days. How long would 16 men working 7 12 hours a day take to complete the same work ?

Question 8If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

If a, b, c are positive real numbers, then 3125a10b5c105 is equal to(a) 5a2bc2(b) 25ab2c(c) 5a3bc3(d) 125a2bc2

Find the value of 3√48−4√75+5√192

Prove that V3+ V5is an irrational number.

If b is the base of the parallelogram, and h is the height of the parallelogram. What is the area of parallelogram?

Question 7Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ΔABC as shown in figure. Show that BC=12QR.

What is the ratio of the total surface area of a sphere to that of a hemisphere if they have the same radius?

The abscissa of the point (2, -3) is ________.

Simplify:- 4√12×7√6

3. What are the five postulates Euclid ?

Which of the following statement is not correct regarding rational number?

If the radius of the base of a cylinder is doubled, keeping the height same, find the ratio of the volume of the new cylinder to that of the original cylinder.

Question 5 (ii)In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:ar(ΔAXS)=12ar(PQRS)

two semicircular rings of linear mass densities 'lemda' and '3lemda' and of radius R each are joining to form a complete ring.the distance of the centre of the mass of complete ring from its geometrical centre is(in terms of R and pi)

The average of long Jump taken by an athlete is 8.05 m. If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m, what will be his 4th jump distance?

45 How many kg of CaCO3 is needed to produce 336 kg of CaO , if % yeild of the reaction gives is 60% . CaCO3 -> CaO + CO2

Prove that √3+√5 is irrational.