32581 + Interview Questions in Mathematics

1.	Is finding roots of quadratic equation same as finding zeroes of it
Answer» Is finding roots of quadratic equation same as finding zeroes of it

Discussion

2.	Question 3 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» Question 3 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

3.	The discriminant of the equation 2x2−5x−2=0 is = ___.
Answer» The discriminant of the equation $2 x^{2} - 5 x - 2 = 0$ is = ___.

Discussion

4.	Question 6 Value(s) of K for which the quadratic equation 2x2 =- kx = 0 are equal root is are (A) 0 only (B) 4 (C) 8 only (D) 0, 8
Answer» Question 6 Value(s) of K for which the quadratic equation $2 x^{2}$ =- kx = 0 are equal root is are (A) 0 only (B) 4 (C) 8 only (D) 0, 8

Discussion

5.	A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
Answer» A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

Discussion

6.	Find the two numbers which pn multplication with √180 gives a rational number.
Answer» Find the two numbers which pn multplication with √180 gives a rational number.

Discussion

7.	Given tan(A+B)=√3 and tan(A−B)=1√3 If B<A<90∘, then, ∠B = ___ (If your answer is 20∘, then type 20)
Answer» Given $t a n (A + B) = \sqrt{3}$ and $t a n (A - B) = \frac{1}{\sqrt{3}}$ If $B < A < 90^{\circ}$ , then, $∠ B$ = ___ (If your answer is $20^{\circ}$ , then type 20)

Discussion

8.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

9.	Using trigonometric tables, find the value of sin(25.7)∘.
Answer» Using trigonometric tables, find the value of $s i n (25.7)^{\circ}$ .

Discussion

10.	The area of right-angled triangle is 96m3. If its base is three times its altitude, find the base.
Answer» The area of right-angled triangle is 96m³. If its base is three times its altitude, find the base.

Discussion

11.	In the given figure, A is the centre of the circle. ∠ABC=45o and AC=7√2cm. Find the area of segment BXC. (Use π=227 )
Answer» In the given figure, A is the centre of the circle. $∠ A B C = 45^{o}$ and $A C = 7 \sqrt{2} c m .$ Find the area of segment BXC. (Use $π = \frac{22}{7}$ )

Discussion

12.	Prove that root 2 + root 5 is an irrational number
Answer» Prove that root 2 + root 5 is an irrational number

Discussion

13.	The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.
Answer» The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

Discussion

14.	Question 16 In the figure, line segment DF intersects the side AC of a ΔABC at the point E such that E is the midpoint of CA and ∠AEF and ∠AFE. Prove that BDCD=BFCE.
Answer» Question 16 In the figure, line segment DF intersects the side AC of a $Δ A B C$ at the point E such that E is the midpoint of CA and $∠ A E F$ and $∠ A F E$ . Prove that $\frac{B D}{C D} = \frac{B F}{C E}$ .

Discussion

15.	Question 7 (ii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ₹ 250 and it increases by ₹ 50 for the next higher class.
Answer» Question 7 (ii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ₹ 250 and it increases by ₹ 50 for the next higher class.

Discussion

16.	(5cos²60+4sec²30-tan²45)÷(sin²30sin²30+cos²30)
Answer» (5cos²60+4sec²30-tan²45)÷(sin²30sin²30+cos²30)

Discussion

17.	For 10th grade (Q) Use Euclid's division lemma to show cube of any positive integer is of the form 9m, 9m+1 or 9m+8. (Please do provide an explanation....Thank you)
Answer» For 10th grade (Q) Use Euclid's division lemma to show cube of any positive integer is of the form 9m, 9m+1 or 9m+8. (Please do provide an explanation....Thank you)

Discussion

18.	Suman brought a fridge for Rs. 23760 which includes a sales tax of 8%. The customer also got 12% discount on marked price of fridge. The marked price of fridge is equal to Rs.__________
Answer» Suman brought a fridge for Rs. 23760 which includes a sales tax of 8%. The customer also got 12% discount on marked price of fridge. The marked price of fridge is equal to Rs.__________

Discussion

19.	A company with 10,000 shares of nominal value of Rs 100 declares an annual dividend of 8% to the shareholders. (i) Calculate the amount of dividend paid by the company. (ii) Ramesh had bought 90 shares of the company at Rs 150 per share. Calculate the dividend he receives and the percentage return on his investment. [4 MARKS]
Answer» A company with 10,000 shares of nominal value of Rs 100 declares an annual dividend of $8 %$ to the shareholders. (i) Calculate the amount of dividend paid by the company. (ii) Ramesh had bought 90 shares of the company at Rs 150 per share. Calculate the dividend he receives and the percentage return on his investment. [4 MARKS]

Discussion

20.	If α and β are zero 's of x2+7x+7find value of 1/α+1/β-2αβ
Answer» If α and β are zero 's of x^{2_{+7x+7find value of 1/α+1/β-2αβ}}

Discussion

21.	The sum of n terms of an AP is n^2+3n . Find its 20^th term
Answer» The sum of n terms of an AP is n^2+3n . Find its 20^th term

Discussion

22.	How to visualize a section formula through area. Because I do not able to understand in byju's tablet clearly.
Answer» How to visualize a section formula through area. Because I do not able to understand in byju's tablet clearly.

Discussion

23.	Ramu was stacking ₹1 coins as a tower. What could be the volume, if Ramu stacked 50 ₹1 coins as a tower?
Answer» Ramu was stacking ₹1 coins as a tower. What could be the volume, if Ramu stacked 50 ₹1 coins as a tower?

Discussion

24.	Solve for x and y: 3x−1y+9=0,2x+3y=5 (x≠0,y≠0).
Answer» Solve for x and y: $\frac{3}{x} - \frac{1}{y} + 9 = 0, \frac{2}{x} + \frac{3}{y} = 5 (x \neq 0, y \neq 0) .$

24.

Solve for x and y: 3x−1y+9=0,2x+3y=5 (x≠0,y≠0).

Answer»

Solve for x and y:

$\frac{3}{x} - \frac{1}{y} + 9 = 0, \frac{2}{x} + \frac{3}{y} = 5 (x \neq 0, y \neq 0) .$

Discussion

25.	Solve the quadratic equationn x2−5x−10=0 correct to 2 decimal places.
Answer» Solve the quadratic equationn $x^{2} - 5 x - 10 = 0$ correct to 2 decimal places.

Discussion

26.	Rational expression y3−8y2−4 written in its lowest form is .
Answer» Rational expression $\frac{y^{3} - 8}{y^{2} - 4}$ written in its lowest form is .

Discussion

27.	A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π=3.14). [3 MARKS]
Answer» A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use $π = 3.14$ ). [3 MARKS]

27.

A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π=3.14). [3 MARKS]

Answer»

A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use $π = 3.14$ ). [3 MARKS]

Discussion

28.	Question 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is a) 25 cm b) 20 cm c) 26 cm d) 3.5 cm
Answer» Question 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is a) 25 cm b) 20 cm c) 26 cm d) 3.5 cm

Discussion

29.	In a seminar, the numberof participants in Hindi, English and mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.
Answer» In a seminar, the numberof participants in Hindi, English and mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

Discussion

30.	The orthocentre of the triangle with vertices (2,√3−12),(12,−12)and(2,−12) is
Answer» The orthocentre of the triangle with vertices $(2, \frac{\sqrt{3} - 1}{2}), (\frac{1}{2}, - \frac{1}{2}) a n d (2, - \frac{1}{2})$ is

Discussion

31.	Find the slope of a line perpendicular to a line whose slope is 1.
Answer» Find the slope of a line perpendicular to a line whose slope is 1.

Discussion

32.	ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 1100 and angle BAC = 500. Select the statements that are true.
Answer» ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = $110^{0}$ and angle BAC = $50^{0}$ . Select the statements that are true.

32.

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 1100 and angle BAC = 500. Select the statements that are true.

Answer»

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = $110^{0}$ and angle BAC = $50^{0}$ . Select the statements that are true.

Discussion

33.	A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
Answer» A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Discussion

34.	In Fig. 8.68, common tangents PQ and RS to two circles intersect at A. Prove that PQ=RS.
Answer» In Fig. 8.68, common tangents PQ and RS to two circles intersect at A. Prove that PQ=RS.

Discussion

35.	If f(x)=x+1x, x ≠ 0; then (f(x)]3=
Answer» If $f (x) = x + \frac{1}{x}, x \neq 0; then {(f (x)]}^{3} =$

Discussion

36.	While calculating the mean of a given data by the assumed-mean method,the following values were obtained: A=25, ∑fidi=110,∑fi=50. Find the mean.
Answer» While calculating the mean of a given data by the assumed-mean method,the following values were obtained: A=25, $\sum f_{i} d_{i} = 110, \sum f_{i} = 50.$ Find the mean.

36.

While calculating the mean of a given data by the assumed-mean method,the following values were obtained: A=25, ∑fidi=110,∑fi=50. Find the mean.

Answer»

While calculating the mean of a given data by the assumed-mean method,the following values were obtained:

A=25, $\sum f_{i} d_{i} = 110, \sum f_{i} = 50.$

Find the mean.

Discussion

37.	Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the line joining of the middle points of its diagonals meet in a point and bisect one another.
Answer» Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the line joining of the middle points of its diagonals meet in a point and bisect one another.

Discussion

38.	Water is flowing at the rate of 15 kmph through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm ?
Answer» Water is flowing at the rate of 15 kmph through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm ?

Discussion

39.	The value of cos 30∘ is
Answer» The value of $cos$ $30^{\circ}$ is

Discussion

40.	The volume of a right circular cone is 110 m3 and diameter is 2√15. Calculate i.) Slant height ii.) Curved Surface area and iii.) Height of the cone
Answer» The volume of a right circular cone is 110 $m^{3}$ and diameter is 2 $\sqrt{15}$ . Calculate i.) Slant height ii.) Curved Surface area and iii.) Height of the cone

Discussion

41.	A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied? [2 MARKS]
Answer» A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied? [2 MARKS]

Discussion

42.	Find the slope of the line passing through the points A(4,-1) and B(-3,5).
Answer» Find the slope of the line passing through the points A(4,-1) and B(-3,5).

Discussion

43.	Question 4 Diagonals of a trapezium PQRS intersect each other at the point O, PQIIRS and PQ = 3 RS. Find the ratio of the areas of ΔPOQ and ΔROS.
Answer» Question 4 Diagonals of a trapezium PQRS intersect each other at the point O, PQIIRS and PQ = 3 RS. Find the ratio of the areas of $Δ$ POQ and $Δ$ ROS.

Discussion

44.	Question 20(ii) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?
Answer» Question 20(ii) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

Discussion

45.	Question 6 From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.
Answer» Question 6 From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Discussion

46.	A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.
Answer» A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string, assuming that there is no slack in the string.

Discussion

47.	The median for grouped data is formed by using the formula:
Answer» The median for grouped data is formed by using the formula:

Discussion

48.	Question: Ajay and Vijay solved a quadratic equation. In solving it, Ajay made a mistake in the constant term and got the roots as 6 and 2, while Vijay made a mistake in the coefficient of x only and obtained the roots as –7 and –1. The correct roots of the equations. In answer it is written Ajay sum of the root is correct but if he done mistake in constant term his roots will be in correct.please explain in details
Answer» Question: Ajay and Vijay solved a quadratic equation. In solving it, Ajay made a mistake in the constant term and got the roots as 6 and 2, while Vijay made a mistake in the coefficient of x only and obtained the roots as –7 and –1. The correct roots of the equations. In answer it is written Ajay sum of the root is correct but if he done mistake in constant term his roots will be in correct.please explain in details

48.

Question: Ajay and Vijay solved a quadratic equation. In solving it, Ajay made a mistake in the constant term and got the roots as 6 and 2, while Vijay made a mistake in the coefficient of x only and obtained the roots as –7 and –1. The correct roots of the equations. In answer it is written Ajay sum of the root is correct but if he done mistake in constant term his roots will be in correct.please explain in details

Answer»

Question:

Ajay and Vijay solved a quadratic equation. In solving it, Ajay made a mistake in the constant term and got the roots as 6 and 2, while Vijay made a mistake in the coefficient of x only and obtained the roots as –7 and –1. The correct roots of the equations. In answer it is written Ajay sum of the root is correct but if he done mistake in constant term his roots will be in correct.please explain in details

Discussion

49.	Find the value of p for which the lines 2x+3y−7=0 and 4y−px−12=0 are perpendicular to each other.
Answer» Find the value of p for which the lines $2 x + 3 y - 7 = 0$ and $4 y - p x - 12 = 0$ are perpendicular to each other.

Discussion

50.	Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line: 3x-7 > 2(x-6),6-x > 11 -2x
Answer» Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line: 3x-7 > 2(x-6),6-x > 11 -2x

50.

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line: 3x-7 > 2(x-6),6-x > 11 -2x

Answer»

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line:

3x-7 > 2(x-6),6-x > 11 -2x

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Is finding roots of quadratic equation same as finding zeroes of it

Question 3 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.

The discriminant of the equation 2x2−5x−2=0 is = ___.

Question 6 Value(s) of K for which the quadratic equation 2x2 =- kx = 0 are equal root is are (A) 0 only (B) 4 (C) 8 only (D) 0, 8​​​​​​

A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

Find the two numbers which pn multplication with √180 gives a rational number.

Given tan(A+B)=√3 and tan(A−B)=1√3 If B&lt;A&lt;90∘, then, ∠B = ___ (If your answer is 20∘, then type 20)

Which of the following should be the LAST sentence after rearrangement?

Using trigonometric tables, find the value of sin(25.7)∘.

The area of right-angled triangle is 96m3. If its base is three times its altitude, find the base.

In the given figure, A is the centre of the circle. ∠ABC=45o and AC=7√2cm. Find the area of segment BXC. (Use π=227 )

Prove that root 2 + root 5 is an irrational number

The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

Question 16 In the figure, line segment DF intersects the side AC of a ΔABC at the point E such that E is the midpoint of CA and ∠AEF and ∠AFE. Prove that BDCD=BFCE.

Question 7 (ii) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ₹ 250 and it increases by ₹ 50 for the next higher class.

(5cos²60+4sec²30-tan²45)÷(sin²30sin²30+cos²30)

*For 10th grade* (Q) Use Euclid's division lemma to show cube of any positive integer is of the form 9m, 9m+1 or 9m+8. (Please do provide an explanation....Thank you)

Suman brought a fridge for Rs. 23760 which includes a sales tax of 8%. The customer also got 12% discount on marked price of fridge. The marked price of fridge is equal to Rs.__________

If α and β are zero 's of x2​​​​​+7x+7find value of 1/α+1/β-2αβ

The sum of n terms of an AP is n^2+3n . Find its 20^th term

How to visualize a section formula through area. Because I do not able to understand in byju's tablet clearly.

Ramu was stacking ₹1 coins as a tower. What could be the volume, if Ramu stacked 50 ₹1 coins as a tower?

Solve for x and y: 3x−1y+9=0,2x+3y=5 (x≠0,y≠0).

Solve the quadratic equationn x2−5x−10=0 correct to 2 decimal places.

Rational expression y3−8y2−4 written in its lowest form is .

Question 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is a) 25 cm b) 20 cm c) 26 cm d) 3.5 cm

In a seminar, the numberof participants in Hindi, English and mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.

The orthocentre of the triangle with vertices (2,√3−12),(12,−12)and(2,−12) is

Find the slope of a line perpendicular to a line whose slope is 1.

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 1100 and angle BAC = 500. Select the statements that are true.

A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

In Fig. 8.68, common tangents PQ and RS to two circles intersect at A. Prove that PQ=RS.

If f(x)=x+1x, x ≠ 0; then (f(x)]3=

While calculating the mean of a given data by the assumed-mean method,the following values were obtained: A=25, ∑fidi=110,∑fi=50. Find the mean.

Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the line joining of the middle points of its diagonals meet in a point and bisect one another.

Water is flowing at the rate of 15 kmph through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm ?

The value of cos 30∘ is

The volume of a right circular cone is 110 m3 and diameter is 2√15. Calculate i.) Slant height ii.) Curved Surface area and iii.) Height of the cone

A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied? [2 MARKS]

Find the slope of the line passing through the points A(4,-1) and B(-3,5).

Question 4 Diagonals of a trapezium PQRS intersect each other at the point O, PQIIRS and PQ = 3 RS. Find the ratio of the areas of ΔPOQ and ΔROS.

Question 20(ii) Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

Question 6 From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.

The median for grouped data is formed by using the formula:

Find the value of p for which the lines 2x+3y−7=0 and 4y−px−12=0 are perpendicular to each other.

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line: 3x-7 &gt; 2(x-6),6-x &gt; 11 -2x

Question 6 Value(s) of K for which the quadratic equation 2x2 =- kx = 0 are equal root is are (A) 0 only (B) 4 (C) 8 only (D) 0, 8

Given tan(A+B)=√3 and tan(A−B)=1√3 If B<A<90∘, then, ∠B = ___ (If your answer is 20∘, then type 20)

For 10th grade (Q) Use Euclid's division lemma to show cube of any positive integer is of the form 9m, 9m+1 or 9m+8. (Please do provide an explanation....Thank you)

If α and β are zero 's of x2+7x+7find value of 1/α+1/β-2αβ

Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line: 3x-7 > 2(x-6),6-x > 11 -2x