25365 + Interview Questions in Mathematics Page 114 InterviewSolution

5651.	In Fig. 7.142, if AB ⊥ BC, DC ⊥ BC and DE ⊥ AC, prove that ∆CED ~ ∆ABC.
Answer» In Fig. 7.142, if AB ⊥ BC, DC ⊥ BC and DE ⊥ AC, prove that ∆CED ~ ∆ABC.

Discussion

5652.	A water tank is 1.5 m long, 1 m wide and 0.6 m deep. Find the volume of the tank in litres.
Answer» A water tank is 1.5 m long, 1 m wide and 0.6 m deep. Find the volume of the tank in litres.

Discussion

5653.	Which of the following is not a polynomial? [1 mark]
Answer» Which of the following is not a polynomial? [1 mark]

Discussion

5654.	Jaya and Seema can together do a piece of work in 10 hours. Seema alone can do it in 15 hours. How long will Jaya take to do it alone? Answer: 30 hours
Answer» Jaya and Seema can together do a piece of work in 10 hours. Seema alone can do it in 15 hours. How long will Jaya take to do it alone? Answer: 30 hours

Discussion

5655.	If P = {x:x ∈ W and 4 ≤ x≤ 8}, and Q = {x:x ∈ N and x < 6}. Find : (i) P∪Q and P∩Q (ii) Is (P∪Q)⊃(P∩Q)
Answer» If P = ${x : x \in W a n d 4 \leq x \leq 8}$ , and Q = ${x : x \in N a n d x < 6}$ . Find : (i) $P \cup Q$ and $P \cap Q$ (ii) Is $(P \cup Q) \supset (P \cap Q)$

Discussion

5656.	Question 88 (i)Factorise the following expression.6ab+12bc
Answer» Question 88 (i) Factorise the following expression. $6 a b + 12 b c$

Discussion

5657.	In a hypothetical sample of 20 people the amounts of money with them were found to be as follows: 114,108,100,98,101,109,117,119,126,131,136,143,156,169,182,195,207,219,235,118. Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).
Answer» In a hypothetical sample of 20 people the amounts of money with them were found to be as follows: 114,108,100,98,101,109,117,119,126,131,136,143,156,169,182,195,207,219,235,118. Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).

Discussion

5658.	What is the difference between convex and concave polygons?
Answer» What is the difference between convex and concave polygons?

Discussion

5659.	(−57)−5 is equal to :
Answer» ${(- \frac{5}{7})}^{- 5}$ is equal to :

Discussion

5660.	A football team wins 7 games, which is 35% of the total games played. How many games were played in all ?
Answer» A football team wins 7 games, which is 35 $%$ of the total games played. How many games were played in all ?

Discussion

5661.	Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
Answer» Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

Discussion

5662.	Find the cost of 325 metres of cloth at Rs 6334 per metre.
Answer» Find the cost of $3 \frac{2}{5}$ metres of cloth at Rs $63 \frac{3}{4}$ per metre.

Discussion

5663.	Find the greatest common factors (GCF / HCF) of the following polynomials : 4a2b3,−12a3b,18a4b3
Answer» Find the greatest common factors (GCF / HCF) of the following polynomials : $4 a^{2} b^{3}, - 12 a^{3} b, 18 a^{4} b^{3}$

5663.

Find the greatest common factors (GCF / HCF) of the following polynomials : 4a2b3,−12a3b,18a4b3

Answer»

Find the greatest common factors (GCF / HCF) of the following polynomials :

$4 a^{2} b^{3}, - 12 a^{3} b, 18 a^{4} b^{3}$

Discussion

5664.	In what time will the interest on a certain sum of money at 7.5% simple interest be 34 of itself?
Answer» In what time will the interest on a certain sum of money at 7.5% simple interest be $\frac{3}{4}$ of itself?

Discussion

5665.	Mohan sells an article for ₹450 at a gain of 20%. Find its cost price.
Answer» Mohan sells an article for ₹450 at a gain of 20%. Find its cost price.

Discussion

5666.	State True or False.Lateral Surface area of the cube =6×side2
Answer» State True or False. Lateral Surface area of the cube $= 6 \times s i d e^{2}$

Discussion

5667.	Question 3Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Answer» Question 3 Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Discussion

5668.	Sarita purchases biscuits costing Rs. 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing Rs.354 on which the rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Answer» Sarita purchases biscuits costing Rs. 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing Rs.354 on which the rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.

Discussion

5669.	Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field, given that side AB is perpendicular to the parallel sides AD and BC.
Answer» Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field, given that side AB is perpendicular to the parallel sides AD and BC.

Discussion

5670.	Evaluate the following products without multiplying directly:(i) 103 × 107 (ii) 95 × 96(iii) 104 × 96
Answer» Evaluate the following products without multiplying directly: (i) 103 $\times$ 107 (ii) 95 $\times$ 96 (iii) 104 $\times$ 96

Discussion

5671.	Write difference between Trial Balance and Balance Sheet.
Answer» Write difference between Trial Balance and Balance Sheet.

Discussion

5672.	Fill in the blanks to make the statements true. (a) In right triangle the hypotenuse is the __________ side. (b) The sum of three altitudes of a triangle is __________ than its perimeter. (c) The sum of any two sides of a triangle is __________ than the third side. (d) If two angles of a triangle are unequal, then the smaller angle has the __________ side opposite to it. (e) Difference of any two sides of triangle is __________ than the third side. (f) If two sides of a triangle are unequal, then the larger side has ___________angle opposite to it.
Answer» Fill in the blanks to make the statements true. (a) In right triangle the hypotenuse is the __________ side. (b) The sum of three altitudes of a triangle is __________ than its perimeter. (c) The sum of any two sides of a triangle is __________ than the third side. (d) If two angles of a triangle are unequal, then the smaller angle has the __________ side opposite to it. (e) Difference of any two sides of triangle is __________ than the third side. (f) If two sides of a triangle are unequal, then the larger side has ___________angle opposite to it.

5672.

Fill in the blanks to make the statements true. (a) In right triangle the hypotenuse is the side. (b) The sum of three altitudes of a triangle is than its perimeter. (c) The sum of any two sides of a triangle is than the third side. (d) If two angles of a triangle are unequal, then the smaller angle has the side opposite to it. (e) Difference of any two sides of triangle is than the third side. (f) If two sides of a triangle are unequal, then the larger side has _angle opposite to it.

Answer»

Fill in the blanks to make the statements true.

(a) In right triangle the hypotenuse is the __________ side.

(b) The sum of three altitudes of a triangle is __________ than its perimeter.

(c) The sum of any two sides of a triangle is __________ than the third side.

(d) If two angles of a triangle are unequal, then the smaller angle has the __________ side opposite to it.

(e) Difference of any two sides of triangle is __________ than the third side.

(f) If two sides of a triangle are unequal, then the larger side has ___________angle opposite to it.

Discussion

5673.	The capacities of three oil tankers are in the ratio 6 : 5 : 9. The biggest of them can hold 2025 litres. How much can the smallest one hold?
Answer» The capacities of three oil tankers are in the ratio 6 : 5 : 9. The biggest of them can hold 2025 litres. How much can the smallest one hold?

5673.

The capacities of three oil tankers are in the ratio 6 : 5 : 9. The biggest of them can hold 2025 litres. How much can the smallest one hold?

Answer»

The capacities of three oil tankers are in the ratio 6 : 5 : 9. The biggest of them can hold 2025 litres.

How much can the smallest one hold?

Discussion

5674.	52 How to insert rational no between 11 and 19
Answer» 52 How to insert rational no between 11 and 19

Discussion

5675.	Suppose a triangle is equilateral. Prove that it is equiangular.
Answer» Suppose a triangle is equilateral. Prove that it is equiangular.

Discussion

5676.	What is parallel method
Answer» What is parallel method

Discussion

5677.	What is the area of the pentagon using either of the approaches?
Answer» What is the area of the pentagon using either of the approaches?

Discussion

5678.	Complete each of the following statements by means of one of those given in brackets against each:(i) If one pair of opposite sides are equal and parallel, then the figure is ........................(parallelogram, rectangle, trapezium)(ii) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................ (square, rectangle, trapezium)(iii) A line drawn from the mid-point of one side of a triangle .............. another side intersects the third side at its mid-point. (perpendicular to parallel to, to meet)(iv) If one angle of a parallelogram is a right angle, then it is necessarily a .................(rectangle, square, rhombus)(v) Consecutive angles of a parallelogram are ...................(supplementary, complementary)(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ...............(rectangle, parallelogram, rhombus)(vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ....................(parallelogram, rhombus, rectangle)(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a ..................(kite, rhombus, square)
Answer» Complete each of the following statements by means of one of those given in brackets against each: (i) If one pair of opposite sides are equal and parallel, then the figure is ........................ (parallelogram, rectangle, trapezium) (ii) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................ (square, rectangle, trapezium) (iii) A line drawn from the mid-point of one side of a triangle .............. another side intersects the third side at its mid-point. (perpendicular to parallel to, to meet) (iv) If one angle of a parallelogram is a right angle, then it is necessarily a ................. (rectangle, square, rhombus) (v) Consecutive angles of a parallelogram are ................... (supplementary, complementary) (vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ............... (rectangle, parallelogram, rhombus) (vii) If opposite angles of a quadrilateral are equal, then it is necessarily a .................... (parallelogram, rhombus, rectangle) (viii) If consecutive sides of a parallelogram are equal, then it is necessarily a .................. (kite, rhombus, square)

Discussion

5679.	Question 4(iv) Obtain the volume of rectangular boxes with the following length, breadth and height respectively: a,2b,3c
Answer» Question 4(iv) Obtain the volume of rectangular boxes with the following length, breadth and height respectively: a,2b,3c

Discussion

5680.	Types of identities
Answer» Types of identities

Discussion

5681.	11. Use the eculid division algorithm find the hcf of. 135 and 225
Answer» 11. Use the eculid division algorithm find the hcf of. 135 and 225

Discussion

5682.	What is the value of 3.2 x 10^2?
Answer» What is the value of 3.2 x 10^2?

Discussion

5683.	Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?
Answer» Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?

Discussion

5684.	If 23×24=2x, then x=
Answer» If $2^{3} \times 2^{4} = 2^{x}$ , then $x =$

Discussion

5685.	Show that:(9p−5q)2+180pq=(9p+5q)2
Answer» Show that: $(9 p - 5 q)^{2} + 180 p q = (9 p + 5 q)^{2}$

Discussion

5686.	Question 55Find the value of the letters in the following question: A 0 1 B+1 0 A B________ B 1 0 8
Answer» Question 55 Find the value of the letters in the following question: $A 01 B + 10 A B________B 108$

5686.

Question 55Find the value of the letters in the following question: A 0 1 B+1 0 A B________ B 1 0 8

Answer»

Question 55

Find the value of the letters in the following question:

$A 01 B + 10 A B________B 108$

Discussion

5687.	ABCD is a quadilateral in which AD=BC. E, F, G and H are the mid-points of AB, BD, CD, and AC respectively. Prove that EFGH is a rhombus
Answer» ABCD is a quadilateral in which AD=BC. E, F, G and H are the mid-points of AB, BD, CD, and AC respectively. Prove that EFGH is a rhombus

Discussion

5688.	A line that intersects with two or more lines at distinct points is known as a/an ______.
Answer» A line that intersects with two or more lines at distinct points is known as a/an ______.

Discussion

5689.	The length of the minute hand of a clock is 21 cm. What is the area swept by the minute hand between 3: 20 and 3: 40?
Answer» The length of the minute hand of a clock is 21 cm. What is the area swept by the minute hand between 3: 20 and 3: 40?

Discussion

5690.	The class interval with the highest frequency is
Answer» The class interval with the highest frequency is

5690.

The class interval with the highest frequency is

Answer»

The class interval with the highest frequency is

Discussion

5691.	How many rectangles does a 4×4 square has?
Answer» How many rectangles does a $4 \times 4$ square has?

Discussion

5692.	If the area of rectangle PQRS (green) is 21 cm2, AB = 7 cm and width of circular path is 1 cm, then find area of circular path(grey). (Take π = 3.14)
Answer» If the area of rectangle PQRS (green) is 21 $c m^{2}$ , AB = 7 cm and width of circular path is 1 cm, then find area of circular path(grey). (Take $π$ = 3.14)

Discussion

5693.	Calculate the total surface areas of cubes whose edges are(1) 8 cm(2) 12 cm(3) (4) 1.5 m
Answer» Calculate the total surface areas of cubes whose edges are (1) 8 cm (2) 12 cm (3) (4) 1.5 m

5693.

Calculate the total surface areas of cubes whose edges are(1) 8 cm(2) 12 cm(3) (4) 1.5 m

Answer»

Calculate the total surface areas of cubes whose edges are

(1) 8 cm

(2) 12 cm

(3)

(4) 1.5 m

Discussion

5694.	The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.
Answer» The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.

Discussion

5695.	The value of a and b for which the identity f(x) – f(x – 1) = 4x + 5 is satisfied, where f(x) = ax2 + bx + c, are
Answer» The value of a and b for which the identity f(x) – f(x – 1) = 4x + 5 is satisfied, where f(x) = ax2 + bx + c, are

Discussion

5696.	Solve the following equations and verify your answer : 3x+54x+2=3x+44x+7
Answer» Solve the following equations and verify your answer : $\frac{3 x + 5}{4 x + 2} = \frac{3 x + 4}{4 x + 7}$

5696.

Solve the following equations and verify your answer : 3x+54x+2=3x+44x+7

Answer»

Solve the following equations and verify your answer :

$\frac{3 x + 5}{4 x + 2} = \frac{3 x + 4}{4 x + 7}$

Discussion

5697.	1) x⁴-7x²+x³-x+6 2) a+b+c=19 ab+bc+ca=-13 Find (a+b+c)²3)3a² -4√3a+44) x³+13x²+32x+205) a⁸+3a⁴+46)a⁸-10a⁴+97)x⁵-x8)2x²+3y²+2√6xy-z²9)x²+4y²+9z²+6xz-4xy-12yz
Answer» 1) x⁴-7x²+x³-x+6 2) a+b+c=19 ab+bc+ca=-13 Find (a+b+c)² 3)3a² -4√3a+4 4) x³+13x²+32x+20 5) a⁸+3a⁴+4 6)a⁸-10a⁴+9 7)x⁵-x 8)2x²+3y²+2√6xy-z² 9)x²+4y²+9z²+6xz-4xy-12yz

Discussion

5698.	A road roller takes 850 complete resolution to move once over to level a road. Find the area of the road if the diameter of road roller is 84 cm and length is 1m.
Answer» A road roller takes 850 complete resolution to move once over to level a road. Find the area of the road if the diameter of road roller is 84 cm and length is 1m.

Discussion

5699.	The cirumference of any circle is exactly times its diameter.
Answer» The cirumference of any circle is exactly times its diameter.

Discussion

5700.	Compute the following difference (11.6×10.4)−(11.3×10.7)
Answer» Compute the following difference $(11.6 \times 10.4) - (11.3 \times 10.7)$

5700.

Compute the following difference (11.6×10.4)−(11.3×10.7)

Answer»

Compute the following difference

$(11.6 \times 10.4) - (11.3 \times 10.7)$

Discussion

Explore topic-wise InterviewSolutions in .

In Fig. 7.142, if AB ⊥ BC, DC ⊥ BC and DE ⊥ AC, prove that ∆CED ~ ∆ABC.

A water tank is 1.5 m long, 1 m wide and 0.6 m deep. Find the volume of the tank in litres.

Which of the following is not a polynomial? [1 mark]

Jaya and Seema can together do a piece of work in 10 hours. Seema alone can do it in 15 hours. How long will Jaya take to do it alone? Answer: 30 hours

If P = {x:x ∈ W and 4 ≤ x≤ 8}, and Q = {x:x ∈ N and x &lt; 6}. Find : (i) P∪Q and P∩Q (ii) Is (P∪Q)⊃(P∩Q)

Question 88 (i)Factorise the following expression.6ab+12bc

In a hypothetical sample of 20 people the amounts of money with them were found to be as follows: 114,108,100,98,101,109,117,119,126,131,136,143,156,169,182,195,207,219,235,118. Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).

What is the difference between convex and concave polygons?

(−57)−5 is equal to :

A football team wins 7 games, which is 35% of the total games played. How many games were played in all ?

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

Find the cost of 325 metres of cloth at Rs 6334 per metre.

Find the greatest common factors (GCF / HCF) of the following polynomials : 4a2b3,−12a3b,18a4b3

In what time will the interest on a certain sum of money at 7.5% simple interest be 34 of itself?

Mohan sells an article for ₹450 at a gain of 20%. Find its cost price.

State True or False.Lateral Surface area of the cube =6×side2

Question 3Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Sarita purchases biscuits costing Rs. 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing Rs.354 on which the rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.

Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field, given that side AB is perpendicular to the parallel sides AD and BC.

Evaluate the following products without multiplying directly:(i) 103 × 107 (ii) 95 × 96(iii) 104 × 96

Write difference between Trial Balance and Balance Sheet.

The capacities of three oil tankers are in the ratio 6 : 5 : 9. The biggest of them can hold 2025 litres. How much can the smallest one hold?

52 How to insert rational no between 11 and 19

Suppose a triangle is equilateral. Prove that it is equiangular.

What is parallel method

What is the area of the pentagon using either of the approaches?

Question 4(iv) Obtain the volume of rectangular boxes with the following length, breadth and height respectively: a,2b,3c

Types of identities

11. Use the eculid division algorithm find the hcf of. 135 and 225

What is the value of 3.2 x 10^2?

Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?

If 23×24=2x, then x=

Show that:(9p−5q)2+180pq=(9p+5q)2

Question 55Find the value of the letters in the following question: A 0 1 B+1 0 A B________ B 1 0 8

ABCD is a quadilateral in which AD=BC. E, F, G and H are the mid-points of AB, BD, CD, and AC respectively. Prove that EFGH is a rhombus

A line that intersects with two or more lines at distinct points is known as a/an ______.

The length of the minute hand of a clock is 21 cm. What is the area swept by the minute hand between 3: 20 and 3: 40?

The class interval with the highest frequency is

How many rectangles does a 4×4 square has?

If the area of rectangle PQRS (green) is 21 cm2, AB = 7 cm and width of circular path is 1 cm, then find area of circular path(grey). (Take π = 3.14)

Calculate the total surface areas of cubes whose edges are(1) 8 cm(2) 12 cm(3) (4) 1.5 m

The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, the sum of their ages will be 70 years. Find their present ages.

The value of a and b for which the identity f(x) – f(x – 1) = 4x + 5 is satisfied, where f(x) = ax2 + bx + c, are

Solve the following equations and verify your answer : 3x+54x+2=3x+44x+7

1) x⁴-7x²+x³-x+6 2) a+b+c=19 ab+bc+ca=-13 Find (a+b+c)²3)3a² -4√3a+44) x³+13x²+32x+205) a⁸+3a⁴+46)a⁸-10a⁴+97)x⁵-x8)2x²+3y²+2√6xy-z²9)x²+4y²+9z²+6xz-4xy-12yz

A road roller takes 850 complete resolution to move once over to level a road. Find the area of the road if the diameter of road roller is 84 cm and length is 1m.

The cirumference of any circle is exactly times its diameter.

Compute the following difference (11.6×10.4)−(11.3×10.7)

If P = {x:x ∈ W and 4 ≤ x≤ 8}, and Q = {x:x ∈ N and x < 6}. Find : (i) P∪Q and P∩Q (ii) Is (P∪Q)⊃(P∩Q)