24740 + Interview Questions in Mathematics

1.	How to substitute√ in the given polynomial by remainder theorem
Answer» How to substitute√ in the given polynomial by remainder theorem

Discussion

2.	A truck carrier measures 10m×4m×5m. What will be the volume of sand that can be filled into the truck? [2 MARKS]
Answer» A truck carrier measures $10 m \times 4 m \times 5 m$ . What will be the volume of sand that can be filled into the truck? [2 MARKS]

Discussion

3.	Question 9 In the figure, which of the two lines are parallel and why?
Answer» Question 9 In the figure, which of the two lines are parallel and why?

Discussion

4.	Question 5 Given sec θ = 1312, calculate all other trigonometric ratios.
Answer» Question 5 Given $s e c θ$ = $\frac{13}{12}$ , calculate all other trigonometric ratios.

Discussion

5.	In figure, ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove APCQ is a parallelogram
Answer» In figure, ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove APCQ is a parallelogram

Discussion

6.	The coordinates of point whose abscissa is 5 and which lies on x-axis, are _________.
Answer» The coordinates of point whose abscissa is 5 and which lies on x-axis, are _________.

Discussion

7.	Simplify each of the following and write as a single polynomial.(i) (ii) (iii) (iv) (v) (v)
Answer» Simplify each of the following and write as a single polynomial. (i) (ii) (iii) (iv) (v) (v)

7.

Simplify each of the following and write as a single polynomial.(i) (ii) (iii) (iv) (v) (v)

Answer»

Simplify each of the following and write as a single polynomial.

(i)

(ii)

(iii)

(iv)

(v)

Discussion

8.	Question 1 (x)Without actually performing the long division, state whether77210 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Answer» Question 1 (x) Without actually performing the long division, state whether $\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Discussion

9.	Calculate : (−57+821)×(73÷215)
Answer» Calculate : $(\frac{- 5}{7} + \frac{8}{21}) \times (\frac{7}{3} \div \frac{2}{15})$

Discussion

10.	For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.
Answer» For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.

Discussion

11.	Complete the following sentences:(i) Every point on the number line corresponds to a .... number which many be either ... or ...(ii) The decimal form of an irrational number is neither ... nor ...(iii) The decimal representation of a rational number is either ... or ...(iv) Every real number is either ... number or ... number.
Answer» Complete the following sentences: (i) Every point on the number line corresponds to a .... number which many be either ... or ... (ii) The decimal form of an irrational number is neither ... nor ... (iii) The decimal representation of a rational number is either ... or ... (iv) Every real number is either ... number or ... number.

Discussion

12.	Question 3(i)Find the products:(a2)×(2a22)×(4a26)
Answer» Question 3(i) Find the products: $(a^{2}) \times (2 a^{22}) \times (4 a^{26})$

Discussion

13.	Question 3 Insert a rational number and an irrational number between the following (i) 2 and 3 (ii) 0 and 0.1 (iii) 13 and 12 (iv) −25 and 12 (v) 0.15 and 0.16 (vi) √2 and √3 (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 3.375289 and 6.375738
Answer» Question 3 Insert a rational number and an irrational number between the following (i) 2 and 3 (ii) 0 and 0.1 (iii) $\frac{1}{3}$ and $\frac{1}{2}$ (iv) $\frac{- 2}{5}$ and $\frac{1}{2}$ (v) 0.15 and 0.16 (vi) $\sqrt{2}$ and $\sqrt{3}$ (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 3.375289 and 6.375738

Discussion

14.	In triangle ABC, points P and Q trisect side AB. Points T and U trisect side AC and points R and S trisect side BC. Then the perimeter of hexagon PQRSTU is how many times of the perimeter of triangle ABC?
Answer» In triangle ABC, points P and Q trisect side AB. Points T and U trisect side AC and points R and S trisect side BC. Then the perimeter of hexagon PQRSTU is how many times of the perimeter of triangle ABC?

Discussion

15.	In the figure, it is given that AB = AC and point D bisects the side BC. Find ∠ADC.
Answer» In the figure, it is given that AB = AC and point D bisects the side BC. Find $∠ A D C$ .

Discussion

16.	Let a circle has a radius of 5 cm and XY be its chord of length 6 cm.Find the distance of the chord from the center of the circle? (in cm)
Answer» Let a circle has a radius of $5$ cm and $X Y$ be its chord of length $6$ cm.Find the distance of the chord from the center of the circle? (in cm)

Discussion

17.	A set of numbers, denoted by letter Z, which include both positive and negative numbers that do not have fractional components is known as __.
Answer» A set of numbers, denoted by letter Z, which include both positive and negative numbers that do not have fractional components is known as __.

Discussion

18.	If 1.666666...... is a rational number and can be expressed in pq form, then find p + q.
Answer» If 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form, then find p + q.

Discussion

19.	Which of the following is equivalent to 1√6+1√5 ?
Answer» Which of the following is equivalent to $\frac{1}{\sqrt{6}} + \frac{1}{\sqrt{5}}$ ?

Discussion

20.	Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.
Answer» Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.

Discussion

21.	Draw 3-√2 on a number line
Answer» Draw 3-√2 on a number line

Discussion

22.	if f(x)=\|5-\|x\|\| and g(x)=7^-\|x\| then1. number of integral coordinates enclosed between the curve y=f(x) and x-axis is 162. number of solutions of f(X)=g(x) is 43. number of integral coordinates enclosed between f(x) and g(x) is 154. number of solutions of f(x)=g(x) is 2
Answer» if f(x)=\|5-\|x\|\| and g(x)=7^-\|x\| then 1. number of integral coordinates enclosed between the curve y=f(x) and x-axis is 16 2. number of solutions of f(X)=g(x) is 4 3. number of integral coordinates enclosed between f(x) and g(x) is 15 4. number of solutions of f(x)=g(x) is 2

Discussion

23.	"Lines in the same plane are parallel to each other if they do not intersect" This is stated in the form of:
Answer» "Lines in the same plane are parallel to each other if they do not intersect" This is stated in the form of:

23.

"Lines in the same plane are parallel to each other if they do not intersect" This is stated in the form of:

Answer»

"Lines in the same plane are parallel to each other if they do not intersect"

This is stated in the form of:

Discussion

24.	The mean of the series x1,x2,x3,.......,xn is ¯x. If x2 is replaced by λ, then the new mean is
Answer» The mean of the series $x_{1}, x_{2}, x_{3}, . . . . . . ., x_{n}$ is $¯ x$ . If $x_{2}$ is replaced by $λ$ , then the new mean is

Discussion

25.	Question 5 (iv) Rationalize the denominators of the following: 1(√7−2)
Answer» Question 5 (iv) Rationalize the denominators of the following: $\frac{1}{(\sqrt{7} - 2)}$

25.

Question 5 (iv) Rationalize the denominators of the following: 1(√7−2)

Answer»

Question 5 (iv)
Rationalize the denominators of the following:

$\frac{1}{(\sqrt{7} - 2)}$

Discussion

26.	Factorize:a2 + b2 + 2(ab + bc + ca)
Answer» Factorize: a² + b² + 2(ab + bc + ca)

Discussion

27.

On April 01, 2010, Bajrang Marbles purchased a Machine for Rs 1,80,000 and spent Rs 10,000 on its carriage and Rs 10,000 on its installation. It is estimated that its working life is 10 years and after 10 years its scrap value will be Rs 20,000. (a) Prepare Machine account and Depreciation account for the first four years by providing depreciation on straight line method. Accounts are closed on March 31st every year. (b) Prepare Machine account, Depreciation account and Provision for depreciation account (or accumulated depreciation account) for the first four years by providing depreciation using straight line method accounts are closed on March 31 every year.

Answer»

On April 01, 2010, Bajrang Marbles purchased a Machine for Rs 1,80,000 and spent Rs 10,000 on its carriage and Rs 10,000 on its installation. It is estimated that its working life is 10 years and after 10 years its scrap value will be Rs 20,000.

(a)	Prepare Machine account and Depreciation account for the first four years by providing depreciation on straight line method. Accounts are closed on March 31st every year.
(b)	Prepare Machine account, Depreciation account and Provision for depreciation account (or accumulated depreciation account) for the first four years by providing depreciation using straight line method accounts are closed on March 31 every year.

Discussion

28.	Question 4If a=3+√52, then find the value of a2+1a2.
Answer» Question 4 If $a = \frac{3 + \sqrt{5}}{2}$ , then find the value of $a^{2} + \frac{1}{a^{2}}$ .

Discussion

29.	Multiply 3+2√2×3-2√2
Answer» Multiply 3+2√2×3-2√2

Discussion

30.	Find the median of:32, 37, 43, 49, 52, 54, 66, 67, 72, 78
Answer» Find the median of: 32, 37, 43, 49, 52, 54, 66, 67, 72, 78

Discussion

31.	THE CIRCUMFERENCE OF A QUADRANT IS 22cm. CALCULATE ITS AREA.
Answer» THE CIRCUMFERENCE OF A QUADRANT IS 22cm. CALCULATE ITS AREA.

Discussion

32.	The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is(a) 307 cm(b) 1572cm(c) 1574cm(d) 30 cm
Answer» The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is (a) $30 \sqrt{7} c m$ (b) $\frac{15 \sqrt{7}}{2} c m$ (c) $\frac{15 \sqrt{7}}{4} c m$ (d) 30 cm

Discussion

33.	Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=x3-6x2+9x+3, gx=x-1.
Answer» Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where $p (x) = x^{3} - 6 x^{2} + 9 x + 3, g (x) = x - 1$ .

Discussion

34.	If we want to construct an angle of 7.5∘,how many times should we do angular bisection and what are the angles that we should bisect? Explain.
Answer» If we want to construct an angle of ${7.5}^{\circ}$ ,how many times should we do angular bisection and what are the angles that we should bisect? Explain.

Discussion

35.	In the given figure, O is the centre of the circle. The measure of ∠QPR is
Answer» In the given figure, O is the centre of the circle. The measure of $∠ Q P R$ is

Discussion

36.	Average performance by Ajay in all his exams has been 85%. The total marks are always 50.If there were exams in every quarter of the academic year, what is the total marks scored by him?
Answer» Average performance by Ajay in all his exams has been 85%. The total marks are always 50. If there were exams in every quarter of the academic year, what is the total marks scored by him?

36.

Average performance by Ajay in all his exams has been 85%. The total marks are always 50.If there were exams in every quarter of the academic year, what is the total marks scored by him?

Answer»

Average performance by Ajay in all his exams has been 85%. The total marks are always 50.

If there were exams in every quarter of the academic year, what is the total marks scored by him?

Discussion

37.	Construct an isosceles triangle whose two equal sides measure 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex
Answer» Construct an isosceles triangle whose two equal sides measure 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex

Discussion

38.	The probability of guessing the correct answer to a certain question is x3. If the probability of not guessing the correct answer is x3, then find x.
Answer» The probability of guessing the correct answer to a certain question is $\frac{x}{3}$ . If the probability of not guessing the correct answer is $\frac{x}{3}$ , then find $x$ .

Discussion

39.	If every side of a triangle is doubled, then increase in the area of the triangle is
Answer» If every side of a triangle is doubled, then increase in the area of the triangle is

Discussion

40.	State True or False. (i) Every natural number is a rational number.(ii) Every integer is a rational number.(iii) 0 is a whole number, but not a rational number.
Answer» State True or False. (i) Every natural number is a rational number. (ii) Every integer is a rational number. (iii) 0 is a whole number, but not a rational number.

40.

State True or False. (i) Every natural number is a rational number.(ii) Every integer is a rational number.(iii) 0 is a whole number, but not a rational number.

Answer» State True or False.

(i) Every natural number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number, but not a rational number.

Discussion

41.	Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
Answer» Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.

Discussion

42.

The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years: Years 1982 1983-1984 1984-1985 1985-1986 1986-1987 Value of Export of Cotton Textiles (in crores of rupees) 300 325 475 450 550 Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.

Answer» The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:

Years	1982	1983-1984	1984-1985	1985-1986	1986-1987
Value of Export of Cotton Textiles (in crores of rupees)	300	325	475	450	550

Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.

Discussion

43.	If the length of each edge of a cube increases by 20%, then the volume of the cube increases by _________.
Answer» If the length of each edge of a cube increases by 20%, then the volume of the cube increases by _________.

Discussion

44.	In the given Figure, line AB \|\| line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively.Prove that m ∠PTQ = 90 °.
Answer» In the given Figure, line AB \|\| line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of $∠$ BPQ and $∠$ PQD respectively. Prove that m $∠$ PTQ = 90 °.

Discussion

45.	if a is equal to x minus y,b is equal to Y minus Z and c is equal to z minus x then find the value of a3+b3+c3
Answer» if a is equal to x minus y,b is equal to Y minus Z and c is equal to z minus x then find the value of a3+b3+c3

Discussion

46.	If x=3-23+2 and y = 3+23-2 , then x2 + y +y2 =(a) 101(b) 99(c) 98(d) 102
Answer» If x= $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and y = $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , then x² + y +y² = (a) 101 (b) 99 (c) 98 (d) 102

Discussion

47.	Question 2 (ii) Find : 3225
Answer» Question 2 (ii) Find : $32^{\frac{2}{5}}$

Discussion

48.	1 Verify Euler's formula for a square pyramid.2 How are prisms and cylinders alike?
Answer» 1 Verify Euler's formula for a square pyramid. 2 How are prisms and cylinders alike?

Discussion

49.

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS. S1 : SX = XY S2 : XY = QY

Answer»

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS.

S1 : SX = XY

S2 : XY = QY

Discussion

50.	46.what is the remainder when (1000000)whole cube divided by 243
Answer» 46.what is the remainder when (1000000)whole cube divided by 243

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How to substitute√ in the given polynomial by remainder theorem

A truck carrier measures 10m×4m×5m. What will be the volume of sand that can be filled into the truck? [2 MARKS]

Question 9 In the figure, which of the two lines are parallel and why?

Question 5 Given sec θ = 1312, calculate all other trigonometric ratios.

In figure, ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove APCQ is a parallelogram

The coordinates of point whose abscissa is 5 and which lies on x-axis, are _________.

Simplify each of the following and write as a single polynomial.(i) (ii) (iii) (iv) (v) (v)

Question 1 (x)Without actually performing the long division, state whether77210 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Calculate : (−57+821)×(73÷215)

For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.

Question 3(i)Find the products:(a2)×(2a22)×(4a26)

Question 3 Insert a rational number and an irrational number between the following (i) 2 and 3 (ii) 0 and 0.1 (iii) 13 and 12 (iv) −25 and 12 (v) 0.15 and 0.16 (vi) √2 and √3 (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 3.375289 and 6.375738

In triangle ABC, points P and Q trisect side AB. Points T and U trisect side AC and points R and S trisect side BC. Then the perimeter of hexagon PQRSTU is how many times of the perimeter of triangle ABC?

In the figure, it is given that AB = AC and point D bisects the side BC. Find ∠ADC.

Let a circle has a radius of 5 cm and XY be its chord of length 6 cm.Find the distance of the chord from the center of the circle? (in cm)

A set of numbers, denoted by letter Z, which include both positive and negative numbers that do not have fractional components is known as __.

If 1.666666...... is a rational number and can be expressed in pq form, then find p + q.

Which of the following is equivalent to 1√6+1√5 ?

Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.

Draw 3-√2 on a number line

if f(x)=|5-|x|| and g(x)=7^-|x| then1. number of integral coordinates enclosed between the curve y=f(x) and x-axis is 162. number of solutions of f(X)=g(x) is 43. number of integral coordinates enclosed between f(x) and g(x) is 154. number of solutions of f(x)=g(x) is 2

"Lines in the same plane are parallel to each other if they do not intersect" This is stated in the form of:

The mean of the series x1,x2,x3,.......,xn is ¯x. If x2 is replaced by λ, then the new mean is

Question 5 (iv) Rationalize the denominators of the following: 1(√7−2)

Factorize:a2 + b2 + 2(ab + bc + ca)

Question 4If a=3+√52, then find the value of a2+1a2.

Multiply 3+2√2×3-2√2

Find the median of:32, 37, 43, 49, 52, 54, 66, 67, 72, 78

THE CIRCUMFERENCE OF A QUADRANT IS 22cm. CALCULATE ITS AREA.

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is(a) 307 cm(b) 1572cm(c) 1574cm(d) 30 cm

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), wherepx=x3-6x2+9x+3, gx=x-1.

If we want to construct an angle of 7.5∘,how many times should we do angular bisection and what are the angles that we should bisect? Explain.

In the given figure, O is the centre of the circle. The measure of ∠QPR is

Average performance by Ajay in all his exams has been 85%. The total marks are always 50.If there were exams in every quarter of the academic year, what is the total marks scored by him?

Construct an isosceles triangle whose two equal sides measure 6 cm each and whose base is 5 cm. Draw the perpendicular bisector of its base and show that it passes through the opposite vertex

The probability of guessing the correct answer to a certain question is x3. If the probability of not guessing the correct answer is x3, then find x.

If every side of a triangle is doubled, then increase in the area of the triangle is

State True or False. (i) Every natural number is a rational number.(ii) Every integer is a rational number.(iii) 0 is a whole number, but not a rational number.

Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.

If the length of each edge of a cube increases by 20%, then the volume of the cube increases by _________.

In the given Figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively.Prove that m ∠PTQ = 90 °.

if a is equal to x minus y,b is equal to Y minus Z and c is equal to z minus x then find the value of a3+b3+c3

If x=3-23+2 and y = 3+23-2 , then x2 + y +y2 =(a) 101(b) 99(c) 98(d) 102

Question 2 (ii) Find : 3225

1 Verify Euler's formula for a square pyramid.2 How are prisms and cylinders alike?

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS. S1 : SX = XY S2 : XY = QY

46.what is the remainder when (1000000)whole cube divided by 243