24740 + Interview Questions in Mathematics

1.	The remainder when x15 is divided by x + 1 is __________.
Answer» The remainder when x¹⁵is divided by x + 1 is __________.

Discussion

2.	54x6y + 2x3y4
Answer» 54x⁶y + 2x³y⁴

Discussion

3.	What is the probability that a leap year, selected at random will contain (i) 53 Fridays (ii) 53 Mondays and 53 Tuesdays (iii) 53 Sundays and 53 Thursdays. [4 MARKS]
Answer» What is the probability that a leap year, selected at random will contain (i) 53 Fridays (ii) 53 Mondays and 53 Tuesdays (iii) 53 Sundays and 53 Thursdays. [4 MARKS]

Discussion

4.	In the following figure: P and Q are the points of intersection of two circles with centres O and O’. If straight lines APB and CQD are parallel to OO’. Prove that(i) OO’ = ½ AB(ii) AB = CD
Answer» In the following figure: P and Q are the points of intersection of two circles with centres O and O’. If straight lines APB and CQD are parallel to OO’. Prove that (i) OO’ = ½ AB (ii) AB = CD

Discussion

5.

Roshan, whose accounts are maintained by Single Entry System, acquired a retail business on 1st April, 2018. He had ₹ 40,000 of his own and he borrowed ₹ 20,000 from his wife. He paid ₹ 15,000 for Goodwill, ₹ 5,000 for Furniture and ₹ 35,000 for Stock.Total cash received by him during the financial year from the Debtors was ₹ 2,30,000. His payments were: ₹ Purchases 1,56,000 Salary and Wages 21,400 Trade Expenses 7,200 Rent: For business premises 5,920 For private house 2,960 Payments made for domestic purposes and drawings 26,400 At the end of the year, the Stock was ₹ 37,500. He owed ₹ 13,500 to Creditors for goods and his customers owed to him ₹ 15,000. Provide 5% for Depreciation on Furniture, Interest at 5% on wife's Loan and ₹ 1,000 for Doubtful Debts.Prepare the Cash Account, the Profit and Loss Account for the year ended 31st March, 2019 and the Balance Sheet at the close of the year.

Answer» Roshan, whose accounts are maintained by Single Entry System, acquired a retail business on 1st April, 2018. He had ₹ 40,000 of his own and he borrowed ₹ 20,000 from his wife. He paid ₹ 15,000 for Goodwill, ₹ 5,000 for Furniture and ₹ 35,000 for Stock.

Total cash received by him during the financial year from the Debtors was ₹ 2,30,000. His payments were:

	₹
Purchases	1,56,000
Salary and Wages	21,400
Trade Expenses	7,200

Rent:

For business premises	5,920
For private house	2,960
Payments made for domestic purposes and drawings	26,400

At the end of the year, the Stock was ₹ 37,500. He owed ₹ 13,500 to Creditors for goods and his customers owed to him ₹ 15,000. Provide 5% for Depreciation on Furniture, Interest at 5% on wife's Loan and ₹ 1,000 for Doubtful Debts.

Prepare the Cash Account, the Profit and Loss Account for the year ended 31st March, 2019 and the Balance Sheet at the close of the year.

Discussion

6.	In a ΔABC, the median to the side BC is of length 1√11−6√3 and it divides the ∠A into angles of 30∘ and 45∘. The length of side BC is:
Answer» In a $Δ A B C$ , the median to the side $B C$ is of length $\frac{1}{\sqrt{11 - 6 \sqrt{3}}}$ and it divides the $∠ A$ into angles of $30^{\circ}$ and $45^{\circ}$ . The length of side $B C$ is:

Discussion

7.	P is any point on base BC of ΔABC and D is the mid-point of BC. DE is drawn parallel to PA to meet AC at E. If ar (ΔABC) = 12 cm2, then find area of ΔEPC.
Answer» P is any point on base BC of ΔABC and D is the mid-point of BC. DE is drawn parallel to PA to meet AC at E. If ar (ΔABC) = 12 cm², then find area of ΔEPC.

Discussion

8.	(a) Mohan started a business on 1st April, 2018 with a capital of ₹ 10,000 and borrowed ₹ 3,000 from a friend. He earned a profit of ₹ 5,000 during the year ended 31st March, 2019 and withdrew cash ₹ 4,000 for personal use. What is his capital on 31st March, 2019?(b) Mahesh started a business with a capital of ₹ 15,000 on 1st April, 2018. During the year, he made a profit of ₹ 3,000. He owes ₹ 2,500 to suppliers of goods. What is the total of assets in his business on 31st March, 2019?
Answer» (a) Mohan started a business on 1st April, 2018 with a capital of ₹ 10,000 and borrowed ₹ 3,000 from a friend. He earned a profit of ₹ 5,000 during the year ended 31st March, 2019 and withdrew cash ₹ 4,000 for personal use. What is his capital on 31st March, 2019? (b) Mahesh started a business with a capital of ₹ 15,000 on 1st April, 2018. During the year, he made a profit of ₹ 3,000. He owes ₹ 2,500 to suppliers of goods. What is the total of assets in his business on 31st March, 2019?

Discussion

9.	In a right angled triangle, which of the following options is correct? (h=hypotenuse, a and b are the perpendicular sides)
Answer» In a right angled triangle, which of the following options is correct? (h=hypotenuse, a and b are the perpendicular sides)

Discussion

10.	If length, breadth and height of cuboid are increased by 40 %, what is the percentage increase in the total surface area of the cuboid?
Answer» If length, breadth and height of cuboid are increased by 40 %, what is the percentage increase in the total surface area of the cuboid?

Discussion

11.	If each edge of a cube is increased by 100%, then find the percentage increase in the surface area of the cube.
Answer» If each edge of a cube is increased by 100%, then find the percentage increase in the surface area of the cube.

Discussion

12.	An isoceles triangle with equal sides of 4 4cm has angle 20 degree between them. What is the length of the third side
Answer» An isoceles triangle with equal sides of 4 4cm has angle 20 degree between them. What is the length of the third side

Discussion

13.	The area of three adjacent faces of a cuboid are 6cm2,15cm2 and 10cm2. The volume of the cuboid is
Answer» The area of three adjacent faces of a cuboid are $6 c m^{2}, 15 c m^{2}$ and $10 c m^{2}$ . The volume of the cuboid is

Discussion

14.	In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax.Find the ratio of hisa) income to income tax.b) income tax to income after paying income tax.
Answer» In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax. Find the ratio of his a) income to income tax. b) income tax to income after paying income tax.

Discussion

15.	Find the point which divides the line segment joining the points (2, -6) and (3, 6) in the ratio 2 : 3.
Answer» Find the point which divides the line segment joining the points (2, -6) and (3, 6) in the ratio 2 : 3.

Discussion

16.	Factorise: 150−6x2
Answer» Factorise: $150 - 6 x^{2}$

Discussion

17.	Question 12 How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm
Answer» Question 12 How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm

Discussion

18.	Find the value of X in the figure below:
Answer» Find the value of X in the figure below:

18.

Find the value of X in the figure below:

Answer»

Find the value of X in the figure below:

Discussion

19.	If logx5=a and log20x=b then find the value of logx10.
Answer» If log_x5=a and log₂₀x=b then find the value of log_x10.

Discussion

20.	Factorise: a7 − ab6
Answer» Factorise: a⁷ − ab⁶

Discussion

21.	Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.
Answer» Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Discussion

22.	Find the value of 382−22216 using a suitable identity.
Answer» Find the value of $\frac{38^{2} - 22^{2}}{16}$ using a suitable identity.

Discussion

23.	Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.
Answer» Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.

Discussion

24.	The bisectors of any two adjacent angles of a parallelogram intersect at
Answer» The bisectors of any two adjacent angles of a parallelogram intersect at

Discussion

25.	In the given figure, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =
Answer» In the given figure, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

Discussion

26.	If 4x - 4x-1 = 24, then (2x)x equals(a) 55(b) 5(c) 255(d) 125
Answer» If $4 x - 4 x^{- 1} = 24,$ then (2x)^x equals (a) $5 \sqrt{5}$ (b) $\sqrt{5}$ (c) $25 \sqrt{5}$ (d) 125

Discussion

27.	The length of the longest pole that can be put in a room of dimensions 10 m × 10 m × 5 m is ________.
Answer» The length of the longest pole that can be put in a room of dimensions 10 m × 10 m × 5 m is ________.

Discussion

28.	A man invests Rs. 5000 at a certain rate of interest, compounded annually. At the end of one year, it amounts to Rs. 5600. The rate of interest per annum is ___ %
Answer» A man invests Rs. 5000 at a certain rate of interest, compounded annually. At the end of one year, it amounts to Rs. 5600. The rate of interest per annum is ___ %

Discussion

29.	If x3 - 1x3=14, then x-1x =(a) 5(b) 4(c) 3(d) 2
Answer» If $x^{3} - \frac{1}{x^{3}} = 14$ , then $x - \frac{1}{x} =$ (a) 5 (b) 4 (c) 3 (d) 2

Discussion

30.	To represent 9.3234 which of the following method would be used.
Answer» To represent 9.3234 which of the following method would be used.

Discussion

31.	3.A right c4.: Find a relationship between X and Y such that the point(x,y) is equidistant from the point (3,6) & (-3,4)ircular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).
Answer» 3.A right c4.: Find a relationship between X and Y such that the point(x,y) is equidistant from the point (3,6) & (-3,4)ircular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).

Discussion

32.	Question 3The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?
Answer» Question 3 The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Discussion

33.	Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.
Answer» Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Discussion

34.	In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
Answer» In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.

Discussion

35.	In the given figure, two rays BD and CE intersect at a point A . The side BC of ΔABChave been produced on both sided to points F and G respectively .If∠ABF=x∘,∠ACG=y∘and ∠DAE=z∘Then z=? (a) x+y−180 (b) x+y+180 (c) 180−(x+y) (d) x+y+360∘
Answer» $In the given figure, two rays BD and CE intersect at a point A . The side BC of Δ A B C have been produced on both sided to points F and G respectively .If ∠ A B F = x^{\circ}, ∠ A C G = y^{\circ} a n d ∠ D A E = z^{\circ} T h e n z = ?$ $(a) x + y - 180 (b) x + y + 180 (c) 180 - (x + y) (d) x + y + 360^{\circ}$

35.

In the given figure, two rays BD and CE intersect at a point A . The side BC of ΔABChave been produced on both sided to points F and G respectively .If∠ABF=x∘,∠ACG=y∘and ∠DAE=z∘Then z=? (a) x+y−180 (b) x+y+180 (c) 180−(x+y) (d) x+y+360∘

Answer»

$In the given figure, two rays BD and CE intersect at a point A . The side BC of Δ A B C have been produced on both sided to points F and G respectively .If ∠ A B F = x^{\circ}, ∠ A C G = y^{\circ} a n d ∠ D A E = z^{\circ} T h e n z = ?$

$(a) x + y - 180 (b) x + y + 180 (c) 180 - (x + y) (d) x + y + 360^{\circ}$

Discussion

36.	Diagonals of a trapezium PQRS intersect each other at the point O. If PQ \|\| RS and PQ = 3RS, then ar∆POQar∆ROS= ________.
Answer» Diagonals of a trapezium PQRS intersect each other at the point O. If PQ \|\| RS and PQ = 3RS, then $\frac{a r (∆ P O Q)}{a r (∆ R O S)}$ = ________.

Discussion

37.	If vec a vec b and vec c are non-zero vectors are such that vec a=2vec b ,vec b=vec c+vec d and vec d=vec a+vec c then the angle between vec a and vec d is?
Answer» If vec a vec b and vec c are non-zero vectors are such that vec a=2vec b ,vec b=vec c+vec d and vec d=vec a+vec c then the angle between vec a and vec d is?

Discussion

38.	In the given figure, line l is the transversal intersecting the two lines m and n at P and Q. Which of the following is the pair of alternate interior angles?
Answer» In the given figure, line l is the transversal intersecting the two lines m and n at P and Q. Which of the following is the pair of alternate interior angles?

38.

In the given figure, line l is the transversal intersecting the two lines m and n at P and Q. Which of the following is the pair of alternate interior angles?

Answer»

In the given figure, line l is the transversal intersecting the two lines m and n at P and Q. Which of the following is the pair of alternate interior angles?

Discussion

39.	Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite direction they meet in 97 hours. Speed of car starting from point A is:
Answer» Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite direction they meet in $\frac{9}{7}$ hours. Speed of car starting from point A is:

Discussion

40.	The blood groups of 30 students of a class are recorded as under:A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.(i) Represent this data in the form of a frequency distribution table.(ii) Find out which is the most common and which is the rarest blood group among these students.
Answer» The blood groups of 30 students of a class are recorded as under: A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. (i) Represent this data in the form of a frequency distribution table. (ii) Find out which is the most common and which is the rarest blood group among these students.

Discussion

41.	Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in with and 5 cm thick is 112 kg. Find the length of the block.
Answer» Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in with and 5 cm thick is 112 kg. Find the length of the block.

Discussion

42.	Find the probability of choosing a point inside the square that lies inside the triangle OPQ if P and Q are the midpoints of the sides of the square.
Answer» Find the probability of choosing a point inside the square that lies inside the triangle OPQ if P and Q are the midpoints of the sides of the square.

Discussion

43.	When a system of linear equations has no solution, what does it mean?
Answer» When a system of linear equations has no solution, what does it mean?

Discussion

44.	equation of circle two of whose diameters are 3x + 4y -7 0 andx-3y 2 - 0 and having area 154 cm2 is
Answer» equation of circle two of whose diameters are 3x + 4y -7 0 andx-3y 2 - 0 and having area 154 cm2 is

Discussion

45.	If the zeroes of the polynomial x3−3x2+x+1 are a−b,a,a+b, find a and b
Answer» If the zeroes of the polynomial $x^{3} - 3 x^{2} + x + 1$ are $a - b, a, a + b,$ find $a$ and $b$

Discussion

46.	Let f(x)=(1+b2)x2+2bx+1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is
Answer» Let $f (x) = (1 + b^{2}) x^{2} + 2 b x + 1$ and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is

Discussion

47.	f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
Answer» f(x) = x⁵ + 3x⁴ − x³ − 3x² + 5x + 15, g(x) = x + 3

Discussion

48.	An equilateral triangle ABC of side 24 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is
Answer» An equilateral triangle ABC of side 24 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

48.

An equilateral triangle ABC of side 24 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

Answer»

An equilateral triangle ABC of side 24 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

Discussion

49.	The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.What is the length of the diagonal SQ?
Answer» The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure. What is the length of the diagonal SQ?

Discussion

50.	A storage tank in the form of a cube has water up to its brim. The amount of water in the tank is 4096 m3. After sometime some water was used and , it is found that the depth of water present is 12 m. Find the volume of water used in cubic meters. 1024
Answer» A storage tank in the form of a cube has water up to its brim. The amount of water in the tank is 4096 m³. After sometime some water was used and , it is found that the depth of water present is 12 m. Find the volume of water used in cubic meters. 1024

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The remainder when x15 is divided by x + 1 is __________.

54x6y + 2x3y4

What is the probability that a leap year, selected at random will contain (i) 53 Fridays (ii) 53 Mondays and 53 Tuesdays (iii) 53 Sundays and 53 Thursdays. [4 MARKS]

In the following figure: P and Q are the points of intersection of two circles with centres O and O’. If straight lines APB and CQD are parallel to OO’. Prove that(i) OO’ = ½ AB(ii) AB = CD

In a ΔABC, the median to the side BC is of length 1√11−6√3 and it divides the ∠A into angles of 30∘ and 45∘. The length of side BC is:

P is any point on base BC of ΔABC and D is the mid-point of BC. DE is drawn parallel to PA to meet AC at E. If ar (ΔABC) = 12 cm2, then find area of ΔEPC.

In a right angled triangle, which of the following options is correct? (h=hypotenuse, a and b are the perpendicular sides)

If length, breadth and height of cuboid are increased by 40 %, what is the percentage increase in the total surface area of the cuboid?

If each edge of a cube is increased by 100%, then find the percentage increase in the surface area of the cube.

An isoceles triangle with equal sides of 4 4cm has angle 20 degree between them. What is the length of the third side

The area of three adjacent faces of a cuboid are 6cm2,15cm2 and 10cm2. The volume of the cuboid is

In a year, Ravi earns ₹3,60,000 and paid ₹24,000 as income tax.Find the ratio of hisa) income to income tax.b) income tax to income after paying income tax.

Find the point which divides the line segment joining the points (2, -6) and (3, 6) in the ratio 2 : 3.

Factorise: 150−6x2

Question 12 How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm

Find the value of X in the figure below:

If logx5=a and log20x=b then find the value of logx10.

Factorise: a7 − ab6

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Find the value of 382−22216 using a suitable identity.

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.

The bisectors of any two adjacent angles of a parallelogram intersect at

In the given figure, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

If 4x - 4x-1 = 24, then (2x)x equals(a) 55(b) 5(c) 255(d) 125

The length of the longest pole that can be put in a room of dimensions 10 m × 10 m × 5 m is ________.

A man invests Rs. 5000 at a certain rate of interest, compounded annually. At the end of one year, it amounts to Rs. 5600. The rate of interest per annum is ___ %

If x3 - 1x3=14, then x-1x =(a) 5(b) 4(c) 3(d) 2

To represent 9.3234 which of the following method would be used.

3.A right c4.: Find a relationship between X and Y such that the point(x,y) is equidistant from the point (3,6) & (-3,4)ircular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).

Question 3The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.

In the given figure, two rays BD and CE intersect at a point A . The side BC of ΔABChave been produced on both sided to points F and G respectively .If∠ABF=x∘,∠ACG=y∘and ∠DAE=z∘Then z=? (a) x+y−180 (b) x+y+180 (c) 180−(x+y) (d) x+y+360∘

Diagonals of a trapezium PQRS intersect each other at the point O. If PQ || RS and PQ = 3RS, then ar∆POQar∆ROS= ________.

If vec a vec b and vec c are non-zero vectors are such that vec a=2vec b ,vec b=vec c+vec d and vec d=vec a+vec c then the angle between vec a and vec d is?

In the given figure, line l is the transversal intersecting the two lines m and n at P and Q. Which of the following is the pair of alternate interior angles?

Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite direction they meet in 97 hours. Speed of car starting from point A is:

Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in with and 5 cm thick is 112 kg. Find the length of the block.

Find the probability of choosing a point inside the square that lies inside the triangle OPQ if P and Q are the midpoints of the sides of the square.

When a system of linear equations has no solution, what does it mean?

equation of circle two of whose diameters are 3x + 4y -7 0 andx-3y 2 - 0 and having area 154 cm2 is

If the zeroes of the polynomial x3−3x2+x+1 are a−b,a,a+b, find a and b

Let f(x)=(1+b2)x2+2bx+1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is

f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3

An equilateral triangle ABC of side 24 cm is inscribed in a circle which is centered at O, as shown below. Then the radius of this circle is

The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.What is the length of the diagonal SQ?

A storage tank in the form of a cube has water up to its brim. The amount of water in the tank is 4096 m3. After sometime some water was used and , it is found that the depth of water present is 12 m. Find the volume of water used in cubic meters. 1024