32581 + Interview Questions in Mathematics

1.	Question 7 In the figure, DE \|\| QR and AP and BP are bisectors of ∠EAB and ∠RBA, respectively. Find ∠APB.
Answer» Question 7 In the figure, DE \|\| QR and AP and BP are bisectors of $∠ E A B a n d ∠ R B A$ , respectively. Find $∠ A P B$ .

Discussion

2.	The length of the minute hand of a clock is 14 cm. What is the area swept by the minute hand in 5 minutes?
Answer» The length of the minute hand of a clock is 14 cm. What is the area swept by the minute hand in 5 minutes?

Discussion

3.	A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.
Answer» A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.

Discussion

4.	A and B are partners. A's Capital is ₹ 1,00,000 and B's Capital is ₹ 60,000. Interest on capital is payable 6% p.a. B is entitled to a salary of ₹ 3,000 per month. Profit for the current year before interest and salary to B is ₹ 80,000.Prepare Profit and Loss Appropriation Account.
Answer» A and B are partners. A's Capital is ₹ 1,00,000 and B's Capital is ₹ 60,000. Interest on capital is payable 6% p.a. B is entitled to a salary of ₹ 3,000 per month. Profit for the current year before interest and salary to B is ₹ 80,000. Prepare Profit and Loss Appropriation Account.

Discussion

5.	The angle between the minute and hour hands of a clock at 8:30 is
Answer» The angle between the minute and hour hands of a clock at 8:30 is

Discussion

6.	Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.
Answer» Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.

Discussion

7.	Find the roots of the quadratic equations by using the quadratic formula in the following equation:(i) 2x2−3x−5=0(ii) 5x2+13x+8=0(iii) −3x2+5x+12=0(iv) −x2+7x−10=0(v) x2+2√2x−6=0(vi) x2−3√5x+10=0(vii) 12x2−√11x+1=0
Answer» Find the roots of the quadratic equations by using the quadratic formula in the following equation: (i) $2 x^{2} - 3 x - 5 = 0$ (ii) $5 x^{2} + 13 x + 8 = 0$ (iii) $- 3 x^{2} + 5 x + 12 = 0$ (iv) $- x^{2} + 7 x - 10 = 0$ (v) $x^{2} + 2 \sqrt{2} x - 6 = 0$ (vi) $x^{2} - 3 \sqrt{5} x + 10 = 0$ (vii) $\frac{1}{2} x^{2} - \sqrt{11} x + 1 = 0$

Discussion

8.	Why do we make the coefficient of x2 equals 1 while solving a quadratic equation by completing the square method?
Answer» Why do we make the coefficient of x²equals 1 while solving a quadratic equation by completing the square method?

Discussion

9.	If a1,a2,a3,a4 are in AP, then
Answer» If $a_{1}, a_{2}, a_{3}, a_{4}$ are in AP, then

Discussion

10.	Find the median of the following data set.12 65 3 8 23 64 19 53 0 24 57 15 39
Answer» Find the median of the following data set. 12 65 3 8 23 64 19 53 0 24 57 15 39

10.

Find the median of the following data set.12 65 3 8 23 64 19 53 0 24 57 15 39

Answer»

Find the median of the following data set.

12 65 3 8 23 64 19 53 0 24 57 15 39

Discussion

11.	Question 76Solve the following:4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)
Answer» Question 76 Solve the following: 4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

11.

Question 76Solve the following:4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

Answer»

Question 76

Solve the following:

4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

Discussion

12.	Let f(x) = x/Tanx and g(x) = x cosecx where 0
Answer» Let f(x) = x/Tanx and g(x) = x cosecx where 0

Discussion

13.	Solve the following quadratic equation by factorization method 1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero
Answer» Solve the following quadratic equation by factorization method 1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

13.

Solve the following quadratic equation by factorization method 1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

Answer»

Solve the following quadratic equation by factorization method

1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

Discussion

14.	A number consists of two digits whose sum is 9. If 27 is added to the number, the digits change their places. Find the number.
Answer» A number consists of two digits whose sum is 9. If 27 is added to the number, the digits change their places. Find the number.

Discussion

15.	If 2 and 5 are factors of a number, what will be the unit’s digit of that number?
Answer» If 2 and 5 are factors of a number, what will be the unit’s digit of that number?

Discussion

16.	The relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of it's volume is 1) 0.027 2) 0.054 3) 0.081 4) 0.046
Answer» The relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of it's volume is 1) 0.027 2) 0.054 3) 0.081 4) 0.046

Discussion

17.	Find the sum of the first 10 natural numbers.(Use S10=1+2+3+…+10 and proceed)
Answer» Find the sum of the first 10 natural numbers. (Use $S_{10} = 1 + 2 + 3 + \dots + 10$ and proceed)

Discussion

18.	If 2 is added to each of two given numbers,their ratio becomes 1:2.However,if 4 is subtracted from each of the given numbers,the ratio becomes 5:11.Find the numbers.
Answer» If 2 is added to each of two given numbers,their ratio becomes 1:2.However,if 4 is subtracted from each of the given numbers,the ratio becomes 5:11.Find the numbers.

Discussion

19.	The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.
Answer» The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.

Discussion

20.	Question 1 (iii)For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?
Answer» Question 1 (iii) For what value(s) of $λ$ , does the pair of linear equations $λ x + y = λ^{2} a n d x + λ y = 1$ have a unique solution?

Discussion

21.	5. What is meant by significant figures?
Answer» 5. What is meant by significant figures?

Discussion

22.	Question 7A cylinderical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m2. How many revolutions did it make?
Answer» Question 7 A cylinderical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of $5500 m^{2}$ . How many revolutions did it make?

Discussion

23.	ABCD is a trapezium with AB ∥ DC. A line parallel to AC intersects AB at X and BC at Y.Prove that ar (△ADX) = ar (△ACY). [3 MARKS]
Answer» ABCD is a trapezium with AB $∥$ DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar ( $△$ ADX) = ar ( $△$ ACY). [3 MARKS]

Discussion

24.	The sum of two numbers is 8. If their sum is four times their difference, find the numbers.
Answer» The sum of two numbers is $8$ . If their sum is four times their difference, find the numbers.

Discussion

25.	A shopkeeper has 50 kg sugar. He sells (17)th of it at ₹21/kg,(37)th of it at ₹35/kg, and the remaining at ₹28/kg. How much money did he collect by selling the sugar?
Answer» A shopkeeper has $50 k g$ sugar. He sells $(\frac{1}{7})^{t h}$ of it at $₹ 21 / k g, (\frac{3}{7})^{t h}$ of it at $₹ 35 / k g$ , and the remaining at $₹ 28 / k g$ . How much money did he collect by selling the sugar?

Discussion

26.	Solve for x and y:23x+2y+33x-2y=17553x+2y+13x-2y=2
Answer» Solve for x and y: $\frac{2}{(3 x + 2 y)} + \frac{3}{(3 x - 2 y)} = \frac{17}{5} \frac{5}{(3 x + 2 y)} + \frac{1}{(3 x - 2 y)} = 2$

Discussion

27.	A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.
Answer» A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.

Discussion

28.	Question 6The 26th, 11th and the last terms of an AP are 0, 3 and −15, respectively. Find the common difference and the number of terms.
Answer» Question 6 The $26^{t h}, 11^{t h}$ and the last terms of an AP are 0, 3 and $- \frac{1}{5}$ , respectively. Find the common difference and the number of terms.

Discussion

29.	5. Find the locus of centres of circles which tuoch two intersecting lines
Answer» 5. Find the locus of centres of circles which tuoch two intersecting lines

Discussion

30.	The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.
Answer» The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.

Discussion

31.	In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?
Answer» In $△ A B C$ , B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

31.

In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

Answer»

In $△ A B C$ , B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

Discussion

32.	In the figure given below, the radius of the circle is 42cm. The angle in the sector is 60∘. What is the area of the segment APB?
Answer» In the figure given below, the radius of the circle is 42cm. The angle in the sector is $60^{\circ}$ . What is the area of the segment APB?

Discussion

33.	Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
Answer» Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

Discussion

34.	A conical hoe is drilled in a circular cylinder of height 12 cm and base radius 5 cm.The height and the base radius of the cone are also the same.Find the whole surface and volume of the remaining cylinder.
Answer» A conical hoe is drilled in a circular cylinder of height 12 cm and base radius 5 cm.The height and the base radius of the cone are also the same.Find the whole surface and volume of the remaining cylinder.

Discussion

35.	Question 1 (ii)Find the roots of the quadratic equations by using the quadratic formula in the following question 5x2+13x+8=0.
Answer» Question 1 (ii) Find the roots of the quadratic equations by using the quadratic formula in the following question $5 x^{2} + 13 x + 8 = 0$ .

35.

Question 1 (ii)Find the roots of the quadratic equations by using the quadratic formula in the following question 5x2+13x+8=0.

Answer»

Question 1 (ii)

Find the roots of the quadratic equations by using the quadratic formula in the following question $5 x^{2} + 13 x + 8 = 0$ .

Discussion

36.	13. Find the locus of the mid points of the chords of the circle X² + Y² =16 that subtends a right angle at origin
Answer» 13. Find the locus of the mid points of the chords of the circle X² + Y² =16 that subtends a right angle at origin

Discussion

37.	Pair the quadratic equation to its graph.
Answer» Pair the quadratic equation to its graph.

Discussion

38.	If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then prove that PA is angle bisector of ∠BPC.
Answer» If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then prove that PA is angle bisector of $∠ B P C$ .

Discussion

39.	What are the factors of x2+5x−24?
Answer» What are the factors of $x^{2} + 5 x - 24$ ?

Discussion

40.	The probability that a year chosen at ramdom has 53 Sundays is given by:(1)1/7 (2)2/7 (3)5/28 (4)3/
Answer» The probability that a year chosen at ramdom has 53 Sundays is given by:(1)1/7 (2)2/7 (3)5/28 (4)3/

Discussion

41.	In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π = 3.14] [CBSE 2014]
Answer» In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π = 3.14] [CBSE 2014]

Discussion

42.	As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30o and 45o. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3=1.732]
Answer» As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are $30^{o}$ and $45^{o}$ . If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use $\sqrt{3} = 1.732$ ]

Discussion

43.	The distance between the points (5, 5) and (3, 3) is ___.
Answer» The distance between the points (5, 5) and (3, 3) is ___.

Discussion

44.	Find the variance and s†an dard deviation of 3,6,9,12,15,18,21,24,27,3
Answer» Find the variance and s†an dard deviation of 3,6,9,12,15,18,21,24,27,3

Discussion

45.	A man buys a number of pens for Rs.180. If he had bought 3 more pens for the same amount, each pen would have cost him Rs.3 less. How many pens did he buy?
Answer» A man buys a number of pens for Rs.180. If he had bought 3 more pens for the same amount, each pen would have cost him Rs.3 less. How many pens did he buy?

Discussion

46.	A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?
Answer» A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Discussion

47.	58.If the points P(m,n), Q(-3,-1) and R(3,4) are such that PQ=PR, then (1) m=n (2) 10n+12m= 15 (3) 5n+6m=7 (4)10n-12m=9
Answer» 58.If the points P(m,n), Q(-3,-1) and R(3,4) are such that PQ=PR, then (1) m=n (2) 10n+12m= 15 (3) 5n+6m=7 (4)10n-12m=9

Discussion

48.	Question 2Prove that one and only one out of n, (n + 2) and (n + 4) is divisible by 3, where n is any positive integer.
Answer» Question 2 Prove that one and only one out of n, (n + 2) and (n + 4) is divisible by 3, where n is any positive integer.

Discussion

49.	Question 3From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.
Answer» Question 3 From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

Discussion

50.	The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum.
Answer» The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 7 In the figure, DE || QR and AP and BP are bisectors of ∠EAB and ∠RBA, respectively. Find ∠APB.

The length of the minute hand of a clock is 14 cm. What is the area swept by the minute hand in 5 minutes?

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.

A and B are partners. A's Capital is ₹ 1,00,000 and B's Capital is ₹ 60,000. Interest on capital is payable 6% p.a. B is entitled to a salary of ₹ 3,000 per month. Profit for the current year before interest and salary to B is ₹ 80,000.Prepare Profit and Loss Appropriation Account.

The angle between the minute and hour hands of a clock at 8:30 is

Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.

Find the roots of the quadratic equations by using the quadratic formula in the following equation:​(i) 2x2−3x−5=0(ii) 5x2+13x+8=0(iii) −3x2+5x+12=0(iv) −x2+7x−10=0(v) x2+2√2x−6=0(vi) x2−3√5x+10=0(vii) 12x2−√11x+1=0

Why do we make the coefficient of x2 equals 1 while solving a quadratic equation by completing the square method?

If a1,a2,a3,a4 are in AP, then

Find the median of the following data set.12 65 3 8 23 64 19 53 0 24 57 15 39

Question 76Solve the following:4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)

Let f(x) = x/Tanx and g(x) = x cosecx where 0

Solve the following quadratic equation by factorization method 1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

A number consists of two digits whose sum is 9. If 27 is added to the number, the digits change their places. Find the number.

If 2 and 5 are factors of a number, what will be the unit’s digit of that number?

The relative error in the measurement of the side of a cube is 0.027. The relative error in the measurement of it's volume is 1) 0.027 2) 0.054 3) 0.081 4) 0.046

Find the sum of the first 10 natural numbers.(Use S10=1+2+3+…+10 and proceed)

If 2 is added to each of two given numbers,their ratio becomes 1:2.However,if 4 is subtracted from each of the given numbers,the ratio becomes 5:11.Find the numbers.

The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.

Question 1 (iii)For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?

5. What is meant by significant figures?

Question 7A cylinderical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m2. How many revolutions did it make?

ABCD is a trapezium with AB ∥ DC. A line parallel to AC intersects AB at X and BC at Y.Prove that ar (△ADX) = ar (△ACY). [3 MARKS]

The sum of two numbers is 8. If their sum is four times their difference, find the numbers.

A shopkeeper has 50 kg sugar. He sells (17)th of it at ₹21/kg,(37)th of it at ₹35/kg, and the remaining at ₹28/kg. How much money did he collect by selling the sugar?

Solve for x and y:23x+2y+33x-2y=17553x+2y+13x-2y=2

A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.

Question 6The 26th, 11th and the last terms of an AP are 0, 3 and −15, respectively. Find the common difference and the number of terms.

5. Find the locus of centres of circles which tuoch two intersecting lines

The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.

In △ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Which of the following is true?

In the figure given below, the radius of the circle is 42cm. The angle in the sector is 60∘​. What is the area of the segment APB?

Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.

A conical hoe is drilled in a circular cylinder of height 12 cm and base radius 5 cm.The height and the base radius of the cone are also the same.Find the whole surface and volume of the remaining cylinder.

Question 1 (ii)Find the roots of the quadratic equations by using the quadratic formula in the following question 5x2+13x+8=0.

13. Find the locus of the mid points of the chords of the circle X² + Y² =16 that subtends a right angle at origin

Pair the quadratic equation to its graph.

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then prove that PA is angle bisector of ∠BPC.

What are the factors of x2+5x−24?

The probability that a year chosen at ramdom has 53 Sundays is given by:(1)1/7 (2)2/7 (3)5/28 (4)3/

In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside' the region. Find the area of the shaded region. [Use π = 3.14] [CBSE 2014]

As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30o and 45o. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3=1.732]

The distance between the points (5, 5) and (3, 3) is ___.

Find the variance and s†an dard deviation of 3,6,9,12,15,18,21,24,27,3

A man buys a number of pens for Rs.180. If he had bought 3 more pens for the same amount, each pen would have cost him Rs.3 less. How many pens did he buy?

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

58.If the points P(m,n), Q(-3,-1) and R(3,4) are such that PQ=PR, then (1) m=n (2) 10n+12m= 15 (3) 5n+6m=7 (4)10n-12m=9

Question 2Prove that one and only one out of n, (n + 2) and (n + 4) is divisible by 3, where n is any positive integer.

Question 3From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum.

Find the roots of the quadratic equations by using the quadratic formula in the following equation:(i) 2x2−3x−5=0(ii) 5x2+13x+8=0(iii) −3x2+5x+12=0(iv) −x2+7x−10=0(v) x2+2√2x−6=0(vi) x2−3√5x+10=0(vii) 12x2−√11x+1=0

In the figure given below, the radius of the circle is 42cm. The angle in the sector is 60∘. What is the area of the segment APB?