25365 + Interview Questions in Mathematics Page 129 InterviewSolution

6401.	If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
Answer» If x + y + z = 8 and xy +yz +zx = 20, find the value of x³ + y³+ z³ −3xyz

Discussion

6402.	-12/30 in standard form
Answer» -12/30 in standard form

Discussion

6403.	(139)2−(138)2 =_____ (139+138)
Answer» $(139)^{2} - (138)^{2}$ =_____ $(139 + 138)$

Discussion

6404.	Question 166Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
Answer» Question 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Discussion

6405.	What is the coordinate of the point if y=4x and y=–x?
Answer» What is the coordinate of the point if y=4x and y=–x?

Discussion

6406.	The dimensional formula of (slug/barn)
Answer» The dimensional formula of (slug/barn)

Discussion

6407.	(a) What kind of numbers do you get if you add consecutive triangular numbers? Give examples. [2 MARKS] (b) ∠E is a complement of ∠F and ∠E= 28∘ . Find ∠F
Answer» (a) What kind of numbers do you get if you add consecutive triangular numbers? Give examples. [2 MARKS] (b) $∠ E$ is a complement of $∠ F$ and $∠ E$ = $28^{\circ}$ . Find $∠ F$

Discussion

6408.	Which of the following is a polynomial?
Answer» Which of the following is a polynomial?

Discussion

6409.	Find the value of (28)3–(78)3+(50)3.
Answer» $Find the value of (28)^{3} - (78)^{3} + (50)^{3} .$

Discussion

6410.	Factorise: a2+b2−c2−d2+2ab−2cd
Answer» Factorise: $a^{2} + b^{2} - c^{2} - d^{2} + 2 a b - 2 c d$

6410.

Factorise: a2+b2−c2−d2+2ab−2cd

Answer»

Factorise:

$a^{2} + b^{2} - c^{2} - d^{2} + 2 a b - 2 c d$

Discussion

6411.	Regular polygon is not only equilateral but also.
Answer» Regular polygon is not only equilateral but also.

Discussion

6412.	1^3+2^3+....+9^3=2025 then0.11^3+0.22^3+....+0.99^3
Answer» 1^3+2^3+....+9^3=2025 then0.11^3+0.22^3+....+0.99^3

Discussion

6413.	What is the differenciation of 9x^3+7x^2-4cosecx
Answer» What is the differenciation of 9x^3+7x^2-4cosecx

Discussion

6414.	Question 26In the given question, fill in the blanks to make the statement true.If B 1 × B____________ 4 9 B, then B = ___.
Answer» Question 26 In the given question, fill in the blanks to make the statement true. If $B 1 \times B____________49 B$ , then B = ___.

Discussion

6415.	Factorise x4 + 4y4. Use this to prove that 20114 + 64 is a composite number.
Answer» Factorise x⁴ + 4y⁴. Use this to prove that 2011⁴ + 64 is a composite number.

Discussion

6416.	Find the.(a) Probability of the pointer stopping on D in ?(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?(c) Probability of getting a red apple. (See figure below)
Answer» Find the. (a) Probability of the pointer stopping on D in ? (b) Probability of getting an ace from a well shuffled deck of 52 playing cards? (c) Probability of getting a red apple. (See figure below)

6416.

Find the.(a) Probability of the pointer stopping on D in ?(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?(c) Probability of getting a red apple. (See figure below)

Answer»

Find the.

(a) Probability of the pointer stopping on D in ?

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?

(c) Probability of getting a red apple. (See figure below)

Discussion

6417.	Difference between cubes of two consecutive number is 1 more than 3 times their product. Verify with an example.
Answer» Difference between cubes of two consecutive number is 1 more than 3 times their product. Verify with an example.

Discussion

6418.	What is x if (2x+2) = (5x-1)?
Answer» What is x if (2x+2) = (5x-1)?

Discussion

6419.	A car was bought for Rs. 200000 after one year it was sold for Rs. 120000, by what percentage was the price reduced at the time of selling?
Answer» A car was bought for Rs. 200000 after one year it was sold for Rs. 120000, by what percentage was the price reduced at the time of selling?

Discussion

6420.	Question 9 (ii)In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:AP = CQ
Answer» Question 9 (ii) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: AP = CQ

Discussion

6421.	Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is
Answer» Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is

Discussion

6422.	Question 3(iii) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 135
Answer» Question 3(iii) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 135

Discussion

6423.	Find: (a+b+c)×(a+b−c)=
Answer» Find: $(a + b + c) \times (a + b - c) =$

Discussion

6424.	If y = f : A → B, then which of the following is true if f(x) is a function in x? (i) x must be able to take each and every value of A. (ii) one value of x must be related to one and only one value of y in set B.
Answer» If y = f : A $\to$ B, then which of the following is true if f(x) is a function in x? (i) x must be able to take each and every value of A. (ii) one value of x must be related to one and only one value of y in set B.

6424.

If y = f : A → B, then which of the following is true if f(x) is a function in x? (i) x must be able to take each and every value of A. (ii) one value of x must be related to one and only one value of y in set B.

Answer»

If y = f : A $\to$ B, then which of the following is true if f(x) is a function in x?

(i) x must be able to take each and every value of A.

(ii) one value of x must be related to one and only one value of y in set B.

Discussion

6425.	What is compound interest?
Answer» What is compound interest?

Discussion

6426.	Write the simplest form: (a-1 + b-1) ÷ (a + b)
Answer» Write the simplest form: (a-1 + b-1) ÷ (a + b)

Discussion

6427.	Evaluate : (i) (1.2)3 (ii) (3.5)3 (iii) (0.8)3 (iv) (0.05)3
Answer» Evaluate : (i) $(1.2)^{3}$ (ii) $(3.5)^{3}$ (iii) $(0.8)^{3}$ (iv) $(0.05)^{3}$

Discussion

6428.	Construct a trapezium RISK in which RI∥KS, RI=7 cm, IS=5 cm, RK=6.5 cm and ∠I=60∘.
Answer» Construct a trapezium $R I S K$ in which $R I ∥ K S$ , $R I = 7 c m, I S = 5 c m, R K = 6.5 c m$ and $∠ I = 60^{\circ}$ .

Discussion

6429.	Plot the points P (1,0);Q (4,0)S (1,3). Find the coordinates of the point R such that PQRS is a squar
Answer» Plot the points P (1,0);Q (4,0)S (1,3). Find the coordinates of the point R such that PQRS is a squar

Discussion

6430.	Question 2 (vi)Write the ordinate of the point H.
Answer» Question 2 (vi) Write the ordinate of the point H.

6430.

Question 2 (vi)Write the ordinate of the point H.

Answer»

Question 2 (vi)

Write the ordinate of the point H.

Discussion

6431.	On dividing 2mp2q−mqp+4npq2 by pq, what do we get?
Answer» On dividing $2 m p^{2} q - m q p + 4 n p q^{2}$ by $p q$ , what do we get?

Discussion

6432.	Prove that 3a²-1 will never becomes a perfect square.
Answer» Prove that 3a²-1 will never becomes a perfect square.

Discussion

6433.	Prove that if a positive integer is of the form 6q+1, then it is of the form 3q+2 for some integer q, but not conversely
Answer» Prove that if a positive integer is of the form 6q+1, then it is of the form 3q+2 for some integer q, but not conversely

Discussion

6434.	If ₹42,000 is spent on wages of 12 men working for 30 days, then what amount would have been spent if there were 18 men working for 24 days?50400
Answer» If ₹42,000 is spent on wages of 12 men working for 30 days, then what amount would have been spent if there were 18 men working for 24 days? 50400

Discussion

6435.	IF 37y4 is exactly divisible by 9,then the least value is _______
Answer» IF 37y4 is exactly divisible by 9,then the least value is _______

Discussion

6436.	46 xyz × 34 x2y2z2 × 6x2y2z2 = ?
Answer» $\frac{4}{6}$ $x y z$ $\times$ $\frac{3}{4}$ $x^{2}$ $y^{2}$ $z^{2}$ $\times$ $\frac{6}{x^{2} y^{2} z^{2}}$ = ?

Discussion

6437.	Question 21In the given question, fill in the blanks to make the statement true.The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ___.
Answer» Question 21 In the given question, fill in the blanks to make the statement true. The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ___.

Discussion

6438.	If x is a digit of the number ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯66784x such that it is divisible by 9, find the possible values of x.
Answer» If x is a digit of the number $¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 66784 x$ such that it is divisible by 9, find the possible values of x.

Discussion

6439.	What is the order of rotational symmetry of an equilateral triangle? [2 MARKS]
Answer» What is the order of rotational symmetry of an equilateral triangle? [2 MARKS]

Discussion

6440.	A micrometre screw gauge has a negative zero error of 0.0018 cm. The main scale reading is 3.6 cm for an object. The baseline coincides with the 45th division of the circular scale. Calculate the true length of the object in mm.36.063
Answer» A micrometre screw gauge has a negative zero error of $0.0018 c m$ . The main scale reading is $3.6 c m$ for an object. The baseline coincides with the $45^{t h}$ division of the circular scale. Calculate the true length of the object in $m m$ . 36.063

Discussion

6441.	"60 साल की बात करने से पहले मैं कुछ साल और पीछे जाना चाहता हूँ। लाहौर को याद करना चाहता हूँ।" ऊपर के वाक्यों को पढ़ो और बताओ कि– (क) लेखक 60 साल की बात करने के लिए क्या चाहता है? (ख) तुम्हें अगर अपने तीन साल के हिंदी सीखने की बात को कहने को कहा जाए तो उसके लिए क्या-क्या करोगे? (ग) क्या पिछली किसी बात को याद करने कि लिए बार-बार रटना ज़रूरी होता है या सोच-समझ के साथ उस पर चर्चा, विचार और उसका आवश्यकतानुसार व्यवहार करना ज़रूरी होता है? तुम्हें जो भी उचित लगे उसे कारण सहित बताओ।
Answer» "60 साल की बात करने से पहले मैं कुछ साल और पीछे जाना चाहता हूँ। लाहौर को याद करना चाहता हूँ।" ऊपर के वाक्यों को पढ़ो और बताओ कि– (क) लेखक 60 साल की बात करने के लिए क्या चाहता है? (ख) तुम्हें अगर अपने तीन साल के हिंदी सीखने की बात को कहने को कहा जाए तो उसके लिए क्या-क्या करोगे? (ग) क्या पिछली किसी बात को याद करने कि लिए बार-बार रटना ज़रूरी होता है या सोच-समझ के साथ उस पर चर्चा, विचार और उसका आवश्यकतानुसार व्यवहार करना ज़रूरी होता है? तुम्हें जो भी उचित लगे उसे कारण सहित बताओ।

6441.

"60 साल की बात करने से पहले मैं कुछ साल और पीछे जाना चाहता हूँ। लाहौर को याद करना चाहता हूँ।" ऊपर के वाक्यों को पढ़ो और बताओ कि– (क) लेखक 60 साल की बात करने के लिए क्या चाहता है? (ख) तुम्हें अगर अपने तीन साल के हिंदी सीखने की बात को कहने को कहा जाए तो उसके लिए क्या-क्या करोगे? (ग) क्या पिछली किसी बात को याद करने कि लिए बार-बार रटना ज़रूरी होता है या सोच-समझ के साथ उस पर चर्चा, विचार और उसका आवश्यकतानुसार व्यवहार करना ज़रूरी होता है? तुम्हें जो भी उचित लगे उसे कारण सहित बताओ।

Answer»

"60 साल की बात करने से पहले मैं कुछ साल और पीछे जाना चाहता हूँ। लाहौर को याद करना चाहता हूँ।"

ऊपर के वाक्यों को पढ़ो और बताओ कि–

(क) लेखक 60 साल की बात करने के लिए क्या चाहता है?

(ख) तुम्हें अगर अपने तीन साल के हिंदी सीखने की बात को कहने को कहा जाए तो उसके लिए क्या-क्या करोगे?

(ग) क्या पिछली किसी बात को याद करने कि लिए बार-बार रटना ज़रूरी होता है या सोच-समझ के साथ उस पर चर्चा, विचार और उसका आवश्यकतानुसार व्यवहार करना ज़रूरी होता है? तुम्हें जो भी उचित लगे उसे कारण सहित बताओ।

Discussion

6442.	The area of the sector whose arc subtends an angle of 90∘ is given as 88 cm2. Find the area of the segment formed.
Answer» The area of the sector whose arc subtends an angle of $90^{\circ}$ is given as $88 {cm}^{2}$ . Find the area of the segment formed.

Discussion

6443.	Theorganizers of an essay competition decide that a winner in thecompetition gets a prize of Rs 100 and a participant who does not wingets a prize of Rs 25. The total prize money distributed is Rs 3000.Find the number of winners, if the total number of participants is63.
Answer» The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.

Discussion

6444.	In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:4(BL2 + CM2) = 5 BC2
Answer» In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that: 4(BL²+ CM²) = 5 BC²

Discussion

6445.	Find the square of 48.
Answer» Find the square of 48.

Discussion

6446.	Simplify:- 1. (a2 _ 3a + 7) × (2a + 3)
Answer» Simplify:- 1. (a^{2 _}3a + 7) × (2a + 3)

6446.

Simplify:- 1. (a2 _ 3a + 7) × (2a + 3)

Answer»

Simplify:-

1. (a^{2 _}3a + 7) × (2a + 3)

Discussion

6447.	The marked price of a shirt was Rs. 165 and it was sold at a discount of 12%. Find the discount allowed on the shirt and also its selling price.[3 MARKS]
Answer» The marked price of a shirt was Rs. 165 and it was sold at a discount of $12 %$ . Find the discount allowed on the shirt and also its selling price.[3 MARKS]

Discussion

6448.	Let x^2+x+k>0,then prove that k>1/4
Answer» Let x^2+x+k>0,then prove that k>1/4

Discussion

6449.	Mean of 11, 10, 12, 12, 9, 10, 14, 12, 9 is ______ .
Answer» Mean of 11, 10, 12, 12, 9, 10, 14, 12, 9 is ______ .

Discussion

6450.	Give the statement and proof of theorm of parallel axes.
Answer» Give the statement and proof of theorm of parallel axes.

Discussion

Explore topic-wise InterviewSolutions in .

If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz

-12/30 in standard form

(139)2−(138)2 =_____ (139+138)

Question 166Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

What is the coordinate of the point if y=4x and y=–x?

The dimensional formula of (slug/barn)

(a) What kind of numbers do you get if you add consecutive triangular numbers? Give examples. [2 MARKS] (b) ∠E is a complement of ∠F and ∠E= 28∘ . Find ∠F

Which of the following is a polynomial?

Find the value of (28)3–(78)3+(50)3.

Factorise: a2+b2−c2−d2+2ab−2cd

Regular polygon is not only equilateral but also.

1^3+2^3+....+9^3=2025 then0.11^3+0.22^3+....+0.99^3

What is the differenciation of 9x^3+7x^2-4cosecx

Question 26In the given question, fill in the blanks to make the statement true.If B 1 × B____________ 4 9 B, then B = ___.

Factorise x4 + 4y4. Use this to prove that 20114 + 64 is a composite number.

Find the.(a) Probability of the pointer stopping on D in ?(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?(c) Probability of getting a red apple. (See figure below)

Difference between cubes of two consecutive number is 1 more than 3 times their product. Verify with an example.

What is x if (2x+2) = (5x-1)?

A car was bought for Rs. 200000 after one year it was sold for Rs. 120000, by what percentage was the price reduced at the time of selling?

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

Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is

Question 3(iii) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 135

Find: (a+b+c)×(a+b−c)=

If y = f : A → B, then which of the following is true if f(x) is a function in x? (i) x must be able to take each and every value of A. (ii) one value of x must be related to one and only one value of y in set B.

What is compound interest?

Write the simplest form: (a-1 + b-1) ÷ (a + b)

Evaluate : (i) (1.2)3 (ii) (3.5)3 (iii) (0.8)3 (iv) (0.05)3

Construct a trapezium RISK in which RI∥KS, RI=7 cm, IS=5 cm, RK=6.5 cm and ∠I=60∘.

Plot the points P (1,0);Q (4,0)S (1,3). Find the coordinates of the point R such that PQRS is a squar

Question 2 (vi)Write the ordinate of the point H.

On dividing 2mp2q−mqp+4npq2 by pq, what do we get?

Prove that 3a²-1 will never becomes a perfect square.

Prove that if a positive integer is of the form 6q+1, then it is of the form 3q+2 for some integer q, but not conversely

If ₹42,000 is spent on wages of 12 men working for 30 days, then what amount would have been spent if there were 18 men working for 24 days?50400

IF 37y4 is exactly divisible by 9,then the least value is _______

46 xyz × 34 x2y2z2 × 6x2y2z2 = ?

Question 21In the given question, fill in the blanks to make the statement true.The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ___.

If x is a digit of the number ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯66784x such that it is divisible by 9, find the possible values of x.

What is the order of rotational symmetry of an equilateral triangle? [2 MARKS]

A micrometre screw gauge has a negative zero error of 0.0018 cm. The main scale reading is 3.6 cm for an object. The baseline coincides with the 45th division of the circular scale. Calculate the true length of the object in mm.36.063

The area of the sector whose arc subtends an angle of 90∘ is given as 88 cm2. Find the area of the segment formed.

Theorganizers of an essay competition decide that a winner in thecompetition gets a prize of Rs 100 and a participant who does not wingets a prize of Rs 25. The total prize money distributed is Rs 3000.Find the number of winners, if the total number of participants is63.

In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:4(BL2 + CM2) = 5 BC2

Find the square of 48.

Simplify:- 1. (a2 _ 3a + 7) × (2a + 3) ​​​

The marked price of a shirt was Rs. 165 and it was sold at a discount of 12%. Find the discount allowed on the shirt and also its selling price.[3 MARKS]

Let x^2+x+k>0,then prove that k>1/4

Mean of 11, 10, 12, 12, 9, 10, 14, 12, 9 is ______ .

Give the statement and proof of theorm of parallel axes.

Question 26In the given question, fill in the blanks to make the statement true.If B 1 × B__________ 4 9 B, then B = _.

Simplify:- 1. (a2 _ 3a + 7) × (2a + 3)