32581 + Interview Questions in Mathematics

1.	Banu is 20 years older than Binu . In 5 years Banu will be twice as old as Binu . Find their present ages .
Answer» Banu is 20 years older than Binu . In 5 years Banu will be twice as old as Binu . Find their present ages .

Discussion

2.	There were 400 tickets sold for a school raffle. Jerry bought 20 of them. Find the probability that one of Jerry's tickets will be the first one drawn. ___ Give the answer up to 2 decimal places
Answer» There were 400 tickets sold for a school raffle. Jerry bought 20 of them. Find the probability that one of Jerry's tickets will be the first one drawn. ___ Give the answer up to 2 decimal places

Discussion

3.	In a rectangle ABCD, AB = 20 cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.
Answer» In a rectangle ABCD, AB = 20 cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.

Discussion

4.	If the sides of a triangle are 13, 14, 15, then the radius of the incircle is
Answer» If the sides of a triangle are $13, 14, 15,$ then the radius of the incircle is

Discussion

5.	the highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder i
Answer» the highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder i

Discussion

6.	The base of a triangle is 80 and one of the base angles is 600. If sum of the lengths of the other two sides is 90, then the shortest side is
Answer» The base of a triangle is $80$ and one of the base angles is $60^{0}$ . If sum of the lengths of the other two sides is $90,$ then the shortest side is

Discussion

7.	What is the factorization of x2+7x−8?
Answer» What is the factorization of $x^{2} + 7 x - 8$ ?

Discussion

8.	A rectangular sheet of paper 40 cm×22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is (a) 3.5 (b) 7 (c) 807 (d) 5
Answer» A rectangular sheet of paper $40 c m \times 22 c m,$ is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is (a) 3.5 (b) 7 (c) $\frac{80}{7}$ (d) 5

8.

A rectangular sheet of paper 40 cm×22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is (a) 3.5 (b) 7 (c) 807 (d) 5

Answer»

A rectangular sheet of paper $40 c m \times 22 c m,$ is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is

(a) 3.5 (b) 7 (c) $\frac{80}{7}$ (d) 5

Discussion

9.	{ (15. If three zeroes of a polynomial }x^4+3x^3-4x^2-12x are }2,0 and }-2, then find the fourth }} zero.
Answer» { (15. If three zeroes of a polynomial }x^4+3x^3-4x^2-12x are }2,0 and }-2, then find the fourth }} zero.

Discussion

10.	Find n if nC8 = nC5
Answer» Find n if ⁿC₈ = ⁿC₅

Discussion

11.	Does Iron shows fcc arrangement o bcc arrangement?
Answer» Does Iron shows fcc arrangement o bcc arrangement?

Discussion

12.	Prove that 3√3 is irrational.
Answer» Prove that $\sqrt[3]{3}$ is irrational.

Discussion

13.	Describe the sample space for the indicated experiment. A die is thrown two times.
Answer» Describe the sample space for the indicated experiment. A die is thrown two times.

Discussion

14.	The median of 50, 42, 35, 2x + 10, 2x, -8, 12, 11, 8 (written in decreasing order) is 25. Find the value of x.
Answer» The median of 50, 42, 35, 2x + 10, 2x, -8, 12, 11, 8 (written in decreasing order) is 25. Find the value of x.

Discussion

15.	If the circumference of a circle exceeds its diameter by 180 cm, then find its radius in cm. (Take π=227)
Answer» If the circumference of a circle exceeds its diameter by 180 cm, then find its radius in cm. (Take $π = \frac{22}{7}$ )

Discussion

16.	The difference between two numbers is 2490. If x and y are the numbers with x>y, then the equation representing this is .
Answer» The difference between two numbers is 2490. If $x$ and $y$ are the numbers with $x > y,$ then the equation representing this is .

Discussion

17.	If the given triangles △ABC and △PQR are similar, then find the lengths of the sides x and y.
Answer» If the given triangles △ABC and △PQR are similar, then find the lengths of the sides x and y.

Discussion

18.	12 : 21 and 72 :126 are in proportion. Which of the following is correct?
Answer» 12 : 21 and 72 :126 are in proportion. Which of the following is correct?

Discussion

19.	Solve each of the following systems of equations by the method of cross-multiplication :xa+yb=2ax-by=a2-b2
Answer» Solve each of the following systems of equations by the method of cross-multiplication : $\frac{x}{a} + \frac{y}{b} = 2 a x - b y = a^{2} - b^{2}$

Discussion

20.	Solve the following systems of equations: 4x+3y=8 6x−4y=−5
Answer» Solve the following systems of equations: $\frac{4}{x} + 3 y = 8$ $\frac{6}{x} - 4 y = - 5$

20.

Solve the following systems of equations: 4x+3y=8 6x−4y=−5

Answer»

Solve the following systems of equations:

$\frac{4}{x} + 3 y = 8$

$\frac{6}{x} - 4 y = - 5$

Discussion

21.	Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)
Answer» Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

Discussion

22.	Very-Short and Short-Answer QuestionsWhat is the 5th term from the end of the AP 2, 7, 12, ..., 47? [CBSE 2011]
Answer» Very-Short and Short-Answer Questions What is the 5th term from the end of the AP 2, 7, 12, ..., 47? [CBSE 2011]

Discussion

23.	A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find : (i) The equation of the line. (ii) The co-ordinates of A and B. (iii) The co-ordinates of M.
Answer» A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find : (i) The equation of the line. (ii) The co-ordinates of A and B. (iii) The co-ordinates of M.

23.

A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find : (i) The equation of the line. (ii) The co-ordinates of A and B. (iii) The co-ordinates of M.

Answer»

A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find :

(i) The equation of the line.

(ii) The co-ordinates of A and B.

(iii) The co-ordinates of M.

Discussion

24.

Srijan, Raman and Manan were partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. On 31st, March, 2017 their Balance Sheet was as follows: BALANCE SHEET OF SRIJAN, RAMAN AND MANAN as on 31st March, 2017 Liabilities Amount (₹) Assets Amount (₹) Capitals: Capital: Manan 10,000 Srijan 2,00,000 Plant 2,20,000 Raman 1,50,000 3,50,000 Investments 70,000 Creditors 75,000 Stock 50,000 Bills Payable 40,000 Debtors 60,000 Outstanding Salary 35,000 Bank 10,000 Profit and Loss Account 80,000 5,00,000 5,00,000 On the above date they decided to dissolve the firm.(a) Srijan was appointed to realise the assets and discharge the liabilities. Srijan was to receive 5% commission on sale of assets (except cash) and was to bear all expenses of realisation.(b) Assets were realised as follows: ₹ Plant 85,000 Stock 33,000 Debtors 47,000 (c) Investments were realised at 95% of the book value.(d) The firm had to pay ₹ 7,500 for an outstanding repair bill not provided for earlier.(e) A contingent liabillity in respect of bills receivable, discounted with the bank had also materialised and had to be discharged for ₹ 15,000.(f) Expenses of realisation amounting to ₹ 3,000 were paid by Srijan.Prepare Realisation Account, Partners' Capital Accounts and Bank Account.

Answer» Srijan, Raman and Manan were partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. On 31st, March, 2017 their Balance Sheet was as follows:

BALANCE SHEET OF SRIJAN, RAMAN AND MANAN as on 31st March, 2017
Liabilities		Amount (₹)	Assets	Amount (₹)
Capitals:			Capital: Manan	10,000
Srijan	2,00,000		Plant	2,20,000
Raman	1,50,000	3,50,000	Investments	70,000
Creditors		75,000	Stock	50,000
Bills Payable		40,000	Debtors	60,000
Outstanding Salary		35,000	Bank	10,000
			Profit and Loss Account	80,000
		5,00,000		5,00,000

On the above date they decided to dissolve the firm.

(a) Srijan was appointed to realise the assets and discharge the liabilities. Srijan was to receive 5% commission on sale of assets (except cash) and was to bear all expenses of realisation.

(b)

Assets were realised as follows:	₹
Plant	85,000
Stock	33,000
Debtors	47,000

(c) Investments were realised at 95% of the book value.

(d) The firm had to pay ₹ 7,500 for an outstanding repair bill not provided for earlier.

(e) A contingent liabillity in respect of bills receivable, discounted with the bank had also materialised and had to be discharged for ₹ 15,000.

(f) Expenses of realisation amounting to ₹ 3,000 were paid by Srijan.

Prepare Realisation Account, Partners' Capital Accounts and Bank Account.

Discussion

25.	A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
Answer» A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

Discussion

26.	The sum of the radii of two circles is 140 cm and the difference of the circumferences is 88 cm. Find the diameters of the circles.
Answer» The sum of the radii of two circles is $140 c m$ and the difference of the circumferences is $88 c m$ . Find the diameters of the circles.

Discussion

27.	For what value of k will the following pair of linear equations have no solution?:2x+3y=9, 6x+k-2y=3k-2
Answer» For what value of k will the following pair of linear equations have no solution?: $2 x + 3 y = 9, 6 x + (k - 2) y = (3 k - 2)$

Discussion

28.	In the given figure, ΔABC has been constructed similar to ΔA'BC'. What is the scale factor?
Answer» In the given figure, ΔABC has been constructed similar to ΔA'BC'. What is the scale factor?

28.

In the given figure, ΔABC has been constructed similar to ΔA'BC'. What is the scale factor?

Answer»

In the given figure, ΔABC has been constructed similar to ΔA'BC'. What is the scale factor?

Discussion

29.	In the given figure, PQ is a diameter and O is the center of the circle. If ∠PRT=∠QTR=90∘ then which of the following statements are correct?
Answer» In the given figure, PQ is a diameter and O is the center of the circle. If $∠ P R T = ∠ Q T R = 90^{\circ}$ then which of the following statements are correct?

29.

In the given figure, PQ is a diameter and O is the center of the circle. If ∠PRT=∠QTR=90∘ then which of the following statements are correct?

Answer»

In the given figure, PQ is a diameter and O is the center of the circle.

If $∠ P R T = ∠ Q T R = 90^{\circ}$

then which of the following statements are correct?

Discussion

30.	If both (x – 2) and x-12 are factors of px2 + 5x + r, prove that p = r.
Answer» If both (x – 2) and $(x - \frac{1}{2})$ are factors of px² + 5x + r, prove that p = r.

Discussion

31.	Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of DO'CO.
Answer» Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of $\frac{D O'}{C O}$ .

Discussion

32.	Q. If k is the ratio of the roots of equations x²-ax+b=0 then find k²+1/k (solve it by componendo and dividendo)
Answer» Q. If k is the ratio of the roots of equations x²-ax+b=0 then find k²+1/k (solve it by componendo and dividendo)

Discussion

33.	Question 5The first four terms of an AP whose first term is – 2 and the common difference is – 2 areA) – 2, 0, 2, 4B) – 2, 4, –8, 16C) – 2, – 4, – 6 , – 8D) – 2, – 4, – 8, – 16
Answer» Question 5 The first four terms of an AP whose first term is – 2 and the common difference is – 2 are A) – 2, 0, 2, 4 B) – 2, 4, –8, 16 C) – 2, – 4, – 6 , – 8 D) – 2, – 4, – 8, – 16

Discussion

34.	If (ax − b) is factor of p(x), then
Answer» If $(a x - b)$ is factor of $p (x)$ , then

Discussion

35.	How to calculate the value of sin18
Answer» How to calculate the value of sin18

Discussion

36.	Choose the correct answer of the following question:The lengths of the sides of a triangular field are 20 m, 21 m and 29 m. The cost of cultivating the field at ₹9 per m2 is(a) ₹2610 (b) ₹3780 (c) ₹1890 (d) ₹1800
Answer» Choose the correct answer of the following question: The lengths of the sides of a triangular field are 20 m, 21 m and 29 m. The cost of cultivating the field at ₹9 per m² is (a) ₹2610 (b) ₹3780 (c) ₹1890 (d) ₹1800

Discussion

37.

Find the mean and variance of frequency distribution given below: xi: 1 ≤ x < 3 3 ≤ x < 5 5 ≤ x < 7 7 ≤ x < 10 fi: 6 4 5 1

Answer» Find the mean and variance of frequency distribution given below:

x_i:	1 ≤ x < 3	3 ≤ x < 5	5 ≤ x < 7	7 ≤ x < 10
f_i:	6	4	5	1

Discussion

38.	Find the point where 2x - 3y = - 9 cuts the y-axis.
Answer» Find the point where 2x - 3y = - 9 cuts the y-axis.

Discussion

39.	What is a composite number ?
Answer» What is a composite number ?

Discussion

40.	derive the formula of area of right triangle
Answer» derive the formula of area of right triangle

Discussion

41.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:4x2-4a2x+a4-b4=0 [CBSE 2015]
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $4 x^{2} - 4 a^{2} x + (a^{4} - b^{4}) = 0$ [CBSE 2015]

Discussion

42.	In the given figure, a circle touches the side BC of ΔABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of ΔABC.__
Answer» In the given figure, a circle touches the side BC of $Δ$ ABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of $Δ$ ABC. __

42.

In the given figure, a circle touches the side BC of ΔABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of ΔABC.__

Answer»

In the given figure, a circle touches the side BC of $Δ$ ABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of $Δ$ ABC.

__

Discussion

43.	The area of the largest triangle inscribed in a semi-circle of radius 8 is_________
Answer» The area of the largest triangle inscribed in a semi-circle of radius 8 is_________

Discussion

44.	A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.
Answer» A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.

Discussion

45.	Class mark of a class = _____.
Answer» Class mark of a class = _____.

Discussion

46.	Find zeroes of polynomial 4x2−7 and verify relationship between the zeroes and its coefficients.
Answer» Find zeroes of polynomial $4 x^{2} - 7$ and verify relationship between the zeroes and its coefficients.

Discussion

47.	On constructing a triangle ABC, with AB = 5 cm, AC = BC = 9 cm, the distance between the points which are both equidistant from AB and AC and also 3 cm from BC is
Answer» On constructing a triangle ABC, with AB = 5 cm, AC = BC = 9 cm, the distance between the points which are both equidistant from AB and AC and also 3 cm from BC is

Discussion

48.	If the distance between the points (4, p) and (1, 0) is 5, then p=.
Answer» If the distance between the points (4, p) and (1, 0) is 5, then p=.

Discussion

49.	A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60o and angle of depression of the base of the hill as 30o. What is the height of the hill?
Answer» A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60^o and angle of depression of the base of the hill as 30^o. What is the height of the hill?

Discussion

50.	Using factor theorem, show that g(x) is a factor of p(x), whenpx=7x2-42x-6, gx=x-2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 7 x^{2} - 4 \sqrt{2} x - 6, g (x) = x - \sqrt{2}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Banu is 20 years older than Binu . In 5 years Banu will be twice as old as Binu . Find their present ages .

There were 400 tickets sold for a school raffle. Jerry bought 20 of them. Find the probability that one of Jerry's tickets will be the first one drawn. ___ Give the answer up to 2 decimal places

In a rectangle ABCD, AB = 20 cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.

If the sides of a triangle are 13, 14, 15, then the radius of the incircle is

the highest power of 2 by which the product of first 100 counting numbers can be divided without any remainder i

The base of a triangle is 80 and one of the base angles is 600. If sum of the lengths of the other two sides is 90, then the shortest side is

What is the factorization of x2+7x−8?

A rectangular sheet of paper 40 cm×22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is (a) 3.5 (b) 7 (c) 807 (d) 5

{ (15. If three zeroes of a polynomial }x^4+3x^3-4x^2-12x are }2,0 and }-2, then find the fourth }} zero.

Find n if nC8 = nC5

Does Iron shows fcc arrangement o bcc arrangement?

Prove that 3√3 is irrational.

Describe the sample space for the indicated experiment. A die is thrown two times.

The median of 50, 42, 35, 2x + 10, 2x, -8, 12, 11, 8 (written in decreasing order) is 25. Find the value of x.

If the circumference of a circle exceeds its diameter by 180 cm, then find its radius in cm. (Take π=227)

The difference between two numbers is 2490. If x and y are the numbers with x&gt;y, then the equation representing this is .

If the given triangles △ABC and △PQR are similar, then find the lengths of the sides x and y.

12 : 21 and 72 :126 are in proportion. Which of the following is correct?

Solve each of the following systems of equations by the method of cross-multiplication :xa+yb=2ax-by=a2-b2

Solve the following systems of equations: 4x+3y=8 6x−4y=−5

Very-Short and Short-Answer QuestionsWhat is the 5th term from the end of the AP 2, 7, 12, ..., 47? [CBSE 2011]

A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find : (i) The equation of the line. (ii) The co-ordinates of A and B. (iii) The co-ordinates of M.

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

The sum of the radii of two circles is 140 cm and the difference of the circumferences is 88 cm. Find the diameters of the circles.

For what value of k will the following pair of linear equations have no solution?:2x+3y=9, 6x+k-2y=3k-2

In the given figure, ΔABC has been constructed similar to ΔA'BC'. What is the scale factor?

In the given figure, PQ is a diameter and O is the center of the circle. If ∠PRT=∠QTR=90∘ then which of the following statements are correct?

If both (x – 2) and x-12 are factors of px2 + 5x + r, prove that p = r.

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O', at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of DO'CO.

Q. If k is the ratio of the roots of equations x²-ax+b=0 then find k²+1/k (solve it by componendo and dividendo)

Question 5The first four terms of an AP whose first term is – 2 and the common difference is – 2 areA) – 2, 0, 2, 4B) – 2, 4, –8, 16C) – 2, – 4, – 6 , – 8D) – 2, – 4, – 8, – 16

If (ax − b) is factor of p(x), then

How to calculate the value of sin18

Choose the correct answer of the following question:The lengths of the sides of a triangular field are 20 m, 21 m and 29 m. The cost of cultivating the field at ₹9 per m2 is(a) ₹2610 (b) ₹3780 (c) ₹1890 (d) ₹1800

Find the mean and variance of frequency distribution given below: xi: 1 ≤ x &lt; 3 3 ≤ x &lt; 5 5 ≤ x &lt; 7 7 ≤ x &lt; 10 fi: 6 4 5 1

Find the point where 2x - 3y = - 9 cuts the y-axis.

What is a composite number ?

derive the formula of area of right triangle

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:4x2-4a2x+a4-b4=0 [CBSE 2015]

In the given figure, a circle touches the side BC of ΔABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of ΔABC.__

The area of the largest triangle inscribed in a semi-circle of radius 8 is_________

A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.

Class mark of a class = _____.

Find zeroes of polynomial 4x2−7 and verify relationship between the zeroes and its coefficients.

On constructing a triangle ABC, with AB = 5 cm, AC = BC = 9 cm, the distance between the points which are both equidistant from AB and AC and also 3 cm from BC is

If the distance between the points (4, p) and (1, 0) is 5, then p=.

A man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60o and angle of depression of the base of the hill as 30o. What is the height of the hill?

Using factor theorem, show that g(x) is a factor of p(x), whenpx=7x2-42x-6, gx=x-2

The difference between two numbers is 2490. If x and y are the numbers with x>y, then the equation representing this is .

Find the mean and variance of frequency distribution given below: xi: 1 ≤ x < 3 3 ≤ x < 5 5 ≤ x < 7 7 ≤ x < 10 fi: 6 4 5 1