25365 + Interview Questions in Mathematics Page 73 InterviewSolution

3601.	Factorise:(i) 4a2−25 (ii) x2−916 (iii) x4−y4 (iv) [7310]2−[2110]2 (v) (0.7)2−(0.3)2 (vi) (5a−2b)2−(2a−b)2
Answer» Factorise: (i) $4 a^{2} - 25$ (ii) $x^{2} - \frac{9}{16}$ (iii) $x^{4} - y^{4}$ (iv) $[7 \frac{3}{10}]^{2} - [2 \frac{1}{10}]^{2}$ (v) $(0.7)^{2} - (0.3)^{2}$ (vi) $(5 a - 2 b)^{2} - (2 a - b)^{2}$

3601.

Factorise:(i) 4a2−25 (ii) x2−916 (iii) x4−y4 (iv) [7310]2−[2110]2 (v) (0.7)2−(0.3)2 (vi) (5a−2b)2−(2a−b)2

Answer»

Factorise:

(i) $4 a^{2} - 25$ (ii) $x^{2} - \frac{9}{16}$ (iii) $x^{4} - y^{4}$ (iv) $[7 \frac{3}{10}]^{2} - [2 \frac{1}{10}]^{2}$ (v) $(0.7)^{2} - (0.3)^{2}$ (vi) $(5 a - 2 b)^{2} - (2 a - b)^{2}$

Discussion

3602.	What is the smallest 6 digit no. which is a perfect square? How to find it using long division method? (WITH FULL STEPS)
Answer» What is the smallest 6 digit no. which is a perfect square? How to find it using long division method? (WITH FULL STEPS)

Discussion

3603.	444^{666 }+ 666^{444 } find the last digit
Answer» 444^{666 }+ 666^{444 } find the last digit

Discussion

3604.	Multiplying 4 and the number 'AA', we get the result as 2A4. The value of A is .
Answer» Multiplying 4 and the number 'AA', we get the result as 2A4. The value of A is .

Discussion

3605.	24. According to Kepler's third law T square is proportional to R cube here the proportionality constant is K. If mass of sun and a planet is M and m respectively. Then the relation between gravitational constant G and K is
Answer» 24. According to Kepler's third law T square is proportional to R cube here the proportionality constant is K. If mass of sun and a planet is M and m respectively. Then the relation between gravitational constant G and K is

Discussion

3606.	If two triangles are congruent, the number of pairs of corresponding parts is ___
Answer» If two triangles are congruent, the number of pairs of corresponding parts is ___

Discussion

3607.	Q. A huge urn with a capacity of 100 litres, contains 35 litres of black tea (without milk). If a person filled the remainder of the urn with tea containing 40% milk b/v, what would be the overall milk content (b/v) in the urn now?Q. 100 लीटर की क्षमता वाले एक विशाल पात्र में 35 लीटर काली चाय (दूध के बिना) है। यदि एक व्यक्ति ने पात्र के शेष भाग को 40% दूध (b/v) वाली चाय से भर दिया, तो अब पात्र में दूध की कुल मात्रा (b/v) क्या होगी?
Answer» Q. A huge urn with a capacity of 100 litres, contains 35 litres of black tea (without milk). If a person filled the remainder of the urn with tea containing $40 %$ milk b/v, what would be the overall milk content (b/v) in the urn now? Q. 100 लीटर की क्षमता वाले एक विशाल पात्र में 35 लीटर काली चाय (दूध के बिना) है। यदि एक व्यक्ति ने पात्र के शेष भाग को $40 %$ दूध (b/v) वाली चाय से भर दिया, तो अब पात्र में दूध की कुल मात्रा (b/v) क्या होगी?

3607.

Q. A huge urn with a capacity of 100 litres, contains 35 litres of black tea (without milk). If a person filled the remainder of the urn with tea containing 40% milk b/v, what would be the overall milk content (b/v) in the urn now?Q. 100 लीटर की क्षमता वाले एक विशाल पात्र में 35 लीटर काली चाय (दूध के बिना) है। यदि एक व्यक्ति ने पात्र के शेष भाग को 40% दूध (b/v) वाली चाय से भर दिया, तो अब पात्र में दूध की कुल मात्रा (b/v) क्या होगी?

Answer»

Q. A huge urn with a capacity of 100 litres, contains 35 litres of black tea (without milk). If a person filled the remainder of the urn with tea containing $40 %$ milk b/v, what would be the overall milk content (b/v) in the urn now?

Q. 100 लीटर की क्षमता वाले एक विशाल पात्र में 35 लीटर काली चाय (दूध के बिना) है। यदि एक व्यक्ति ने पात्र के शेष भाग को $40 %$ दूध (b/v) वाली चाय से भर दिया, तो अब पात्र में दूध की कुल मात्रा (b/v) क्या होगी?

Discussion

3608.	52. If V is the volume of cuboid, S is its total surface area and a,b,c are its edges then prove that 1/V=2/5 (1/a + + 1/b+ 1/c)
Answer» 52. If V is the volume of cuboid, S is its total surface area and a,b,c are its edges then prove that 1/V=2/5 (1/a + + 1/b+ 1/c)

Discussion

3609.	AB+ AB+ B BB A=___;B=___
Answer» $\begin{matrix} A B + A B + B B B \end{matrix}$ A=___;B=___

Discussion

3610.	The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2. The length of the longest edge is(a) 12 cm(b) 6 cm(c) 18 cm(d) 3 cm
Answer» The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm³ and the total surface area is 252 cm². The length of the longest edge is (a) 12 cm (b) 6 cm (c) 18 cm (d) 3 cm

Discussion

3611.	Which of the following equation(s) is/are linear equation(s) in one variable?
Answer» Which of the following equation(s) is/are linear equation(s) in one variable?

Discussion

3612.	The interior angle of a polygon Are in ap.if the smallest angle be 120 ans the common difference be 5 then find the number of sides
Answer» The interior angle of a polygon Are in ap.if the smallest angle be 120 ans the common difference be 5 then find the number of sides

Discussion

3613.	Solve 2kq/a+2k(-q)/astep by step
Answer» Solve 2kq/a+2k(-q)/astep by step

Discussion

3614.	Using the digits 4, 5, 6, 7, 8, each once, construct a 5-digit number which is divisible by 132.
Answer» Using the digits 4, 5, 6, 7, 8, each once, construct a 5-digit number which is divisible by 132.

Discussion

3615.	Test the divisibility of each of the following numers by 5:(i) 95(ii) 470(iii) 1056(iv) 2735(v) 55053(vi) 35790(vii) 98765(viii) 42658(ix) 77990
Answer» Test the divisibility of each of the following numers by 5: (i) 95 (ii) 470 (iii) 1056 (iv) 2735 (v) 55053 (vi) 35790 (vii) 98765 (viii) 42658 (ix) 77990

Discussion

3616.	Evaluate the following products without multiplying directly:(i) 100 × 107 (ii) 95 × 96(iii) 104 × 96
Answer» Evaluate the following products without multiplying directly: (i) 100 $\times$ 107 (ii) 95 $\times$ 96 (iii) 104 $\times$ 96

Discussion

3617.	Question 95 (ii)Look at the map given below and answer the following question. What is the address of the stadium?
Answer» Question 95 (ii) Look at the map given below and answer the following question. What is the address of the stadium?

Discussion

3618.	The value of a machine depreciates every year by 20%. If the present value of the machine be Rs. 160000, what was its value last year ?
Answer» The value of a machine depreciates every year by 20 $%$ . If the present value of the machine be Rs. 160000, what was its value last year ?

Discussion

3619.	Question 3 (v)Find the square root of the following decimal numbers:31.36
Answer» Question 3 (v) Find the square root of the following decimal numbers: 31.36

3619.

Question 3 (v)Find the square root of the following decimal numbers:31.36

Answer»

Question 3 (v)

Find the square root of the following decimal numbers:

31.36

Discussion

3620.	The common factor method of factorization for a polynomial is based on ___ property.
Answer» The common factor method of factorization for a polynomial is based on ___ property.

Discussion

3621.	Question 4 (v)Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Answer» Question 4 (v) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Discussion

3622.	Question 2 Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) 57 and 67 (iv) 14 and 15 Thinking process Use the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x<y and n =3
Answer» Question 2 Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) $\frac{5}{7}$ and $\frac{6}{7}$ (iv) $\frac{1}{4}$ and $\frac{1}{5}$ Thinking process Use the concept that three numbers between x and y are x+d, x+2d and x+3d , where $d = \frac{y - x}{n + 1}, x < y$ and n =3

Discussion

3623.	Bittu tells Kitty " I have 5 chocolates more than 7 times the number of chocolates you have”, if Kitty has 5 chocolates, how many chocolates does Bittu have ?
Answer» Bittu tells Kitty " I have 5 chocolates more than 7 times the number of chocolates you have”, if Kitty has 5 chocolates, how many chocolates does Bittu have ?

Discussion

3624.	The given cube is made up of several small cubes of side 1 cm. How many small cubes are used to make the given cube?
Answer» The given cube is made up of several small cubes of side 1 cm. How many small cubes are used to make the given cube?

Discussion

3625.	Total cost of fencing the park given in the figure is ₹55,000. Find the cost of fencing per meter.
Answer» Total cost of fencing the park given in the figure is ₹55,000. Find the cost of fencing per meter.

Discussion

3626.	Find the height of a cuboid whose volume is 684 m3 and base area is 36 m2.
Answer» Find the height of a cuboid whose volume is 684 $m^{3}$ and base area is 36 $m^{2}$ .

Discussion

3627.	(a) What is the additive inverse of 0?(b) What is the multiplicative inverse of 1?(c) Which integers have their own multiplicative inverses?
Answer» $(a)$ What is the additive inverse of $0$ ? $(b)$ What is the multiplicative inverse of $1$ ? $(c)$ Which integers have their own multiplicative inverses?

3627.

(a) What is the additive inverse of 0?(b) What is the multiplicative inverse of 1?(c) Which integers have their own multiplicative inverses?

Answer»

$(a)$ What is the additive inverse of $0$ ?

$(b)$ What is the multiplicative inverse of $1$ ?

$(c)$ Which integers have their own multiplicative inverses?

Discussion

3628.	Question 7Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.
Answer» Question 7 Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.

Discussion

3629.	In the given figure, ABCD is a cyclic quadrilateral. What is the value of x∘50∘?
Answer» In the given figure, ABCD is a cyclic quadrilateral. What is the value of $\frac{x^{\circ}}{50^{\circ}}$ ?

Discussion

3630.	Find the point of intersection of the straight-lines 3y + 4x = 7 and 4y + 3x = 7, by drawing their graphs and looking for the point where they meet.
Answer» Find the point of intersection of the straight-lines 3y + 4x = 7 and 4y + 3x = 7, by drawing their graphs and looking for the point where they meet.

Discussion

3631.	Question 156 A playground is in the form of a rectangle ATEF. Two players are standing at the point F and B, where EF = EB. Find the values of x and y.
Answer» Question 156 A playground is in the form of a rectangle ATEF. Two players are standing at the point F and B, where EF = EB. Find the values of x and y.

Discussion

3632.	a number when divided by a divisor leaves a remainder of 5 and when divided by twice the divisor leaves remainder 45 . find the divisor.
Answer» a number when divided by a divisor leaves a remainder of 5 and when divided by twice the divisor leaves remainder 45 . find the divisor.

Discussion

3633.	The quantity of fruits sold by a fruit vendor are listed below. Represent this data in the form of a pie-chart.
Answer» The quantity of fruits sold by a fruit vendor are listed below. Represent this data in the form of a pie-chart.

Discussion

3634.	(i) Contrast the Chinese view of art with the European view, with examples.(ii) Explain the concept of shanshui.
Answer» (i) Contrast the Chinese view of art with the European view, with examples. (ii) Explain the concept of shanshui.

3634.

(i) Contrast the Chinese view of art with the European view, with examples.(ii) Explain the concept of shanshui.

Answer»

(i) Contrast the Chinese view of art with the European view, with examples.

(ii) Explain the concept of shanshui.

Discussion

3635.	Find the angle which is equal to its supplement.
Answer» Find the angle which is equal to its supplement.

Discussion

3636.

Consider the following frequency distribution: Class interval : 5 – 10 10 – 15 15 – 25 25 – 45 45 – 75 Frequency : 6 12 10 8 15 To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-45 is(a) 6(b) 5(c) 3(d) 2

Answer» Consider the following frequency distribution:

Class interval :	5 – 10	10 – 15	15 – 25	25 – 45	45 – 75
Frequency :	6	12	10	8	15

To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-45 is

(a) 6

(b) 5

(c) 3

(d) 2

Discussion

3637.	Question 23Two quantities are said to vary___with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
Answer» Question 23 Two quantities are said to vary___with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

3637.

Question 23Two quantities are said to vary___with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Answer»

Question 23

Two quantities are said to vary___with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Discussion

3638.	The perimeter of a square is numerically equal to its area. Find its area
Answer» The perimeter of a square is numerically equal to its area. Find its area

Discussion

3639.	Question 4 For which of the following, diagonals are perpendicular to each other? a) Parallelogram b) Kite c) Trapezium d) Rectangle
Answer» Question 4 For which of the following, diagonals are perpendicular to each other? a) Parallelogram b) Kite c) Trapezium d) Rectangle

Discussion

3640.	If a=3p and b=4p,then find the expansion of (a+b)2+(a−b)2.
Answer» $If a = 3 p and b = 4 p,$ $then find the expansion of$ $(a + b)^{2} + (a - b)^{2} .$

Discussion

3641.	The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ⋃ C′ is equal to(a) B ∩ C′(b) A ∩ C(c) B ∪ C′(d) A ∩ C′
Answer» The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ⋃ C′ is equal to (a) B ∩ C′ (b) A ∩ C (c) B ∪ C′ (d) A ∩ C′

Discussion

3642.	Question 111(ii)At a birthday party, the children spin a wheel to get a gift.Find the probability of Getting a toy car ?
Answer» Question 111(ii) At a birthday party, the children spin a wheel to get a gift. Find the probability of Getting a toy car ?

3642.

Question 111(ii)At a birthday party, the children spin a wheel to get a gift.Find the probability of Getting a toy car ?

Answer»

Question 111(ii)

At a birthday party, the children spin a wheel to get a gift.

Find the probability of Getting a toy car ?

Discussion

3643.	Find x :-(1/√12-1/√15)/(1/√12+1/√15) × (9+4√5)/x=0.25
Answer» Find x :- (1/√12-1/√15)/(1/√12+1/√15) × (9+4√5)/x=0.25

Discussion

3644.	If there are 54 diagonals in a regular polygon, what is the value of its smallest interior angle?
Answer» If there are 54 diagonals in a regular polygon, what is the value of its smallest interior angle?

Discussion

3645.	A number exceeds 20% of itself by 40. The number is??
Answer» A number exceeds 20% of itself by 40. The number is??

Discussion

3646.	If x=2+√3, then the value of x3+1x3 is52
Answer» If $x = 2 + \sqrt{3}$ , then the value of $x^{3} + \frac{1}{x^{3}}$ is 52

Discussion

3647.	62.Draw the graphs of y=x and y=-x in the same graph. Also, find the coordinates of a point where the two line intersect.
Answer» 62.Draw the graphs of y=x and y=-x in the same graph. Also, find the coordinates of a point where the two line intersect.

Discussion

3648.	Question 36The volume of a cylinder which exactly fits in a cube of side a is ___.
Answer» Question 36 The volume of a cylinder which exactly fits in a cube of side a is ___.

3648.

Question 36The volume of a cylinder which exactly fits in a cube of side a is ___.

Answer»

Question 36

The volume of a cylinder which exactly fits in a cube of side a is ___.

Discussion

3649.	A cuboid whose length, breadth and height are equal is called a ___.
Answer» A cuboid whose length, breadth and height are equal is called a ___.

Discussion

3650.	From a pack of 100 cards numbered 1 to 100, a card is choosen at random. Then the probability that the number obtained on the card is divisible by 4 or 5 is
Answer» From a pack of $100$ cards numbered $1$ to $100,$ a card is choosen at random. Then the probability that the number obtained on the card is divisible by $4$ or $5$ is

Discussion

Explore topic-wise InterviewSolutions in .

Factorise:(i) 4a2−25 (ii) x2−916 (iii) x4−y4 (iv) [7310]2−[2110]2 (v) (0.7)2−(0.3)2 (vi) (5a−2b)2−(2a−b)2

What is the smallest 6 digit no. which is a perfect square? How to find it using long division method? (WITH FULL STEPS)

444^{666 }+ 666^{444 } find the last digit

Multiplying 4 and the number 'AA', we get the result as 2A4. The value of A is .

24. According to Kepler's third law T square is proportional to R cube here the proportionality constant is K. If mass of sun and a planet is M and m respectively. Then the relation between gravitational constant G and K is

If two triangles are congruent, the number of pairs of corresponding parts is ___

52. If V is the volume of cuboid, S is its total surface area and a,b,c are its edges then prove that 1/V=2/5 (1/a + + 1/b+ 1/c)

AB+ AB+ B BB A=___;B=___

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2. The length of the longest edge is(a) 12 cm(b) 6 cm(c) 18 cm(d) 3 cm

Which of the following equation(s) is/are linear equation(s) in one variable?

The interior angle of a polygon Are in ap.if the smallest angle be 120 ans the common difference be 5 then find the number of sides

Solve 2kq/a+2k(-q)/astep by step

Using the digits 4, 5, 6, 7, 8, each once, construct a 5-digit number which is divisible by 132.

Test the divisibility of each of the following numers by 5:(i) 95(ii) 470(iii) 1056(iv) 2735(v) 55053(vi) 35790(vii) 98765(viii) 42658(ix) 77990

Evaluate the following products without multiplying directly:(i) 100 × 107 (ii) 95 × 96(iii) 104 × 96

Question 95 (ii)Look at the map given below and answer the following question. What is the address of the stadium?

The value of a machine depreciates every year by 20%. If the present value of the machine be Rs. 160000, what was its value last year ?

Question 3 (v)Find the square root of the following decimal numbers:31.36

The common factor method of factorization for a polynomial is based on ___ property.

Question 2 Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) 57 and 67 (iv) 14 and 15 Thinking process Use the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x&lt;y and n =3

Bittu tells Kitty " I have 5 chocolates more than 7 times the number of chocolates you have”, if Kitty has 5 chocolates, how many chocolates does Bittu have ?

The given cube is made up of several small cubes of side 1 cm. How many small cubes are used to make the given cube?

Total cost of fencing the park given in the figure is ₹55,000. Find the cost of fencing per meter.

Find the height of a cuboid whose volume is 684 m3 and base area is 36 m2.

(a) What is the additive inverse of 0?(b) What is the multiplicative inverse of 1?(c) Which integers have their own multiplicative inverses?

Question 7Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.

In the given figure, ABCD is a cyclic quadrilateral. What is the value of x∘50∘?

Find the point of intersection of the straight-lines 3y + 4x = 7 and 4y + 3x = 7, by drawing their graphs and looking for the point where they meet.

Question 156 A playground is in the form of a rectangle ATEF. Two players are standing at the point F and B, where EF = EB. Find the values of x and y.

a number when divided by a divisor leaves a remainder of 5 and when divided by twice the divisor leaves remainder 45 . find the divisor.

The quantity of fruits sold by a fruit vendor are listed below. Represent this data in the form of a pie-chart.

(i) Contrast the Chinese view of art with the European view, with examples.(ii) Explain the concept of shanshui.

Find the angle which is equal to its supplement.

Consider the following frequency distribution: Class interval : 5 – 10 10 – 15 15 – 25 25 – 45 45 – 75 Frequency : 6 12 10 8 15 To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-45 is(a) 6(b) 5(c) 3(d) 2

Question 23Two quantities are said to vary___with each other, if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

The perimeter of a square is numerically equal to its area. Find its area

Question 4 For which of the following, diagonals are perpendicular to each other? a) Parallelogram b) Kite c) Trapezium d) Rectangle

If a=3p and b=4p,then find the expansion of (a+b)2+(a−b)2.

The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ⋃ C′ is equal to(a) B ∩ C′(b) A ∩ C(c) B ∪ C′(d) A ∩ C′

Question 111(ii)At a birthday party, the children spin a wheel to get a gift.Find the probability of Getting a toy car ?

Find x :-(1/√12-1/√15)/(1/√12+1/√15) × (9+4√5)/x=0.25

If there are 54 diagonals in a regular polygon, what is the value of its smallest interior angle?

A number exceeds 20% of itself by 40. The number is??

If x=2+√3, then the value of x3+1x3 is52

62.Draw the graphs of y=x and y=-x in the same graph. Also, find the coordinates of a point where the two line intersect.

Question 36The volume of a cylinder which exactly fits in a cube of side a is ___.

A cuboid whose length, breadth and height are equal is called a ___.

From a pack of 100 cards numbered 1 to 100, a card is choosen at random. Then the probability that the number obtained on the card is divisible by 4 or 5 is

AB+ AB+ B BB A=_;B=_

Question 2 Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) 57 and 67 (iv) 14 and 15 Thinking process Use the concept that three numbers between x and y are x+d, x+2d and x+3d , where d=y−xn+1,x<y and n =3