24740 + Interview Questions in Mathematics Page 104 InterviewSolution

5151.	A solid triangular prism with equilateral base is 5 centimetres high and its base perimeter is 12 centimetres. Find its surface area.
Answer» A solid triangular prism with equilateral base is 5 centimetres high and its base perimeter is 12 centimetres. Find its surface area.

5151.

A solid triangular prism with equilateral base is 5 centimetres high and its base perimeter is 12 centimetres. Find its surface area.

Answer»

A solid triangular prism with equilateral base is 5 centimetres high and its base perimeter is 12 centimetres. Find its surface area.

Discussion

5152.	What is the value of tan θ in the given triangle?
Answer» What is the value of tan θ in the given triangle?

5152.

What is the value of tan θ in the given triangle?

Answer»

What is the value of tan θ in the given triangle?

Discussion

5153.	Look at several examples of rational numbers in the form pq (q ≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?
Answer» Look at several examples of rational numbers in the form $\frac{p}{q} (q \neq 0),$ where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

Discussion

5154.	Question 20A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for six days, while Anand paid Rs.16 for the book kept for four days. Find the fixed charges and the charge for each extra day.
Answer» Question 20 A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for six days, while Anand paid Rs.16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

Discussion

5155.	fourth root of 193-4\sqrt{2178} is
Answer» fourth root of 193-4\sqrt{2178} is

Discussion

5156.	In an equilateral triangle, the sides are ___
Answer» In an equilateral triangle, the sides are ___

Discussion

5157.	Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that □ABCD is a rhombus.
Answer» Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that $□$ ABCD is a rhombus.

Discussion

5158.	A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and takes two hours longer to cover the distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.
Answer» A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and takes two hours longer to cover the distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.

Discussion

5159.	Given the point(3, 7), find the equation of a line on which it lies
Answer» Given the point(3, 7), find the equation of a line on which it lies

Discussion

5160.	Factorisex²+1/x²+2-2x-2/x
Answer» Factorise x²+1/x²+2-2x-2/x

Discussion

5161.	If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
Answer» If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Discussion

5162.	The value of √2+3√2+5√3
Answer» The value of $\sqrt{2} + 3 \sqrt{2} + 5 \sqrt{3}$

Discussion

5163.	The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m3 is_____.
Answer» The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in $k g / m^{3}$ is_____.

Discussion

5164.	In a rectangle ABCD, AB=20cm, ∠BAC=60∘, Then side BC=
Answer» In a rectangle $A B C D$ , $A B = 20 c m$ , $∠ B A C = 60^{\circ}$ , Then side $B C =$

Discussion

5165.	If I=[1001] and E=[0100], then (aI+bE)3=
Answer» If $I = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ and $E = [\begin{matrix} 0 & 1 0 & 0 \end{matrix}],$ then $(a I + b E)^{3} =$

Discussion

5166.	If( a2+1)/a =4 find the value of 2a3 + 2/a3
Answer» If( a²+1)/a =4 find the value of 2a³+ 2/a³

Discussion

5167.	The height h of a cylinder equals the circumference of the cylinder. In terms of h what is the volume of the cylinder?
Answer» The height h of a cylinder equals the circumference of the cylinder. In terms of h what is the volume of the cylinder?

Discussion

5168.	Question 90(ii)Look at the histogram below and answer the questions that follow. ?Which class interval has the least numebr of students ?
Answer» Question 90(ii) Look at the histogram below and answer the questions that follow. ? Which class interval has the least numebr of students ?

5168.

Question 90(ii)Look at the histogram below and answer the questions that follow. ?Which class interval has the least numebr of students ?

Answer»

Question 90(ii)

Look at the histogram below and answer the questions that follow. ?

Which class interval has the least numebr of students ?

Discussion

5169.	INSERT 2 irrational numbers between 2.3 AND 3.7
Answer» INSERT 2 irrational numbers between 2.3 AND 3.7

Discussion

5170.	If (4+√13)×(5−√13)×(7−√13)= 6x, then find x. 6
Answer» If $(4 + \sqrt{13}) \times (5 - \sqrt{13}) \times (7 - \sqrt{13}) =$ $6 x$ , then find $x$ . 6

Discussion

5171.	In the following figure, if OQ is angle bisector of ∠POA, then ∠POQ will be equal to ___.
Answer» In the following figure, if OQ is angle bisector of $∠$ POA, then $∠$ POQ will be equal to ___.

5171.

In the following figure, if OQ is angle bisector of ∠POA, then ∠POQ will be equal to ___.

Answer»

In the following figure, if OQ is angle bisector of $∠$ POA, then $∠$ POQ will be equal to ___.

Discussion

5172.	Rationalize the denominator of :1(√7−√6) .
Answer» Rationalize the denominator of : $\frac{1}{(\sqrt{7} - \sqrt{6})}$ .

Discussion

5173.	An iron spherical ball of radius 21 cm is melted and re-casted in spheres of radius 7 cm. The number of spheres formed will be ___
Answer» An iron spherical ball of radius $21 c m$ is melted and re-casted in spheres of radius $7 c m .$ The number of spheres formed will be ___

Discussion

5174.	Question 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Answer» Question 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

5174.

Question 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Answer»

Question 11
On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Discussion

5175.	In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ
Answer» In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ

Discussion

5176.	The factors of polynomial p(x)=x2+2x+1 are x + a and x + b. Find the value of a + b.2
Answer» The factors of polynomial $p (x) = x^{2} + 2 x + 1$ are x + a and x + b. Find the value of a + b. 2

Discussion

5177.	Is a perpendicular bisector a line or a line segment? __
Answer» Is a perpendicular bisector a line or a line segment? __

Discussion

5178.	If x=12 is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
Answer» If $x = \frac{1}{2}$ is a zero of the polynomial f(x) = 8x³ + ax² − 4x + 2, find the value of a.

Discussion

5179.	Find the point on 5x - 3y = 4 where the ordinate is equal to the abscissa
Answer» Find the point on 5x - 3y = 4 where the ordinate is equal to the abscissa

Discussion

5180.	If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.
Answer» If the side BC of $Δ A B C$ is produced on both sides, then write the difference between the sum of the exterior angles so formed and $∠ A .$

Discussion

5181.	Two numbers x and y (x y) are selected from the set of first 50 natural numbers. The number of ways of selectingthem such that 53.) xsquare-ysquare is divisible by 5 is(A) 470(C) 280(B) 425(D) 140 Q 54. x power4- ypower4 is divisible by 5 is(A) 470(C) 835(B) 235(D) 825
Answer» Two numbers x and y (x y) are selected from the set of first 50 natural numbers. The number of ways of selectingthem such that 53.) xsquare-ysquare is divisible by 5 is(A) 470(C) 280(B) 425(D) 140 Q 54. x power4- ypower4 is divisible by 5 is(A) 470(C) 835(B) 235(D) 825

Discussion

5182.	The height of a solid cone is 12 cm and the area of the circular base is 64 \lbrack 22/7\}cm 2 . A planeparallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is
Answer» The height of a solid cone is 12 cm and the area of the circular base is 64 \lbrack 22/7\}cm 2 . A planeparallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is

Discussion

5183.	Find the lateral surface area and total surface area of a cube of edge 10 cm.
Answer» Find the lateral surface area and total surface area of a cube of edge 10 cm.

Discussion

5184.	A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?
Answer» A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?

Discussion

5185.	Question 12In the given question, out of four options, only one is correct. Write the correct answer.If x + y + z = 6 and z is an odd digit, then the three- digit number xyz is (a) an odd multiple of 3(b) an odd multiple of 6(c) an even multiple of 3(d) an even multiple of 9
Answer» Question 12 In the given question, out of four options, only one is correct. Write the correct answer. If x + y + z = 6 and z is an odd digit, then the three- digit number xyz is (a) an odd multiple of 3 (b) an odd multiple of 6 (c) an even multiple of 3 (d) an even multiple of 9

Discussion

5186.	The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is
Answer» The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is

Discussion

5187.	What is the difference between zero polynomial and zeroes of the polynomial
Answer» What is the difference between zero polynomial and zeroes of the polynomial

Discussion

5188.	The polar form of (i25)3 is ____________.
Answer» The polar form of (i²⁵)³ is ____________.

Discussion

5189.	From the following balances, prepare Final Accounts of M/s Raja & Sons for the year ended 31st March, 2019:Salary ₹ 5,400; Insurance ₹ 2,500; Cash ₹ 400; Purchases ₹ 84,170; Rent Received ₹ 3,150; Drawings ₹ 2,100; Bills Payable ₹ 3,900; Debtors ₹ 38,080; Stock (1st April, 2018) ₹ 29,500; Bank Overdraft ₹ 9,700; Carriage ₹ 2,200; Creditors ₹ 4,200; Trade Expenses ₹ 4,900; Sales Return ₹ 4,700; Machinery ₹ 12,000; Wages ₹ 45,000; Sales ₹ 1,47,200; Purchases Return ₹ 3,900; Capital ₹ 58,900; Closing Stock (31st March, 2019) ₹ 36,200.
Answer» From the following balances, prepare Final Accounts of M/s Raja & Sons for the year ended 31st March, 2019: Salary ₹ 5,400; Insurance ₹ 2,500; Cash ₹ 400; Purchases ₹ 84,170; Rent Received ₹ 3,150; Drawings ₹ 2,100; Bills Payable ₹ 3,900; Debtors ₹ 38,080; Stock (1st April, 2018) ₹ 29,500; Bank Overdraft ₹ 9,700; Carriage ₹ 2,200; Creditors ₹ 4,200; Trade Expenses ₹ 4,900; Sales Return ₹ 4,700; Machinery ₹ 12,000; Wages ₹ 45,000; Sales ₹ 1,47,200; Purchases Return ₹ 3,900; Capital ₹ 58,900; Closing Stock (31st March, 2019) ₹ 36,200.

Discussion

5190.	Find five rational numbers between 35 and 45.
Answer» Find five rational numbers between $\frac{3}{5} a n d \frac{4}{5}$ .

Discussion

5191.	The lateral surface area of a triangular prism having base as equilateral triangle of side 3cm and height 10 cm will be equal to
Answer» The lateral surface area of a triangular prism having base as equilateral triangle of side 3cm and height 10 cm will be equal to

Discussion

5192.	Question 8Using converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
Answer» Question 8 Using converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Discussion

5193.	Question 9 (i)In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:ΔAPD≅ΔCQB
Answer» Question 9 (i) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: $Δ A P D ≅ Δ C Q B$

Discussion

5194.	Ellie was giving a treat to herself after her maths exam. She divided a pizza into 6 equal parts about the center.She ate a slice of pizza.Comment on the part of pizza yet to be eaten in terms of angle.
Answer» Ellie was giving a treat to herself after her maths exam. She divided a pizza into $6$ equal parts about the center. She ate a slice of pizza. Comment on the part of pizza yet to be eaten in terms of angle.

Discussion

5195.	In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB=OD. If AB=CD, then show that 1. ar(DOC)=ar(AOB) 2. ar(DCB)=ar(ACB) 3. DA\|\|CD or ABCD is a parallelogram.
Answer» In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB=OD. If AB=CD, then show that 1. ar(DOC)=ar(AOB) 2. ar(DCB)=ar(ACB) 3. DA\|\|CD or ABCD is a parallelogram.

Discussion

5196.	If V is the volume of a cuboid of dimensions a,b,c and S is its surface ara then prove that1V=2S(1a+1b+1c).
Answer» $If V is the volume of a cuboid of dimensions a,b,c and S is its surface ara then prove that \frac{1}{V} = \frac{2}{S} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) .$

Discussion

5197.	Question 13D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2+BD2=AB2+DE2.
Answer» Question 13 D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $A E^{2} + B D^{2} = A B^{2} + D E^{2}$ .

Discussion

5198.	If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is(a) 1 : 2(b) 1 : 4(c) 1 : 8(d) 1 : 16
Answer» If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is (a) 1 : 2 (b) 1 : 4 (c) 1 : 8 (d) 1 : 16

Discussion

5199.	If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral ?
Answer» If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral ?

Discussion

5200.	Question 03.Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table:No.of spokes4681012Angle between a pair of consecutive spokes90∘60∘………(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40∘ ?
Answer» Question 03. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table: $\begin{matrix} N o . o f s p o k e s & 4 & 6 & 8 & 10 & 12 A n g l e b e t w e e n a p a i r o f c o n s e c u t i v e s p o k e s & 90^{\circ} & 60^{\circ} & \dots & \dots & \dots \end{matrix}$ (i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion? (ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. (iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is $40^{\circ}$ ?

Discussion

Explore topic-wise InterviewSolutions in .

A solid triangular prism with equilateral base is 5 centimetres high and its base perimeter is 12 centimetres. Find its surface area.

What is the value of tan θ in the given triangle?

Look at several examples of rational numbers in the form pq (q ≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

fourth root of 193-4\sqrt{2178} is

In an equilateral triangle, the sides are ___

Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that □ABCD is a rhombus.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and takes two hours longer to cover the distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.

Given the point(3, 7), find the equation of a line on which it lies

Factorisex²+1/x²+2-2x-2/x

If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

The value of √2+3√2+5√3

The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m3 is_____.

In a rectangle ABCD, AB=20cm, ∠BAC=60∘, Then side BC=

If I=[1001] and E=[0100], then (aI+bE)3=

If( ​​​​​​a2+1)/a =4 find the value of 2a3 + 2/a3

The height h of a cylinder equals the circumference of the cylinder. In terms of h what is the volume of the cylinder?

Question 90(ii)Look at the histogram below and answer the questions that follow. ?Which class interval has the least numebr of students ?

INSERT 2 irrational numbers between 2.3 AND 3.7

If (4+√13)×(5−√13)×(7−√13)= 6x, then find x. 6

In the following figure, if OQ is angle bisector of ∠POA, then ∠POQ will be equal to ___.

Rationalize the denominator of :1(√7−√6) .

An iron spherical ball of radius 21 cm is melted and re-casted in spheres of radius 7 cm. The number of spheres formed will be ___

Question 11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ

The factors of polynomial p(x)=x2+2x+1 are x + a and x + b. Find the value of a + b.2

Is a perpendicular bisector a line or a line segment? __

If x=12 is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.

Find the point on 5x - 3y = 4 where the ordinate is equal to the abscissa

If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

Two numbers x and y (x y) are selected from the set of first 50 natural numbers. The number of ways of selectingthem such that 53.) xsquare-ysquare is divisible by 5 is(A) 470(C) 280(B) 425(D) 140 Q 54. x power4- ypower4 is divisible by 5 is(A) 470(C) 835(B) 235(D) 825

The height of a solid cone is 12 cm and the area of the circular base is 64 \lbrack 22/7\}cm 2 . A planeparallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is

Find the lateral surface area and total surface area of a cube of edge 10 cm.

A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?

Question 12In the given question, out of four options, only one is correct. Write the correct answer.If x + y + z = 6 and z is an odd digit, then the three- digit number xyz is (a) an odd multiple of 3(b) an odd multiple of 6(c) an even multiple of 3(d) an even multiple of 9

The length of a chord which is at a distance of 5 cm from the centre a circle of radius 13 cm is

What is the difference between zero polynomial and zeroes of the polynomial

The polar form of (i25)3 is ____________.

Find five rational numbers between 35 and 45.

The lateral surface area of a triangular prism having base as equilateral triangle of side 3cm and height 10 cm will be equal to

Question 8Using converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Question 9 (i)In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:ΔAPD≅ΔCQB

Ellie was giving a treat to herself after her maths exam. She divided a pizza into 6 equal parts about the center.She ate a slice of pizza.Comment on the part of pizza yet to be eaten in terms of angle.

In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB=OD. If AB=CD, then show that 1. ar(DOC)=ar(AOB) 2. ar(DCB)=ar(ACB) 3. DA||CD or ABCD is a parallelogram.

If V is the volume of a cuboid of dimensions a,b,c and S is its surface ara then prove that1V=2S(1a+1b+1c).

Question 13D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2+BD2=AB2+DE2.

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is(a) 1 : 2(b) 1 : 4(c) 1 : 8(d) 1 : 16

If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral ?

If( a2+1)/a =4 find the value of 2a3 + 2/a3