19743 + Interview Questions in Mathematics Page 127 InterviewSolution

6301.	Simplify and write the expression in exponential form: 43 x 4−2 x 162
Answer» Simplify and write the expression in exponential form: $4^{3}$ x $4^{- 2}$ x $16^{2}$

Discussion

6302.	Solve the following problems.What sum will get an interest of Rs. 252 at the rate of 14% p.a in 3 years?
Answer» Solve the following problems. What sum will get an interest of Rs. 252 at the rate of 14% p.a in 3 years?

6302.

Solve the following problems.What sum will get an interest of Rs. 252 at the rate of 14% p.a in 3 years?

Answer»

Solve the following problems.

What sum will get an interest of Rs. 252 at the rate of 14% p.a in 3 years?

Discussion

6303.	1. If PQR is an equilateral Triangle inscribed in a circle and A be any point in minor arc RQ which does not coincide with R and Q . Prove that angle PAR = angle QAP= 60 degree
Answer» 1. If PQR is an equilateral Triangle inscribed in a circle and A be any point in minor arc RQ which does not coincide with R and Q . Prove that angle PAR = angle QAP= 60 degree

Discussion

6304.	Add: a+b−3,b−a+3,a−b+3
Answer» Add: $a + b - 3, b - a + 3, a - b + 3$

6304.

Add: a+b−3,b−a+3,a−b+3

Answer»

Add:

$a + b - 3, b - a + 3, a - b + 3$

Discussion

6305.	Question: In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, find PB
Answer» Question: In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, find PB

Discussion

6306.	Which of the following nets can be folded to make a cylinder?
Answer» Which of the following nets can be folded to make a cylinder?

Discussion

6307.	The volume of a cuboid is 3840 cm3 and the length of the cuboid is 20 cm. If the ratio of its breadth and its height is 4 : 3, then the total surface area of the cuboid is __________.
Answer» The volume of a cuboid is 3840 cm³ and the length of the cuboid is 20 cm. If the ratio of its breadth and its height is 4 : 3, then the total surface area of the cuboid is __________.

Discussion

6308.	Question 2One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II].
Answer» Question 2 One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II].

Discussion

6309.	Product of two negative integers is:
Answer» Product of two negative integers is:

Discussion

6310.	Solve the following equations:(i) 3x+1=27×34(ii) 42x=163-6y=82(iii) 3x-1×52y-3=225(iv) 8x+1=16y+2 and, 123+x=143y(v) 4x-1×0.53-2x=18x(vi) ab=ba1-2x, where a and b are distinct primes
Answer» Solve the following equations: (i) $3^{x + 1} = 27 \times 3^{4}$ (ii) $4^{2 x} = {(\sqrt[3]{16})}^{- \frac{6}{y}} = {(\sqrt{8})}^{2}$ (iii) $3^{x - 1} \times 5^{2 y - 3} = 225$ (iv) $8^{x + 1} = 16^{y + 2} and, {(\frac{1}{2})}^{3 + x} = {(\frac{1}{4})}^{3 y}$ (v) $4^{x - 1} \times {(0.5)}^{3 - 2 x} = {(\frac{1}{8})}^{x}$ (vi) $\sqrt{\frac{a}{b}} = {(\frac{b}{a})}^{1 - 2 x}$ , where a and b are distinct primes

Discussion

6311.	Question 6It is given that ΔABC≅ΔRPQ. It is true to say that BC = QR ? why?
Answer» Question 6 It is given that $Δ A B C ≅ Δ R P Q$ . It is true to say that BC = QR ? why?

Discussion

6312.	A boy walks at a steady speed of 5km/h . Find A) How much distance Will he walk in 1 hour 45 minutes at this rate? B) How much time will he take to walk a distance of 8 km?
Answer» A boy walks at a steady speed of $5 k m / h$ . Find A) How much distance Will he walk in $1$ hour $45$ minutes at this rate? B) How much time will he take to walk a distance of $8$ km?

Discussion

6313.	Question 8In ΔPQR,∠P=70∘ and ∠R=30∘ which side of this triangle is the longest? Give reason for your answer.
Answer» Question 8 In $Δ P Q R, ∠ P = 70^{\circ}$ and $∠ R = 30^{\circ}$ which side of this triangle is the longest? Give reason for your answer.

Discussion

6314.	ABCD isquadrilateral.Is AB + BC+ CD + DA >AC + BD?
Answer» ABCD is quadrilateral. Is AB + BC + CD + DA >AC + BD?

6314.

ABCD isquadrilateral.Is AB + BC+ CD + DA >AC + BD?

Answer»

ABCD is
quadrilateral.

Is AB + BC
+ CD + DA >AC + BD?

Discussion

6315.	44. Construct an angle of 127 1/2 and verify by measuring them by protactor
Answer» 44. Construct an angle of 127 1/2 and verify by measuring them by protactor

Discussion

6316.	47. Venn diagram of ((A union b) intersection c) whole complement
Answer» 47. Venn diagram of ((A union b) intersection c) whole complement

Discussion

6317.	Find thevalue of the unknown exterior angle x in the followingdiagrams:
Answer» Find the value of the unknown exterior angle x in the following diagrams:

6317.

Find thevalue of the unknown exterior angle x in the followingdiagrams:

Answer»

Find the
value of the unknown exterior angle x in the following
diagrams:

Discussion

6318.	If 1 kg of mangoes costs ₹ 36, what is the cost of 34 kg of mangoes?
Answer» If 1 kg of mangoes costs ₹ 36, what is the cost of $\frac{3}{4}$ kg of mangoes?

Discussion

6319.	What is 40% of 30% of 1000?
Answer» What is 40% of 30% of 1000?

Discussion

6320.	Once Tom answered the question to unlock the car, he hopped in and drove off to reach his destination – a building calledTheArchitecture.This building closelyresembles a Rubik’s Cube, in the sense that the “rooms” of The Architectureare like the “cubes” of the Rubik’s Cube, as shown: This building has 3 floors and each floor has 3 × 3 [read 3 by 3 – which means there are 3 rows and 3 columns] rooms which are all identical in size and shape.Tom stopped the car in front of the building.To enter this architecture, he should enterapasscodewhich is equal to the total number of rooms [cubes] in the building. What is the passcode that Tom has to enter? ______ [Enter a numerical value] ___
Answer» Once Tom answered the question to unlock the car, he hopped in and drove off to reach his destination – a building calledTheArchitecture.This building closelyresembles a Rubik’s Cube, in the sense that the “rooms” of The Architectureare like the “cubes” of the Rubik’s Cube, as shown: This building has 3 floors and each floor has 3 $\times$ 3 [read 3 by 3 – which means there are 3 rows and 3 columns] rooms which are all identical in size and shape.Tom stopped the car in front of the building.To enter this architecture, he should enterapasscodewhich is equal to the total number of rooms [cubes] in the building. What is the passcode that Tom has to enter? ______ [Enter a numerical value] ___

6320.

Once Tom answered the question to unlock the car, he hopped in and drove off to reach his destination – a building calledTheArchitecture.This building closelyresembles a Rubik’s Cube, in the sense that the “rooms” of The Architectureare like the “cubes” of the Rubik’s Cube, as shown: This building has 3 floors and each floor has 3 × 3 [read 3 by 3 – which means there are 3 rows and 3 columns] rooms which are all identical in size and shape.Tom stopped the car in front of the building.To enter this architecture, he should enterapasscodewhich is equal to the total number of rooms [cubes] in the building. What is the passcode that Tom has to enter? ____ [Enter a numerical value] _

Answer»

Once Tom answered the question to unlock the car, he hopped in and drove off to reach his destination – a building calledTheArchitecture.This building closelyresembles a Rubik’s Cube, in the sense that the “rooms” of The Architectureare like the “cubes” of the Rubik’s Cube, as shown:

This building has 3 floors and each floor has 3 $\times$ 3 [read 3 by 3 – which means there are 3 rows and 3 columns] rooms which are all identical in size and shape.Tom stopped the car in front of the building.To enter this architecture, he should enterapasscodewhich is equal to the total number of rooms [cubes] in the building.

What is the passcode that Tom has to enter? ______ [Enter a numerical value]

___

Discussion

6321.	What is the perimeter of a square of side 10 meters?
Answer» What is the perimeter of a square of side 10 meters?

Discussion

6322.	Use the formula to multiply the following.(i) (x + y) (x -y) (ii) (3x-5) (3x + 5) (iii) (a + 6) (a -6) (iv) x5 + 6 x5 - 6
Answer» Use the formula to multiply the following. (i) (x + y) (x $-$ y) (ii) (3x $-$ 5) (3x + 5) (iii) (a + 6) (a $-$ 6) (iv) $(\frac{x}{5} + 6) (\frac{x}{5} - 6)$

Discussion

6323.	Three cans contain 23.265 ml, 60.5 ml and 71.486 ml of kerosene. What should be the minimum capacity of a can that can hold the total quantity of kerosene rounded off to 2 decimal places?
Answer» Three cans contain 23.265 ml, 60.5 ml and 71.486 ml of kerosene. What should be the minimum capacity of a can that can hold the total quantity of kerosene rounded off to 2 decimal places?

Discussion

6324.	How many different (non-congruent) triangles can you draw with two sides 8 and 6 centimetres and area 12 square centimetres? What if the area is to be 24 square centimetres?
Answer» How many different (non-congruent) triangles can you draw with two sides 8 and 6 centimetres and area 12 square centimetres? What if the area is to be 24 square centimetres?

Discussion

6325.	In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Find the area of the big square in the second figure.
Answer» In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Find the area of the big square in the second figure.

6325.

In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Find the area of the big square in the second figure.

Answer»

In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Find the area of the big square in the second figure.

Discussion

6326.	Question 1(a) Following number line shows the temperature in degree Celsius (°C)at different places on a particular day. Observe this number line and write the temperature of the places marked on it.
Answer» Question 1(a) Following number line shows the temperature in degree Celsius (°C)at different places on a particular day. Observe this number line and write the temperature of the places marked on it.

Discussion

6327.	Question 3(iv) Say true or false and justify your answer: (iv) 30=(1000)0
Answer» Question 3(iv) Say true or false and justify your answer: (iv) $3^{0} = (1000)^{0}$

Discussion

6328.	At least number of unparallel straight lines are required to form a transversal.
Answer» At least number of unparallel straight lines are required to form a transversal.

Discussion

6329.	15×15×15×15 can be written as
Answer» $\frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} \times \frac{1}{5}$ can be written as

Discussion

6330.	The length and breadth of a rectangular field are in the ratio 5 : 3 and its perimeter is 480 m.The area of the field is(a) 7200 m2 (b) 13500 m2 (c) 15000 m2 (d) 54000 m2
Answer» The length and breadth of a rectangular field are in the ratio 5 : 3 and its perimeter is 480 m. The area of the field is (a) 7200 m² (b) 13500 m² (c) 15000 m² (d) 54000 m²

Discussion

6331.	David cuts a cake into two equal halves. He cuts one half into smaller pieces of equal size. Each of these small pieces weighs twenty grams. If he has seven pieces of the cake in total, how heavy is the original cake?
Answer» David cuts a cake into two equal halves. He cuts one half into smaller pieces of equal size. Each of these small pieces weighs twenty grams. If he has seven pieces of the cake in total, how heavy is the original cake?

Discussion

6332.	For positive integers m and n, let gcd(m, n) denote the largest integer that is a factorof both m and n. Compute gcd(1, 155) + gcd(2, 155) + + gcd(155, 155).
Answer» For positive integers m and n, let gcd(m, n) denote the largest integer that is a factorof both m and n. Compute gcd(1, 155) + gcd(2, 155) + + gcd(155, 155).

Discussion

6333.	Question 121 The flag of Japan is shown below. How many lines of symmetry does the flag have?
Answer» Question 121 The flag of Japan is shown below. How many lines of symmetry does the flag have?

6333.

Question 121 The flag of Japan is shown below. How many lines of symmetry does the flag have?

Answer»

Question 121
The flag of Japan is shown below. How many lines of symmetry does the flag have?

Discussion

6334.	Area and perimeter of a square of side 4 m _______.
Answer» Area and perimeter of a square of side 4 m _______.

Discussion

6335.	Draw a pie-chart representing the data in the above table.
Answer» Draw a pie-chart representing the data in the above table.

Discussion

6336.	Ram has x different physics books and Sandeep have y different mathematics books. Find the number of ways in which Ram and Sandeep can exchange their books in such a way that after exchanging they still have same number of books and same set.
Answer» Ram has x different physics books and Sandeep have y different mathematics books. Find the number of ways in which Ram and Sandeep can exchange their books in such a way that after exchanging they still have same number of books and same set.

Discussion

6337.	Calculate the area of a rectangle whose length and breadth are 16 cm and 6 cm respectively.
Answer» Calculate the area of a rectangle whose length and breadth are 16 cm and 6 cm respectively.

Discussion

6338.	Find the value of the letters in the following question: 8 A B C−A B C 5________ D 4 8 8
Answer» Find the value of the letters in the following question: $8 A B C - A B C 5________D 488$

Discussion

6339.

Which of the following double bar graphs represents the data where maximum and minimum temperature are recorded in a place in winter and summer respectively. (Take scale 1 unit = 5℃) Vizag Chennai Pune Delhi Summer 35℃ 40℃ 30℃ 45℃ Winter 25℃ 25℃ 10℃ 15℃

Answer» Which of the following double bar graphs represents the data where maximum and minimum temperature are recorded in a place in winter and summer respectively. (Take scale 1 unit = 5℃)

	Vizag	Chennai	Pune	Delhi
Summer	35℃	40℃	30℃	45℃
Winter	25℃	25℃	10℃	15℃

Discussion

6340.	If two lines l and m are parallel then it is denoted by:
Answer» If two lines l and m are parallel then it is denoted by:

Discussion

6341.	In a triangle, base is given and 2 adjacent angles are of more than 90 degrees. Is it possible to construct such a triangle?
Answer» In a triangle, base is given and 2 adjacent angles are of more than 90 degrees. Is it possible to construct such a triangle?

Discussion

6342.	Question 7 (iv)In the below figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that(iv) ΔPDC∼ΔBEC
Answer» Question 7 (iv) In the below figure, altitudes AD and CE of $Δ A B C$ intersect each other at the point P. Show that (iv) $Δ P D C \sim Δ B E C$

Discussion

6343.	AD and BE are altitudes of AABC such that AE = BD. Prove that AD = BE.
Answer» AD and BE are altitudes of AABC such that AE = BD. Prove that AD = BE.

Discussion

6344.	Study the double Bar Graph and state which sport is most famous among boys?
Answer» Study the double Bar Graph and state which sport is most famous among boys?

Discussion

6345.	Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = −4, c = 2 (b) a = (− 10), b = 1, c = 1
Answer» Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = −4, c = 2 (b) a = (− 10), b = 1, c = 1

6345.

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = −4, c = 2 (b) a = (− 10), b = 1, c = 1

Answer»

Verify
that a ÷ (b +
c) ≠ (a ÷
b) + (a ÷ c)
for each of the following values of a, b and c.

(a) a
= 12, b = −4, c = 2

(b) a
= (− 10), b = 1, c = 1

Discussion

6346.	H.C.F of 17, 34 and 51 is:
Answer» H.C.F of 17, 34 and 51 is:

Discussion

6347.	Express 5126000 in standard form.
Answer» Express 5126000 in standard form.

Discussion

6348.	Question 78 In the given figurel \|\| m \|\| n. ∠QPS=35∘and∠QRT=55∘. Find ∠PQR.
Answer» Question 78 In the given figure $l \| \| m \| \| n . ∠ Q P S = 35^{\circ} a n d ∠ Q R T = 55^{\circ} .$ Find $∠ P Q R$ .

6348.

Question 78 In the given figurel || m || n. ∠QPS=35∘and∠QRT=55∘. Find ∠PQR.

Answer»

Question 78

In the given figure $l | | m | | n . ∠ Q P S = 35^{\circ} a n d ∠ Q R T = 55^{\circ} .$ Find $∠ P Q R$ .

Discussion

6349.	A binomial expression is an expression which contains unlike terms in it after simplification.
Answer» A binomial expression is an expression which contains unlike terms in it after simplification.

Discussion

6350.	Which of the following illustrates the distributive property?
Answer» Which of the following illustrates the distributive property?

Discussion

Explore topic-wise InterviewSolutions in .

Simplify and write the expression in exponential form: 43 x 4−2 x 162

Solve the following problems.What sum will get an interest of Rs. 252 at the rate of 14% p.a in 3 years?

1. If PQR is an equilateral Triangle inscribed in a circle and A be any point in minor arc RQ which does not coincide with R and Q . Prove that angle PAR = angle QAP= 60 degree

Add: a+b−3,b−a+3,a−b+3

Question: In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, find PB

Which of the following nets can be folded to make a cylinder?

The volume of a cuboid is 3840 cm3 and the length of the cuboid is 20 cm. If the ratio of its breadth and its height is 4 : 3, then the total surface area of the cuboid is __________.

Question 2One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II].

Product of two negative integers is:

Solve the following equations:(i) 3x+1=27×34(ii) 42x=163-6y=82(iii) 3x-1×52y-3=225(iv) 8x+1=16y+2 and, 123+x=143y(v) 4x-1×0.53-2x=18x(vi) ab=ba1-2x, where a and b are distinct primes

Question 6It is given that ΔABC≅ΔRPQ. It is true to say that BC = QR ? why?

A boy walks at a steady speed of 5km/h . Find A) How much distance Will he walk in 1 hour 45 minutes at this rate? B) How much time will he take to walk a distance of 8 km?

Question 8In ΔPQR,∠P=70∘ and ∠R=30∘ which side of this triangle is the longest? Give reason for your answer.

ABCD isquadrilateral.Is AB + BC+ CD + DA &gt;AC + BD?

44. Construct an angle of 127 1/2 and verify by measuring them by protactor

47. Venn diagram of ((A union b) intersection c) whole complement

Find thevalue of the unknown exterior angle x in the followingdiagrams:

If 1 kg of mangoes costs ₹ 36, what is the cost of 34 kg of mangoes?

What is 40% of 30% of 1000?

What is the perimeter of a square of side 10 meters?

Use the formula to multiply the following.(i) (x + y) (x -y) (ii) (3x-5) (3x + 5) (iii) (a + 6) (a -6) (iv) x5 + 6 x5 - 6

Three cans contain 23.265 ml, 60.5 ml and 71.486 ml of kerosene. What should be the minimum capacity of a can that can hold the total quantity of kerosene rounded off to 2 decimal places?

How many different (non-congruent) triangles can you draw with two sides 8 and 6 centimetres and area 12 square centimetres? What if the area is to be 24 square centimetres?

In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Find the area of the big square in the second figure.

Question 1(a) Following number line shows the temperature in degree Celsius (°C)at different places on a particular day. Observe this number line and write the temperature of the places marked on it.

Question 3(iv) Say true or false and justify your answer: (iv) 30=(1000)0

At least number of unparallel straight lines are required to form a transversal.

15×15×15×15 can be written as

The length and breadth of a rectangular field are in the ratio 5 : 3 and its perimeter is 480 m.The area of the field is(a) 7200 m2 (b) 13500 m2 (c) 15000 m2 (d) 54000 m2

David cuts a cake into two equal halves. He cuts one half into smaller pieces of equal size. Each of these small pieces weighs twenty grams. If he has seven pieces of the cake in total, how heavy is the original cake?

For positive integers m and n, let gcd(m, n) denote the largest integer that is a factorof both m and n. Compute gcd(1, 155) + gcd(2, 155) + + gcd(155, 155).

Question 121 The flag of Japan is shown below. How many lines of symmetry does the flag have?

Area and perimeter of a square of side 4 m _______.

Draw a pie-chart representing the data in the above table.

Ram has x different physics books and Sandeep have y different mathematics books. Find the number of ways in which Ram and Sandeep can exchange their books in such a way that after exchanging they still have same number of books and same set.

Calculate the area of a rectangle whose length and breadth are 16 cm and 6 cm respectively.

Find the value of the letters in the following question: 8 A B C−A B C 5________ D 4 8 8

Which of the following double bar graphs represents the data where maximum and minimum temperature are recorded in a place in winter and summer respectively. (Take scale 1 unit = 5℃) Vizag Chennai Pune Delhi Summer 35℃ 40℃ 30℃ 45℃ Winter 25℃ 25℃ 10℃ 15℃

If two lines l and m are parallel then it is denoted by:

In a triangle, base is given and 2 adjacent angles are of more than 90 degrees. Is it possible to construct such a triangle?

Question 7 (iv)In the below figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that(iv) ΔPDC∼ΔBEC

AD and BE are altitudes of AABC such that AE = BD. Prove that AD = BE.

Study the double Bar Graph and state which sport is most famous among boys?

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = −4, c = 2 (b) a = (− 10), b = 1, c = 1

H.C.F of 17, 34 and 51 is:

Express 5126000 in standard form.

Question 78 In the given figurel || m || n. ∠QPS=35∘and∠QRT=55∘. Find ∠PQR.

A binomial expression is an expression which contains unlike terms in it after simplification.

Which of the following illustrates the distributive property?

ABCD isquadrilateral.Is AB + BC+ CD + DA >AC + BD?