25365 + Interview Questions in Mathematics

1.	Sameerrao has taken a loan of ₹12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually then how many rupees should he pay to clear his loan?
Answer» Sameerrao has taken a loan of ₹12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually then how many rupees should he pay to clear his loan?

Discussion

2.	Which of the following is(are) the common factor(s) of monomials 6xy and 8x2?
Answer» Which of the following is(are) the common factor(s) of monomials $6 x y$ and $8 x^{2} ?$

Discussion

3.	Factorize 2xy+8x+4y+y2
Answer» Factorize $2 x y + 8 x + 4 y + y^{2}$

3.

Factorize 2xy+8x+4y+y2

Answer»

Factorize

$2 x y + 8 x + 4 y + y^{2}$

Discussion

4.	5x−2y=7 and xy=2, find the value of (5x+2y)2
Answer» $5 x - 2 y = 7 a n d x y = 2$ , find the value of $(5 x + 2 y)^{2}$

Discussion

5.	Simplify: (3k−4r−2m)2−(3k+4r−2m)2
Answer» Simplify: $(3 k - 4 r - 2 m)^{2} - (3 k + 4 r - 2 m)^{2}$

Discussion

6.	Unlike terms can be _______.
Answer» Unlike terms can be _______.

Discussion

7.	Reenu types 540 words during half an hour. How many words Would she type in 8 minutes ?
Answer» Reenu types 540 words during half an hour. How many words Would she type in 8 minutes ?

Discussion

8.	The table provided below represents the number of females and males in a family.What is the total number of people in this family?
Answer» The table provided below represents the number of females and males in a family. What is the total number of people in this family?

Discussion

9.	The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.
Answer» The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹ $25$ . The total prize money distributed is ₹ $3, 000$ . Find the number of winners, if the total number of participants is $63$ .

Discussion

10.	If the selling price of 15 articles is equal to the cost price of 12 articles, then the loss percent is ___.
Answer» If the selling price of 15 articles is equal to the cost price of 12 articles, then the loss percent is ___.

Discussion

11.	When will the process be non spon†an eous at all temperature? 1) △ H=-ve and △ S=-ve 2) △ H= +ve and △ S=-ve 3) △ H=+ve and △ S=+ve 4)△ H=-ve and △ S=+ve
Answer» When will the process be non spon†an eous at all temperature? 1) △ H=-ve and △ S=-ve 2) △ H= +ve and △ S=-ve 3) △ H=+ve and △ S=+ve 4)△ H=-ve and △ S=+ve

Discussion

12.	In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125°. Find the measures of ∠S.
Answer» In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125°. Find the measures of ∠S.

12.

In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125°. Find the measures of ∠S.

Answer»

In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125°. Find the measures of ∠S.

Discussion

13.	Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP > CP.Statement 2: Loss is found when CP > SP.Choose the correct option with respect to the above statements.
Answer» Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP > CP. Statement 2: Loss is found when CP > SP. Choose the correct option with respect to the above statements.

13.

Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP > CP.Statement 2: Loss is found when CP > SP.Choose the correct option with respect to the above statements.

Answer»

Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP > CP.

Statement 2: Loss is found when CP > SP.

Choose the correct option with respect to the above statements.

Discussion

14.	If A = {x : x is a natural number} B = {x : x is an even natural number} C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .
Answer» If A = {x : x is a natural number} B = {x : x is an even natural number} C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

14.

If A = {x : x is a natural number} B = {x : x is an even natural number} C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

Answer»

If A = {x : x is a natural number}

B = {x : x is an even natural number}

C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

Discussion

15.	In figure, OP bisects ∠BOC and OQ bisects ∠AOC. Show that ∠POQ=90∘
Answer» In figure, $O P$ bisects $∠ B O C$ and $O Q$ bisects $∠ A O C$ . Show that $∠ P O Q = 90^{\circ}$

Discussion

16.	Find the area of a rectangle whose length is 5xy units and breadth is 8xy2 units.
Answer» Find the area of a rectangle whose length is $5 x y$ units and breadth is $8 x y^{2}$ units.

Discussion

17.	Factorise : (l+m)2−(l−m)2
Answer» Factorise : $(l + m)^{2} - (l - m)^{2}$

17.

Factorise : (l+m)2−(l−m)2

Answer»

Factorise :

$(l + m)^{2} - (l - m)^{2}$

Discussion

18.	Question 15 (i)Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?
Answer» Question 15 (i) Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?

Discussion

19.	Mohit, Akbar and Rajeev live in the same city. Mohit sells an article to Akbar marked at ₹50000. Akbar sells the same article to Rajeev at a profit of ₹4000 for consumption. If all the transactions are under a GST of 12%, find the total tax received by the Central government(CGST).
Answer» Mohit, Akbar and Rajeev live in the same city. Mohit sells an article to Akbar marked at ₹50000. Akbar sells the same article to Rajeev at a profit of ₹4000 for consumption. If all the transactions are under a GST of 12%, find the total tax received by the Central government(CGST).

Discussion

20.	In the given figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ∼ ∆ADE and hence find the length of AE and DE.
Answer» In the given figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ∼ ∆ADE and hence find the length of AE and DE.

Discussion

21.	In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar(ΔABC)ar(ΔDBC)=AODO.
Answer» In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that $\frac{a r (Δ A B C)}{a r (Δ D B C)} = \frac{A O}{D O}$ .

Discussion

22.	There are three consecutive numbers whose sum is 129. Find the square of the middle one.
Answer» There are three consecutive numbers whose sum is 129. Find the square of the middle one.

Discussion

23.	If a + b + c = 5 and ab + bc + ca = 10, then what will be the value of a3+b3+c3−3abc ? -25
Answer» If a + b + c = 5 and ab + bc + ca = 10, then what will be the value of $a^{3} + b^{3} + c^{3} - 3 a b c ?$ -25

Discussion

24.	If a is the number of lines of symmetry and b is the order of rotational symmetry in a regular polygon of n sides, then what is the relation between them?
Answer» If $a$ is the number of lines of symmetry and $b$ is the order of rotational symmetry in a regular polygon of $n$ sides, then what is the relation between them?

Discussion

25.	Which of the following has 1 as its unit digit in its cube root?
Answer» Which of the following has 1 as its unit digit in its cube root?

Discussion

26.	Find the product of a² × 2a²² × 4a²
Answer» Find the product of a² × 2a²² × 4a²

Discussion

27.	For any non-zero vector r→,r→×i^2+r→×j^2+r→×k^2=λr→2, then λ= ___________________.
Answer» For any non-zero vector $\vec{r}, {\|\vec{r} \times \hat{i}\|}^{2} + {\|\vec{r} \times \hat{j}\|}^{2} + {\|\vec{r} \times \hat{k}\|}^{2} = λ {\|\vec{r}\|}^{2}, then λ =___________________.$

Discussion

28.	Let P = 2^4 × 3^5 × 4^2 × 5^2 × 6^5 × 8^2 then the sum of all factors of P is what?
Answer» Let P = 2^4 × 3^5 × 4^2 × 5^2 × 6^5 × 8^2 then the sum of all factors of P is what?

Discussion

29.	In triangle ABC, AP is perpendicular TO BC. AB=a units, AC=b units , BP=c units, PC=d units. Prove that (a + b) (a - b) = (c + d) (c - d)
Answer» In triangle ABC, AP is perpendicular TO BC. AB=a units, AC=b units , BP=c units, PC=d units. Prove that (a + b) (a - b) = (c + d) (c - d)

Discussion

30.	Find the value of a. 22
Answer» Find the value of a. 22

30.

Find the value of a. 22

Answer»

Find the value of a.

22

Discussion

31.	The value of x in the equation 2x+14x+9=1 is:
Answer» $T h e v a l u e o f x i n t h e e q u a t i o n \frac{2 x + 1}{4 x + 9} = 1 i s :$

Discussion

32.	A sum of ₹10,000 is borrowed at an interest rate of 7% compounded annualy, then the interest for the fourth year is_______.
Answer» A sum of ₹10,000 is borrowed at an interest rate of 7% compounded annualy, then the interest for the fourth year is_______.

Discussion

33.	If 5 person can finish a job in 10 days then in how many days will 15 persons finish the same job?
Answer» If 5 person can finish a job in 10 days then in how many days will 15 persons finish the same job?

Discussion

34.	Find the circumcentre of the triangle whose vertices are (-2,-3),-1,0) and (7,-6). Also find the radius of the circumcircle.
Answer» Find the circumcentre of the triangle whose vertices are (-2,-3),-1,0) and (7,-6). Also find the radius of the circumcircle.

Discussion

35.	Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their present age?
Answer» Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their present age?

Discussion

36.	The area of a trapezium is 384 cm2.Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12 cm.Find the length of each of the parallel sides.
Answer» The area of a trapezium is 384 $c m^{2}$ .Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12 cm.Find the length of each of the parallel sides.

Discussion

37.	the differential equation of all the non vertical lines in the x-y plane
Answer» the differential equation of all the non vertical lines in the x-y plane

Discussion

38.

Following balances appear in the books of X Ltd. as on 1st April, 2017: ₹ Machinery A/c 5,00,000 Provision for Depreciation A/c 2,25,000 The machinery is depreciated 10% p.a. on the Fixed Instalment Method. The accounting year being April-March. On 1st October, 2017, a machinery which was purchased on 1st July, 2014 for ₹ 1,00,000 was sold for ₹ 42,000 plus CGST and SGST 6% each and on the same date a new machine was purchased for ₹ 2,00,000 paying IGST 12%. Prepare Machinery Account and Provision for Depreciation Account for the year ended 31st March, 2018.

Answer» Following balances appear in the books of X Ltd. as on 1st April, 2017:

	₹
Machinery A/c	5,00,000
Provision for Depreciation A/c	2,25,000

The machinery is depreciated 10% p.a. on the Fixed Instalment Method. The accounting year being April-March. On 1st October, 2017, a machinery which was purchased on 1st July, 2014 for ₹ 1,00,000 was sold for ₹ 42,000 plus CGST and SGST 6% each and on the same date a new machine was purchased for ₹ 2,00,000 paying IGST 12%. Prepare Machinery Account and Provision for Depreciation Account for the year ended 31st March, 2018.

Discussion

39.	Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.
Answer» Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

39.

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

Answer»

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

Discussion

40.	The factors of (2x-3y)²+2(2x+3y)(X+y)+(X+y)² is(1)(2x-3y) and (3x-2y) (2)(2x+3y) and (3x+2y)(3)(3x+2y) and (3x-2y) (4) (3x-2y) and (3x-2y)
Answer» The factors of (2x-3y)²+2(2x+3y)(X+y)+(X+y)² is (1)(2x-3y) and (3x-2y) (2)(2x+3y) and (3x+2y) (3)(3x+2y) and (3x-2y) (4) (3x-2y) and (3x-2y)

Discussion

41.	If the median of 10, 12, x, 6, 18 is 10, then which of the following is correct?(a) 6≤x≤10 (b) x < 6 (c) x > 18 (d) Either (a) or (b)
Answer» If the median of 10, 12, x, 6, 18 is 10, then which of the following is correct? (a) $6 \leq x \leq 10$ (b) x < 6 (c) x > 18 (d) Either (a) or (b)

Discussion

42.	Question 4(v) Divide as directed x(x+1)(x+2)(x+3)÷x(x+1)
Answer» Question 4(v) Divide as directed $x (x + 1) (x + 2) (x + 3) \div x (x + 1)$

Discussion

43.	If a2−b2=48 and a−b=8, then what is the value of a+b? 6
Answer» If $a^{2} - b^{2} = 48$ and $a - b = 8$ , then what is the value of $a + b$ ? 6

Discussion

44.	Question 32The value of (a+b)2+(a−b)2 isa) 2a+2bb) 2a−2bc) 2a2+2b2a) 2a2+2b2
Answer» Question 32 The value of $(a + b)^{2} + (a - b)^{2}$ is a) $2 a + 2 b$ b) $2 a - 2 b$ c) $2 a^{2} + 2 b^{2}$ a) $2 a^{2} + 2 b^{2}$

Discussion

45.	Question 111(i) Use the distributivity of multiplication of rational numbers over addition to simplify. 35×[3524+101]
Answer» Question 111(i) Use the distributivity of multiplication of rational numbers over addition to simplify. $\frac{3}{5} \times [\frac{35}{24} + \frac{10}{1}]$

Discussion

46.	If A and B are disjoint sets then,n(A U B) = ____.
Answer» If A and B are disjoint sets then, n(A U B) = ____.

46.

If A and B are disjoint sets then,n(A U B) = ____.

Answer»

If A and B are disjoint sets then,

n(A U B) = ____.

Discussion

47.	In Fig. it is given that AB = BC and AD = EC. Prove that ΔABE ≅ ΔCBD [3 MARKS]
Answer» In Fig. it is given that AB = BC and AD = EC. Prove that $Δ$ ABE $≅$ $Δ$ CBD [3 MARKS]

47.

In Fig. it is given that AB = BC and AD = EC. Prove that ΔABE ≅ ΔCBD [3 MARKS]

Answer»

In Fig. it is given that AB = BC and AD = EC. Prove that $Δ$ ABE $≅$ $Δ$ CBD

[3 MARKS]

Discussion

48.	The value of 64×78 calculated using binomial multiplication is
Answer» The value of $64 \times 78$ calculated using binomial multiplication is

Discussion

49.	Question 53(ii)The graph given below shows the marks obtained out of 10 by Sonia in two different tests. Study the graph and answer the questions that follow.In which subject did she score the highest in Test I?
Answer» Question 53(ii) The graph given below shows the marks obtained out of 10 by Sonia in two different tests. Study the graph and answer the questions that follow. In which subject did she score the highest in Test I?

Discussion

50.	Question 92The negative of a negative rational number is a positive rational number.
Answer» Question 92 The negative of a negative rational number is a positive rational number.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Sameerrao has taken a loan of ₹12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually then how many rupees should he pay to clear his loan?

Which of the following is(are) the common factor(s) of monomials 6xy and 8x2?

Factorize 2xy+8x+4y+y2

5x−2y=7 and xy=2, find the value of (5x+2y)2

Simplify: (3k−4r−2m)2−(3k+4r−2m)2

Unlike terms can be _______.

Reenu types 540 words during half an hour. How many words Would she type in 8 minutes ?

The table provided below represents the number of females and males in a family.What is the total number of people in this family?

The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

If the selling price of 15 articles is equal to the cost price of 12 articles, then the loss percent is ___.

When will the process be non spon†an eous at all temperature? 1) △ H=-ve and △ S=-ve 2) △ H= +ve and △ S=-ve 3) △ H=+ve and △ S=+ve 4)△ H=-ve and △ S=+ve

In the fig, suppose ∠P and ∠Q are supplementary angles and ∠R = 125°. Find the measures of ∠S.

Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP &gt; CP.Statement 2: Loss is found when CP &gt; SP.Choose the correct option with respect to the above statements.

If A = {x : x is a natural number} B = {x : x is an even natural number} C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

In figure, OP bisects ∠BOC and OQ bisects ∠AOC. Show that ∠POQ=90∘

Find the area of a rectangle whose length is 5xy units and breadth is 8xy2 units.

Factorise : (l+m)2−(l−m)2

Question 15 (i)Five cards – ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?

Mohit, Akbar and Rajeev live in the same city. Mohit sells an article to Akbar marked at ₹50000. Akbar sells the same article to Rajeev at a profit of ₹4000 for consumption. If all the transactions are under a GST of 12%, find the total tax received by the Central government(CGST).

In the given figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ∼ ∆ADE and hence find the length of AE and DE.

In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar(ΔABC)ar(ΔDBC)=AODO.

There are three consecutive numbers whose sum is 129. Find the square of the middle one.

If a + b + c = 5 and ab + bc + ca = 10, then what will be the value of a3+b3+c3−3abc ? -25

If a is the number of lines of symmetry and b is the order of rotational symmetry in a regular polygon of n sides, then what is the relation between them?

Which of the following has 1 as its unit digit in its cube root?

Find the product of a² × 2a²² × 4a² ​​​​

For any non-zero vector r→,r→×i^2+r→×j^2+r→×k^2=λr→2, then λ= ___________________.

Let P = 2^4 × 3^5 × 4^2 × 5^2 × 6^5 × 8^2 then the sum of all factors of P is what?

In triangle ABC, AP is perpendicular TO BC. AB=a units, AC=b units , BP=c units, PC=d units. Prove that (a + b) (a - b) = (c + d) (c - d)

Find the value of a. 22

The value of x in the equation 2x+14x+9=1 is:

A sum of ₹10,000 is borrowed at an interest rate of 7% compounded annualy, then the interest for the fourth year is_______.

If 5 person can finish a job in 10 days then in how many days will 15 persons finish the same job?

Find the circumcentre of the triangle whose vertices are (-2,-3),-1,0) and (7,-6). Also find the radius of the circumcircle.

Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their present age?

The area of a trapezium is 384 cm2.Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12 cm.Find the length of each of the parallel sides.

the differential equation of all the non vertical lines in the x-y plane

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

The factors of (2x-3y)²+2(2x+3y)(X+y)+(X+y)² is(1)(2x-3y) and (3x-2y) (2)(2x+3y) and (3x+2y)(3)(3x+2y) and (3x-2y) (4) (3x-2y) and (3x-2y)

If the median of 10, 12, x, 6, 18 is 10, then which of the following is correct?(a) 6≤x≤10 (b) x < 6 (c) x > 18 (d) Either (a) or (b)

Question 4(v) Divide as directed x(x+1)(x+2)(x+3)÷x(x+1)

If a2−b2=48 and a−b=8, then what is the value of a+b? 6

Question 32The value of (a+b)2+(a−b)2 isa) 2a+2bb) 2a−2bc) 2a2+2b2a) 2a2+2b2

Question 111(i) Use the distributivity of multiplication of rational numbers over addition to simplify. 35×[3524+101]

If A and B are disjoint sets then,n(A U B) = ____.

In Fig. it is given that AB = BC and AD = EC. Prove that ΔABE ≅ ΔCBD [3 MARKS]

The value of 64×78 calculated using binomial multiplication is

Question 53(ii)The graph given below shows the marks obtained out of 10 by Sonia in two different tests. Study the graph and answer the questions that follow.In which subject did she score the highest in Test I?

Question 92The negative of a negative rational number is a positive rational number.

Statement 1: Profit is defined as the positive difference between selling price and cost price whenever SP > CP.Statement 2: Loss is found when CP > SP.Choose the correct option with respect to the above statements.

Find the product of a² × 2a²² × 4a²