25365 + Interview Questions in Mathematics Page 61 InterviewSolution

3001.	Question 1(vi)Find the common factors of the terms16x3,−4x2,32x
Answer» Question 1(vi) Find the common factors of the terms $16 x^{3}, - 4 x^{2}, 32 x$

Discussion

3002.	Find the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.
Answer» Find the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.

Discussion

3003.	Solve for x: 8x+13x+2=2
Answer» $Solve for x:$ $\frac{8 x + 1}{3 x + 2} = 2$

Discussion

3004.	Question 27Amount when interest is compounded annually, is given by the formula ___
Answer» Question 27 Amount when interest is compounded annually, is given by the formula ___

3004.

Question 27Amount when interest is compounded annually, is given by the formula ___

Answer»

Question 27

Amount when interest is compounded annually, is given by the formula ___

Discussion

3005.	if x∧3-1/x∧3=14 then x-1/x
Answer» if x∧3-1/x∧3=14 then x-1/x

Discussion

3006.	Find the area of a rhombus having diagonals of length 10 cm and 20 cm.
Answer» Find the area of a rhombus having diagonals of length 10 cm and 20 cm.

Discussion

3007.	The adjacent figure PQRS is a trapezium in which SP∥RQ, find the measures of ∠P and ∠R. [2 MARKS]
Answer» The adjacent figure PQRS is a trapezium in which $S P ∥ R Q$ , find the measures of $∠ P$ and $∠ R$ . [2 MARKS]

Discussion

3008.	If a + b + c = 5 and ab + bc + ca = 10, then prove that a3+b3+c3−3abc=−25.
Answer» If a + b + c = 5 and ab + bc + ca = 10, then prove that $a^{3} + b^{3} + c^{3} - 3 a b c = - 25$ .

Discussion

3009.	Evaluate : 3√−1331
Answer» Evaluate : $\sqrt[3]{- 1331}$

Discussion

3010.	If (2x2−x−1)5=a0+a1x+a2x2..........a10x10 then a2+a4+a6+a8+a10 = __
Answer» If $(2 x^{2} - x - 1)^{5} = a_{0} + a_{1} x + a_{2} x^{2} . . . . . . . . . . a_{10} x^{10}$ then $a_{2} + a_{4} + a_{6} + a_{8} + a_{10}$ = __

Discussion

3011.	17. Two regular polygons are inscrived in same circle. The first polygon has 1982 sides and the second has 2973 sides. If the polygons have at least one common vertex then total no. Of common vertices of both polygons are A) 989 B) 1 C) 991 D) 992
Answer» 17. Two regular polygons are inscrived in same circle. The first polygon has 1982 sides and the second has 2973 sides. If the polygons have at least one common vertex then total no. Of common vertices of both polygons are A) 989 B) 1 C) 991 D) 992

Discussion

3012.	Ques 9f a^b=c,b^c=a d c^a=b Then find the value of a+b+c+ab+bc+ca=? Where a,b,c are anyreal no.
Answer» Ques 9f a^b=c,b^c=a d c^a=b Then find the value of a+b+c+ab+bc+ca=? Where a,b,c are anyreal no.

Discussion

3013.	Question 18Find and correct the errors in the statement: 3x3x+2=12
Answer» Question 18 Find and correct the errors in the statement: $\frac{3 x}{3 x + 2} = \frac{1}{2}$

Discussion

3014.	Question 110 (ii)A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50.For each method, calculate the amount Sheela would have to pay. Show your work.
Answer» Question 110 (ii) A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50. For each method, calculate the amount Sheela would have to pay. Show your work.

3014.

Question 110 (ii)A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50.For each method, calculate the amount Sheela would have to pay. Show your work.

Answer»

Question 110 (ii)

A store is having a 25% discount sale. Sheela has a Rs.50 gift voucher and wants to use it to buy a board game marked for Rs.320. She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable. Method 1 Subtract Rs.50 from the price and take 25% off the resulting price. Method 2 Take 25% off the original price and then subtract Rs.50.

For each method, calculate the amount Sheela would have to pay. Show your work.

Discussion

3015.	Question 7x=45(x+10)
Answer» Question 7 $x = \frac{4}{5} (x + 10)$

Discussion

3016.	What is vector sum? Explain it in detail?
Answer» What is vector sum? Explain it in detail?

Discussion

3017.	Proove that interior angle of a regular Pentagon is 3 times the exterior angle of decagon.
Answer» Proove that interior angle of a regular Pentagon is 3 times the exterior angle of decagon.

Discussion

3018.	Use appropriate formulae and compute:(i) (103)2; (ii) (96)2; (iii) 107 × 93; (iv) 1008 × 992; (v) 1852 − 1152.
Answer» Use appropriate formulae and compute: (i) (103)²; (ii) (96)²; (iii) 107 × 93; (iv) 1008 × 992; (v) 185² − 115².

3018.

Use appropriate formulae and compute:(i) (103)2; (ii) (96)2; (iii) 107 × 93; (iv) 1008 × 992; (v) 1852 − 1152.

Answer»

Use appropriate formulae and compute:

(i) (103)²; (ii) (96)²; (iii) 107 × 93; (iv) 1008 × 992; (v) 185² − 115².

Discussion

3019.	The two diagonals of a rhombus are 6 units and 8 units.The dimension of each side of the rhombus is units.
Answer» The two diagonals of a rhombus are 6 units and 8 units.The dimension of each side of the rhombus is units.

Discussion

3020.	Five workers take 12 days to weed a field. How many days would 6 workers take ? How many would 15 take ?
Answer» Five workers take 12 days to weed a field. How many days would 6 workers take ? How many would 15 take ?

Discussion

3021.	10^x=-10,then find the value of x?
Answer» 10^x=-10,then find the value of x?

Discussion

3022.	Arrange the following rational numbers in ascending order:−710,−58,−34
Answer» Arrange the following rational numbers in ascending order: $\frac{- 7}{10}, \frac{- 5}{8}, \frac{- 3}{4}$

Discussion

3023.	The value of (111)2 is
Answer» The value of $(111)^{2}$ is

Discussion

3024.	X2-4√5x+15. Factorise it. Explain it briefly
Answer» X²-4√5x+15. Factorise it. Explain it briefly

Discussion

3025.	In which year is the population the least?
Answer» In which year is the population the least?

3025.

In which year is the population the least?

Answer»

In which year is the population the least?

Discussion

3026.	Question 2 (b) Convert the following temperatures to the Kelvin scale. (b)373∘C.
Answer» Question 2 (b) Convert the following temperatures to the Kelvin scale. $(b) 373^{\circ} C$ .

Discussion

3027.	A tap can fill 100 L of water in half an hour. What fraction of a tank of 1000 L it can fill in 2.5 hours?
Answer» A tap can fill 100 L of water in half an hour. What fraction of a tank of 1000 L it can fill in 2.5 hours?

Discussion

3028.	Find the digit A B A×B 3 57A
Answer» Find the digit A $\begin{matrix} B A \times B 3 57 A \end{matrix}$

Discussion

3029.	Identify the corresponding sides and corresponding angles in the following congruent triangles:(a) (b)
Answer» Identify the corresponding sides and corresponding angles in the following congruent triangles: (a) (b)

3029.

Identify the corresponding sides and corresponding angles in the following congruent triangles:(a) (b)

Answer»

Identify the corresponding sides and corresponding angles in the following congruent triangles:

(a)

(b)

Discussion

3030.	A net of a cube contains ______ squares.
Answer» A net of a cube contains ______ squares.

Discussion

3031.	Question 85 The rational number 5723 lies to the left of zero on the number line.
Answer» Question 85 The rational number $\frac{57}{23}$ lies to the left of zero on the number line.

Discussion

3032.	Why we study number system?
Answer» Why we study number system?

Discussion

3033.	The reduced form of the algebraic expression is: 2(a2 − b2)(a + b) is ___
Answer» The reduced form of the algebraic expression is: $\frac{2 (a^{2} - b^{2})}{(a + b)}$ is ___

Discussion

3034.	Anupams takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes.
Answer» Anupams takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes.

Discussion

3035.	After 12 years, I shall be 3 times as old as I was 4 years ago. Find my present age.
Answer» After 12 years, I shall be 3 times as old as I was 4 years ago. Find my present age.

Discussion

3036.	Question 13 A rational number is such that when you multiply it by 52 and add 23 to the product, you get −712. What is the number?
Answer» Question 13 A rational number is such that when you multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product, you get $- \frac{7}{12}$ . What is the number?

Discussion

3037.	What should be added to 3xy−4a2+5b2+2 to get −5+4a2+2b2−7xy?
Answer» What should be added to $3 x y - 4 a^{2} + 5 b^{2} + 2$ to get $- 5 + 4 a^{2} + 2 b^{2} - 7 x y$ ?

Discussion

3038.	if 12p + 1 is the cube of a positive intiger , where p is a positive odd intiger , then find cube root of 12p + 1
Answer» if 12p + 1 is the cube of a positive intiger , where p is a positive odd intiger , then find cube root of 12p + 1

Discussion

3039.	if XY is the mirror, which among the given options is congruent to the following triangle ABC?
Answer» if XY is the mirror, which among the given options is congruent to the following triangle ABC?

3039.

if XY is the mirror, which among the given options is congruent to the following triangle ABC?

Answer»

if XY is the mirror, which among the given options is congruent to the following triangle ABC?

Discussion

3040.	Shishir is making a cube of side 6cm using cubes of side 2cm. How many such cubes are needed.
Answer» Shishir is making a cube of side 6cm using cubes of side 2cm. How many such cubes are needed.

Discussion

3041.	Find the total number of diagonals in a triangle.\N
Answer» Find the total number of diagonals in a triangle. \N

Discussion

3042.	ABC is a right triangle, right-angled at B. D and E trisect BC, prove that 8AE²=3AC²+5AD².
Answer» ABC is a right triangle, right-angled at B. D and E trisect BC, prove that 8AE²=3AC²+5AD².

Discussion

3043.	Let ABC be a triangle. Draw a triangle BDC externally on BC such that AB = BD and AC = CD. Prove that ΔABC ≅ ΔDBC.
Answer» Let ABC be a triangle. Draw a triangle BDC externally on BC such that AB = BD and AC = CD. Prove that ΔABC ≅ ΔDBC.

Discussion

3044.	The perimeter of a triangle is 36cm if the altitudes of the triangle are in the ratio of 1:2:3then find the lengths of the corresponding sides of the triangle
Answer» The perimeter of a triangle is 36cm if the altitudes of the triangle are in the ratio of 1:2:3then find the lengths of the corresponding sides of the triangle

Discussion

3045.	8. For any natural number n, expressed in base 10 , let S(n) denote the sum of all digits of n. Find all natural numbers n such that n cube= 8S(n) cube + 6nS(n) + 1.
Answer» 8. For any natural number n, expressed in base 10 , let S(n) denote the sum of all digits of n. Find all natural numbers n such that n cube= 8S(n) cube + 6nS(n) + 1.

Discussion

3046.	Solve (i) (3x + 24) / (2x + 7) = 2: (ii) (1 − 9y) / (11 − 3y) = (5/8).
Answer» Solve (i) (3x + 24) / (2x + 7) = 2: (ii) (1 − 9y) / (11 − 3y) = (5/8).

Discussion

3047.	If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Answer» If 3x − 2y = 11 and xy = 12, find the value of 27x³ − 8y³

Discussion

3048.	The sum of rational numbers from the list 17/5 ,16/5 ,16/5 ,14/5 ,13/5 ,11/5 ,12/4 ,11/4 ,9/4 ,8/4 ,6/4, 9/3 ,8/3 ,6/3 ,7/2 ,6/2, 5/2 ,4/2, -3, -5, -7 , -4/2 ,-3/2 ,-2/2 which are also integers ?
Answer» The sum of rational numbers from the list 17/5 ,16/5 ,16/5 ,14/5 ,13/5 ,11/5 ,12/4 ,11/4 ,9/4 ,8/4 ,6/4, 9/3 ,8/3 ,6/3 ,7/2 ,6/2, 5/2 ,4/2, -3, -5, -7 , -4/2 ,-3/2 ,-2/2 which are also integers ?

Discussion

3049.	Question 24In the given question, fill in the blanks to make the statement true.If 2 B+A8BA, then A = ___ and B = ___ .
Answer» Question 24 In the given question, fill in the blanks to make the statement true. If $2 B \frac{+ A}{8} \frac{B}{A}$ , then A = ___ and B = ___ .

Discussion

3050.	Name the property used in each of the following: 13+[49+(−43)]=[13+49]+[−43]
Answer» Name the property used in each of the following: $\frac{1}{3} + [\frac{4}{9} + (\frac{- 4}{3})] = [\frac{1}{3} + \frac{4}{9}] + [\frac{- 4}{3}]$

Discussion

Explore topic-wise InterviewSolutions in .

Question 1(vi)Find the common factors of the terms16x3,−4x2,32x

Find the CI paid when a sum of Rs 20,000 is invested for one year and six months at 5% per annum compounded annually.

Solve for x: 8x+13x+2=2

Question 27Amount when interest is compounded annually, is given by the formula ___

if x∧3-1/x∧3=14 then x-1/x

Find the area of a rhombus having diagonals of length 10 cm and 20 cm.

The adjacent figure PQRS is a trapezium in which SP∥RQ, find the measures of ∠P and ∠R. [2 MARKS]

If a + b + c = 5 and ab + bc + ca = 10, then prove that a3+b3+c3−3abc=−25.

Evaluate : 3√−1331

If (2x2−x−1)5=a0+a1x+a2x2..........a10x10 then a2+a4+a6+a8+a10 = __

17. Two regular polygons are inscrived in same circle. The first polygon has 1982 sides and the second has 2973 sides. If the polygons have at least one common vertex then total no. Of common vertices of both polygons are A) 989 B) 1 C) 991 D) 992

Ques 9f a^b=c,b^c=a d c^a=b Then find the value of a+b+c+ab+bc+ca=? Where a,b,c are anyreal no.

Question 18Find and correct the errors in the statement: 3x3x+2=12

Question 7x=45(x+10)

What is vector sum? Explain it in detail?

Proove that interior angle of a regular Pentagon is 3 times the exterior angle of decagon.

Use appropriate formulae and compute:(i) (103)2; (ii) (96)2; (iii) 107 × 93; (iv) 1008 × 992; (v) 1852 − 1152.

The two diagonals of a rhombus are 6 units and 8 units.The dimension of each side of the rhombus is units.

Five workers take 12 days to weed a field. How many days would 6 workers take ? How many would 15 take ?

10^x=-10,then find the value of x?

Arrange the following rational numbers in ascending order:−710,−58,−34

The value of (111)2 is

X​​​​​​2​​​​​-4√5x+15. Factorise it. Explain it briefly

In which year is the population the least?

Question 2 (b) Convert the following temperatures to the Kelvin scale. (b)373∘C.

A tap can fill 100 L of water in half an hour. What fraction of a tank of 1000 L it can fill in 2.5 hours?

Find the digit A B A×B 3 57A

Identify the corresponding sides and corresponding angles in the following congruent triangles:(a) (b)

A net of a cube contains ______ squares.

Question 85 The rational number 5723 lies to the left of zero on the number line.

Why we study number system?

The reduced form of the algebraic expression is: 2(a2 − b2)(a + b) is ___

Anupams takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes.

After 12 years, I shall be 3 times as old as I was 4 years ago. Find my present age.

Question 13 A rational number is such that when you multiply it by 52 and add 23 to the product, you get −712. What is the number?

What should be added to 3xy−4a2+5b2+2 to get −5+4a2+2b2−7xy?

if 12p + 1 is the cube of a positive intiger , where p is a positive odd intiger , then find cube root of 12p + 1

if XY is the mirror, which among the given options is congruent to the following triangle ABC?

Shishir is making a cube of side 6cm using cubes of side 2cm. How many such cubes are needed.

Find the total number of diagonals in a triangle.\N

ABC is a right triangle, right-angled at B. D and E trisect BC, prove that 8AE²=3AC²+5AD².

Let ABC be a triangle. Draw a triangle BDC externally on BC such that AB = BD and AC = CD. Prove that ΔABC ≅ ΔDBC.

The perimeter of a triangle is 36cm if the altitudes of the triangle are in the ratio of 1:2:3then find the lengths of the corresponding sides of the triangle

8. For any natural number n, expressed in base 10 , let S(n) denote the sum of all digits of n. Find all natural numbers n such that n cube= 8S(n) cube + 6nS(n) + 1.

Solve (i) (3x + 24) / (2x + 7) = 2: (ii) (1 − 9y) / (11 − 3y) = (5/8).

If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3

The sum of rational numbers from the list 17/5 ,16/5 ,16/5 ,14/5 ,13/5 ,11/5 ,12/4 ,11/4 ,9/4 ,8/4 ,6/4, 9/3 ,8/3 ,6/3 ,7/2 ,6/2, 5/2 ,4/2, -3, -5, -7 , -4/2 ,-3/2 ,-2/2 which are also integers ?

Question 24In the given question, fill in the blanks to make the statement true.If 2 B+A8BA, then A = ___ and B = ___ .

Name the property used in each of the following: 13+[49+(−43)]=[13+49]+[−43]

X2-4√5x+15. Factorise it. Explain it briefly

Question 24In the given question, fill in the blanks to make the statement true.If 2 B+A8BA, then A = _ and B = _ .