32581 + Interview Questions in Mathematics

1.

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Number of mangoes 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64 Number of boxes 15 110 135 115 25 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Answer»

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	50 − 52	53 − 55	56 − 58	59 − 61	62 − 64
Number of boxes	15	110	135	115	25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Discussion

2.	Define cardinality of a set.
Answer» Define cardinality of a set.

Discussion

3.	If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.
Answer» If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.

Discussion

4.	Solve for x and y by method of cross multiplication: 3x+2y+25=0 2x+y+10=0
Answer» Solve for x and y by method of cross multiplication: $3 x + 2 y + 25 = 0$ $2 x + y + 10 = 0$

Discussion

5.	Question 3A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Answer» Question 3 A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

Discussion

6.	The x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is_______.
Answer» The x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is_______.

Discussion

7.	Obtain the condition for the following system of linear equations to have a unique solution ax + by = c lx + my = n
Answer» Obtain the condition for the following system of linear equations to have a unique solution ax + by = c lx + my = n

7.

Obtain the condition for the following system of linear equations to have a unique solution ax + by = c lx + my = n

Answer»

Obtain the condition for the following system of linear equations to have a unique solution

ax + by = c

lx + my = n

Discussion

8.	Choose the correct answer in each of the following questions:Which term of the AP 72, 63, 54, ... is 0?(a) 8th (b) 9th (c) 10th (d) 11th
Answer» Choose the correct answer in each of the following questions: Which term of the AP 72, 63, 54, ... is 0? (a) 8th (b) 9th (c) 10th (d) 11th

Discussion

9.	What is the value of sin θ for the given right triangle, right angled at B?
Answer» What is the value of sin $θ$ for the given right triangle, right angled at B?

9.

What is the value of sin θ for the given right triangle, right angled at B?

Answer»

What is the value of sin $θ$ for the given right triangle, right angled at B?

Discussion

10.	Find the volume of a cuboid whose base area is 10 square metres and the height is 5 metre.
Answer» Find the volume of a cuboid whose base area is 10 square metres and the height is 5 metre.

Discussion

11.	Verify that the number given along each of the cubic polynomial below are its zeros if it is so then verify the relationship between the zeros and the cofficients in each case. I) 6x³+5x²-2x-1;-1/3, 1/2, -1II) 2x³+3x²+√3x+1;-2, -1, -1/2
Answer» Verify that the number given along each of the cubic polynomial below are its zeros if it is so then verify the relationship between the zeros and the cofficients in each case. I) 6x³+5x²-2x-1;-1/3, 1/2, -1 II) 2x³+3x²+√3x+1;-2, -1, -1/2

Discussion

12.	In the given figure, PA, QB and RC are each perpendicular to AC. Prove that 1x+1z=1y.
Answer» In the given figure, PA, QB and RC are each perpendicular to AC. Prove that $\frac{1}{x} + \frac{1}{z} = \frac{1}{y}$ .

Discussion

13.	A parachutist is descending vertically and makes angles of elevation of 45° and 60° at two observing points 100 m apart from each other on the left side of himself. Find the maximum height from which he falls and the distance of the point where he falls on the ground form the just observation point.
Answer» A parachutist is descending vertically and makes angles of elevation of 45° and 60° at two observing points 100 m apart from each other on the left side of himself. Find the maximum height from which he falls and the distance of the point where he falls on the ground form the just observation point.

Discussion

14.	In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB \|\|\| ΔTPQ.
Answer» In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB \|\|\| ΔTPQ.

14.

In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB ||| ΔTPQ.

Answer»

In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB ||| ΔTPQ.

Discussion

15.	Apply Euclid’s lemma on 36 and 5 and find the value of q and r such that 36=q×5+r.
Answer» Apply Euclid’s lemma on 36 and 5 and find the value of q and r such that $36 = q \times 5 + r .$

Discussion

16.	In the given figure, a triangel ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point o f contant D, are of lengths 6 cm and 9 cm respectively. If the area of Δ = 54 cm2 then find the lengths of sides AB and AC.
Answer» In the given figure, a triangel ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point o f contant D, are of lengths 6 cm and 9 cm respectively. If the area of $Δ$ = 54 $c m^{2}$ then find the lengths of sides AB and AC.

16.

In the given figure, a triangel ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point o f contant D, are of lengths 6 cm and 9 cm respectively. If the area of Δ = 54 cm2 then find the lengths of sides AB and AC.

Answer»

In the given figure, a triangel ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point o f contant D, are of lengths 6 cm and 9 cm respectively. If the area of $Δ$ = 54 $c m^{2}$ then find the lengths of sides AB and AC.

Discussion

17.	The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2 Class: 0-20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency: 5 f1 10 f2 7 8
Answer» The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $f_{1}$ and $f_{2}$ Class: 0-20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency: 5 $f_{1}$ 10 $f_{2}$ 7 8

Discussion

18.	Find the 11th term from the last term (towards the first term) of the AP : 10,7,4,...,–62.
Answer» Find the $11^{t h}$ term from the last term (towards the first term) of the AP : $10, 7, 4, . . ., - 62.$

Discussion

19.	Match the following solid objects with the expressions of their volume.
Answer» Match the following solid objects with the expressions of their volume.

Discussion

20.	If x-1x=3+22, find the value of x3-1x3
Answer» If $x - \frac{1}{x} = 3 + 2 \sqrt{2}$ , find the value of $x^{3} - \frac{1}{x^{3}}$

Discussion

21.	Juhi sold a washing machine for Rs13,500 at the loss of 20%. Find the cost price of the washing machine. At what price she must sell to gain 20%? [4 MARKS]
Answer» Juhi sold a washing machine for Rs13,500 at the loss of $20 %$ . Find the cost price of the washing machine. At what price she must sell to gain 20 $%$ ? [4 MARKS]

Discussion

22.	In the following figure, ABC is a right-angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.
Answer» In the following figure, ABC is a right-angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.

Discussion

23.	(-√3)^2 is a real number or not?
Answer» (-√3)^2 is a real number or not?

Discussion

24.	A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC
Answer» A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC

24.

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC

Answer»

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC

Discussion

25.	From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.
Answer» From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

25.

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

Answer»

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

Discussion

26.	24. If A= {1,2,3,4,5,6} then the number of subsets of A which contains atleaSt 3 elements a) 6P2 b) 6P3 c) 6C2 d) 6C3
Answer» 24. If A= {1,2,3,4,5,6} then the number of subsets of A which contains atleaSt 3 elements a) 6P2 b) 6P3 c) 6C2 d) 6C3

Discussion

27.	Which of the quadratic functions has the narrowest graph?
Answer» Which of the quadratic functions has the narrowest graph?

Discussion

28.	A cricketer has a certain average of runs for his 64 innings. In his 65th inning, he is bowledout for no score on his part. This brings down his average by 3 runs. His new average ofruns is:
Answer» A cricketer has a certain average of runs for his 64 innings. In his 65th inning, he is bowledout for no score on his part. This brings down his average by 3 runs. His new average ofruns is:

Discussion

29.	An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. (Take π=227) [4 MARKS]
Answer» An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. (Take $π = \frac{22}{7}$ ) [4 MARKS]

29.

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. (Take π=227) [4 MARKS]

Answer»

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. (Take $π = \frac{22}{7}$ ) [4 MARKS]

Discussion

30.	The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is(a) 7 + 5 (b) 5 (c) 10 (d) 12 [CBSE 2014]
Answer» The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is (a) 7 + $\sqrt{5}$ (b) 5 (c) 10 (d) 12 [CBSE 2014]

Discussion

31.	The points (7, 9), (3, -7),(-3, 3) are the vertices of
Answer» The points (7, 9), (3, -7),(-3, 3) are the vertices of

Discussion

32.	Write a program that has a user defined function to accept the coefficients of a quadratic equation in variables and calculates its determinant. For example : if the coefficients are stored in the variables a,b,c then calculate determinant as b2 - 4ac. Write the appropriate condition to check determinants on positive, zero and negative and output appropriate result.
Answer» Write a program that has a user defined function to accept the coefficients of a quadratic equation in variables and calculates its determinant. For example : if the coefficients are stored in the variables a,b,c then calculate determinant as b² - 4ac. Write the appropriate condition to check determinants on positive, zero and negative and output appropriate result.

Discussion

33.	Write the maximum and minimum values of cos θ.
Answer» Write the maximum and minimum values of cos θ.

Discussion

34.	Solve the equation(1) (2) m2 − 1 = 143(3) (4) (5) (2m − 5)2 = 81(6)
Answer» Solve the equation (1) ₍₂₎_m²_{− 1 = 143} ₍₃₎ ₍₄₎ _{(5) (2m − 5)}²_{= 81} ₍₆₎

34.

Solve the equation(1) (2) m2 − 1 = 143(3) (4) (5) (2m − 5)2 = 81(6)

Answer»

Solve the equation

(1)

₍₂₎_m²_{− 1 = 143}

₍₃₎

₍₄₎

_{(5) (2m − 5)}²_{= 81}

₍₆₎

Discussion

35.	If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE.
Answer» If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE.

Discussion

36.	If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior, (ii) exterior of the triangle.
Answer» If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior, (ii) exterior of the triangle.

Discussion

37.	Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company that manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at the debt of 4 crores. For what value of k is the above scenario possible?
Answer» Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company that manufactures airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at the debt of 4 crores. For what value of k is the above scenario possible?

Discussion

38.	(i) Find the 37th term of the AP 5,412,4,312,3,.... (ii) Find the 25th term of the AP 5,412,4,312,3,...
Answer» (i) Find the 37th term of the AP $5, 4 \frac{1}{2}, 4, 3 \frac{1}{2}, 3, . . . .$ (ii) Find the 25th term of the AP $5, 4 \frac{1}{2}, 4, 3 \frac{1}{2}, 3, . . .$

Discussion

39.	Find the sum of first 15 multiples of 8.
Answer» Find the sum of first 15 multiples of 8.

Discussion

40.	In the given figure(1) m(arc CE) = 54°, m(arc BD) = 23°, find measure of ∠CAE.(2) If AB = 4.2, BC = 5.4, AE = 12.0, find AD(3) If AB = 3.6, AC = 9.0, AD = 5.4, find AE
Answer» In the given figure (1) m(arc CE) = 54°, m(arc BD) = 23°, find measure of ∠CAE. (2) If AB = 4.2, BC = 5.4, AE = 12.0, find AD (3) If AB = 3.6, AC = 9.0, AD = 5.4, find AE

Discussion

41.	(sin230∘+4 cot245∘−sec260∘)(cosec245∘ sec230∘)
Answer» $(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ})$

Discussion

42.	What is a "Discriminant"?
Answer» What is a "Discriminant"?

Discussion

43.	Question 5 In the following figure, DE\|\|OQ and DF\|\|OR, show that EF\|\|QR.
Answer» Question 5 In the following figure, DE\|\|OQ and DF\|\|OR, show that EF\|\|QR.

Discussion

44.	The sums of n terms of two arithmetic progressions are in the ratio 5 n + 4: 9 n + 6. Find the ratio of their 18 th terms.
Answer» The sums of n terms of two arithmetic progressions are in the ratio 5 n + 4: 9 n + 6. Find the ratio of their 18 th terms.

Discussion

45.	Two triangles are similar by SAS similarity if,
Answer» Two triangles are similar by SAS similarity if,

Discussion

46.	If ∆ABC and ∆DEF are two triangles such that ABDE=BCEF=CAFD=34, then write Area (∆ABC) : Area (∆DEF)
Answer» If ∆ABC and ∆DEF are two triangles such that $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}$ , then write Area (∆ABC) : Area (∆DEF)

Discussion

47.	Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.
Answer» Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

Discussion

48.	Question 8The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is
Answer» Question 8 The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is

Discussion

49.	Look at the following table below.Class IntervalClass mark0−6a6−12b12−181518−2121The missing class marks a and b are respectively ____.
Answer» Look at the following table below. $\begin{matrix} Class Interval & Class mark 0 - 6 & a 6 - 12 & b 12 - 18 & 15 18 - 21 & 21 \end{matrix}$ The missing class marks $a$ and $b$ are respectively ____.

Discussion

50.	Question 12From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.
Answer» Question 12 From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$ . Determine the height of the tower.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Define cardinality of a set.

If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.

Solve for x and y by method of cross multiplication: 3x+2y+25=0 2x+y+10=0

Question 3A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

The x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is_______.

Obtain the condition for the following system of linear equations to have a unique solution ax + by = c lx + my = n

Choose the correct answer in each of the following questions:Which term of the AP 72, 63, 54, ... is 0?(a) 8th (b) 9th (c) 10th (d) 11th

What is the value of sin θ for the given right triangle, right angled at B?

Find the volume of a cuboid whose base area is 10 square metres and the height is 5 metre.

Verify that the number given along each of the cubic polynomial below are its zeros if it is so then verify the relationship between the zeros and the cofficients in each case. I) 6x³+5x²-2x-1;-1/3, 1/2, -1II) 2x³+3x²+√3x+1;-2, -1, -1/2

In the given figure, PA, QB and RC are each perpendicular to AC. Prove that 1x+1z=1y.

In the figure AT and BT are the tangents to a circle with centre O. Another tangent PQ is drawn such that TP = TQ. Show that ΔTAB ||| ΔTPQ.

Apply Euclid’s lemma on 36 and 5 and find the value of q and r such that 36=q×5+r.

In the given figure, a triangel ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point o f contant D, are of lengths 6 cm and 9 cm respectively. If the area of Δ = 54 cm2 then find the lengths of sides AB and AC.

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2 Class: 0-20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency: 5 f1 10 f2 7 8

Find the 11th term from the last term (towards the first term) of the AP : 10,7,4,...,–62.

Match the following solid objects with the expressions of their volume.

If x-1x=3+22, find the value of x3-1x3

Juhi sold a washing machine for Rs13,500 at the loss of 20%. Find the cost price of the washing machine. At what price she must sell to gain 20%? [4 MARKS]

In the following figure, ABC is a right-angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.

(-√3)^2 is a real number or not?

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC

From the figure find the length of the tangent CD given AP = 3 cm, and PC = 8 cm.

24. If A= {1,2,3,4,5,6} then the number of subsets of A which contains atleaSt 3 elements a) 6P2 b) 6P3 c) 6C2 d) 6C3

Which of the quadratic functions has the narrowest graph?

A cricketer has a certain average of runs for his 64 innings. In his 65th inning, he is bowledout for no score on his part. This brings down his average by 3 runs. His new average ofruns is:

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is(a) 7 + 5 (b) 5 (c) 10 (d) 12 [CBSE 2014]

The points (7, 9), (3, -7),(-3, 3) are the vertices of

Write the maximum and minimum values of cos θ.

Solve the equation(1) (2) m2 − 1 = 143(3) (4) (5) (2m − 5)2 = 81(6)

If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE.

If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior, (ii) exterior of the triangle.

(i) Find the 37th term of the AP 5,412,4,312,3,.... (ii) Find the 25th term of the AP 5,412,4,312,3,...

Find the sum of first 15 multiples of 8.

In the given figure(1) m(arc CE) = 54°, m(arc BD) = 23°, find measure of ∠CAE.(2) If AB = 4.2, BC = 5.4, AE = 12.0, find AD(3) If AB = 3.6, AC = 9.0, AD = 5.4, find AE

(sin230∘+4 cot245∘−sec260∘)(cosec245∘ sec230∘)

What is a "Discriminant"?

Question 5 In the following figure, DE||OQ and DF||OR, show that EF||QR.

The sums of n terms of two arithmetic progressions are in the ratio 5 n + 4: 9 n + 6. Find the ratio of their 18 th terms.

Two triangles are similar by SAS similarity if,

If ∆ABC and ∆DEF are two triangles such that ABDE=BCEF=CAFD=34, then write Area (∆ABC) : Area (∆DEF)

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

Question 8The area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm, is

Look at the following table below.Class IntervalClass mark0−6a6−12b12−181518−2121The missing class marks a and b are respectively ____.

Question 12From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60∘ and the angle of depression of its foot is 45∘. Determine the height of the tower.