24740 + Interview Questions in Mathematics

1.	If I is a unit matrix, then 3I will be
Answer» If I is a unit matrix, then 3I will be

Discussion

2.	If x+1x=2, find the value of x64+1x64
Answer» If $x + \frac{1}{x} = 2$ , find the value of $x^{64} + \frac{1}{x^{64}}$

Discussion

3.	A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Answer» A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.

Discussion

4.	In the figure, PQRS in an isosceles trapezium. Find x and y.
Answer» In the figure, PQRS in an isosceles trapezium. Find x and y.

Discussion

5.	In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD=146∘, find ∠AOB.
Answer» In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If $∠ E C D = 146^{\circ}$ , find $∠ A O B$ .

5.

In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD=146∘, find ∠AOB.

Answer»

In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If $∠ E C D = 146^{\circ}$ , find $∠ A O B$ .

Discussion

6.	The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point (a) (2, 0) (b) (3, 0) (c) (0, 2) (d) (0, 3)
Answer» The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point (a) (2, 0) (b) (3, 0) (c) (0, 2) (d) (0, 3)

6.

The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point (a) (2, 0) (b) (3, 0) (c) (0, 2) (d) (0, 3)

Answer»

The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point

(a) (2, 0)

(b) (3, 0)

(c) (0, 2)

(d) (0, 3)

Discussion

7.	The diameters of two cones are equal.If their slant heights are in the ratio 5:4,find the ratio of their curved surfaces.
Answer» The diameters of two cones are equal.If their slant heights are in the ratio 5:4,find the ratio of their curved surfaces.

Discussion

8.	Question 94 In the following question, state whether the given statement is true (T) or false (F). Any two consecutive numbers are coprime.
Answer» Question 94 In the following question, state whether the given statement is true (T) or false (F). Any two consecutive numbers are coprime.

Discussion

9.	The diagonals of a rectangle ABCD meet at O. If ∠BOC=44∘, find ∠OAD. [2 MARKS]
Answer» The diagonals of a rectangle $A B C D$ meet at $O$ . If $∠ B O C = 44^{\circ}$ , find $∠ O A D$ . [2 MARKS]

Discussion

10.	Using factor theorem, show that g(x) is a factor of p(x), when p(x)=7x2−4√2x−6,g(x)=x−√2
Answer» Using factor theorem, show that g(x) is a factor of p(x), when $p (x) = 7 x^{2} - 4 \sqrt{2} x - 6, g (x) = x - \sqrt{2}$

Discussion

11.	Andy spent Rs. 450 in fencing the parallelogram shaped land (leaving 1 m for the gate) that he had before. If Andy would start from a point 5 m away from A (on side AB) and take the shortest possible path to the opposite side, he would reach exactly at D. As you know Land Grabbers restructured Andy’s land to be a rectangle having the same base and same width. Find the cost of fencing the new land in same way at Rs. 6 per metre.
Answer» Andy spent Rs. 450 in fencing the parallelogram shaped land (leaving 1 m for the gate) that he had before. If Andy would start from a point 5 m away from A (on side AB) and take the shortest possible path to the opposite side, he would reach exactly at D. As you know Land Grabbers restructured Andy’s land to be a rectangle having the same base and same width. Find the cost of fencing the new land in same way at Rs. 6 per metre.

11.

Andy spent Rs. 450 in fencing the parallelogram shaped land (leaving 1 m for the gate) that he had before. If Andy would start from a point 5 m away from A (on side AB) and take the shortest possible path to the opposite side, he would reach exactly at D. As you know Land Grabbers restructured Andy’s land to be a rectangle having the same base and same width. Find the cost of fencing the new land in same way at Rs. 6 per metre.

Answer»

Andy spent Rs. 450 in fencing the parallelogram shaped land (leaving 1 m for the gate) that he had before. If Andy would start from a point 5 m away from A (on side AB) and take the shortest possible path to the opposite side, he would reach exactly at D. As you know Land Grabbers restructured Andy’s land to be a rectangle having the same base and same width. Find the cost of fencing the new land in same way at Rs. 6 per metre.

Discussion

12.	The number if planks of dimensions 4m×59cm×20cm that can be stored in a pit which is 16m long,12m wide, and 4m deep is?
Answer» The number if planks of dimensions 4m×59cm×20cm that can be stored in a pit which is 16m long,12m wide, and 4m deep is?

Discussion

13.	A, B, C are three sets of values as given below: A : 2, 3, 7, 1, 3, 2, 3 B : 7, 5, 9, 12, 5, 3, 8 C : 4, 4, 11, 7, 2, 3, 4 Which one of the following statements is correct?
Answer» A, B, C are three sets of values as given below: A : 2, 3, 7, 1, 3, 2, 3 B : 7, 5, 9, 12, 5, 3, 8 C : 4, 4, 11, 7, 2, 3, 4 Which one of the following statements is correct?

Discussion

14.	You have deposited Rs 1000.00 in the bank. The rate of interest is 7% per annum(simple interest). How much money will you have after 5 years?
Answer» You have deposited Rs 1000.00 in the bank. The rate of interest is 7% per annum(simple interest). How much money will you have after 5 years?

Discussion

15.	In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram. 3
Answer» In the figure, $Δ A B C$ has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of $Δ A B C$ is constructed. Find the height DF of the parallelogram. 3

Discussion

16.	A sphere and a cube have same surface area. Show that the ratio of the volume of sphere to that of cube is √6:√π.
Answer» A sphere and a cube have same surface area. Show that the ratio of the volume of sphere to that of cube is √6:√π.

Discussion

17.	Angle between hour and minute hand of a clock at 12:30 p.m. (in degrees) is ______________.
Answer» Angle between hour and minute hand of a clock at 12:30 p.m. (in degrees) is ______________.

Discussion

18.	If ∆ABC ≅ ∆PQR then which of the following is true:
Answer» If ∆ABC ≅ ∆PQR then which of the following is true:

Discussion

19.	A polynomial of degree 3 is called a __ polynomial
Answer» A polynomial of degree 3 is called a __ polynomial

Discussion

20.	If abscissa of a point is zero, on which axis do the point lies
Answer» If abscissa of a point is zero, on which axis do the point lies

Discussion

21.	What is componendo dividends?
Answer» What is componendo dividends?

Discussion

22.	A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source. Find the intensity 10 m away from it?
Answer» A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source. Find the intensity 10 m away from it?

22.

A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source. Find the intensity 10 m away from it?

Answer»

A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source.

Find the intensity 10 m away from it?

Discussion

23.	If x=5-2root6,find x^2+1/x^2
Answer» If x=5-2root6,find x^2+1/x^2

Discussion

24.	Factorise 3x^2-x-4
Answer» Factorise 3x^2-x-4

Discussion

25.	Area of a square whose perimeter is 36 cm is
Answer» Area of a square whose perimeter is 36 cm is

Discussion

26.	What is a terminating number?
Answer» What is a terminating number?

Discussion

27.	Find 3 rational no between root2 and root3
Answer» Find 3 rational no between root2 and root3

Discussion

28.	If a10 = b4 = c6 = 4a−3b+9cx. Find the value of x.82
Answer» If $\frac{a}{10}$ = $\frac{b}{4}$ = $\frac{c}{6}$ = $\frac{4 a - 3 b + 9 c}{x}$ . Find the value of $x .$ 82

Discussion

29.	Factor theorem
Answer» Factor theorem

Discussion

30.	Question 1 (ii) ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that ΔABP≅ΔACP
Answer» Question 1 (ii) $Δ$ ABC and $Δ$ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that $Δ A B P ≅ Δ A C P$

Discussion

31.	The base of a prism is a right-angled triangle having its base and altitude as 10 cm and 24 cm respectively. If the height of prism is 30 cm, what will be the lateral surface area ?
Answer» The base of a prism is a right-angled triangle having its base and altitude as 10 cm and 24 cm respectively. If the height of prism is 30 cm, what will be the lateral surface area ?

Discussion

32.	How many equations are required to obtain a unique solution for a linear equation in two variables? ___
Answer» How many equations are required to obtain a unique solution for a linear equation in two variables? ___

Discussion

33.	If log 2 = 0.3010 and log 3 = 0.4771, the value of log5512 is:
Answer» If log 2 = 0.3010 and log 3 = 0.4771, the value of $l o g_{5} 512$ is:

Discussion

34.	The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Answer» The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Discussion

35.	Prove that in a triangle, other than an equilateral triangle, angle opposite to the longest side is greater than 2/3 of a right angle.
Answer» Prove that in a triangle, other than an equilateral triangle, angle opposite to the longest side is greater than 2/3 of a right angle.

Discussion

36.	The volume of hemisphere with total surface area 115.62 cm2 is approximately (Take π= 22/7)
Answer» The volume of hemisphere with total surface area 115.62 cm² is approximately (Take π= 22/7)

Discussion

37.	In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ABC.
Answer» In the given figure, A, B and C are three points on the circle with centre O such that $∠ B O C = 30^{\circ}$ and $∠ A O B = 60^{\circ}$ . If D is a point on the circle that is not on the arc ABC, then find $∠ A B C .$

Discussion

38.	The volume of cuboid is given by the expression x3 + 2x2 – x -2 . The dimension of the cuboid for x = 5 is:
Answer» The volume of cuboid is given by the expression x³ + 2x² – x -2 . The dimension of the cuboid for x = 5 is:

Discussion

39.	A base of a triangle QR touches a circle at S. The other two sides PQ and QR of ∆PQR is extended such a way that they touch the circle at T and U respectively .If the perimeter of ∆PQR is 10 cm, then length of PT is
Answer» A base of a triangle QR touches a circle at S. The other two sides PQ and QR of ∆PQR is extended such a way that they touch the circle at T and U respectively .If the perimeter of ∆PQR is 10 cm, then length of PT is

Discussion

40.	Two dice are rolled simultaneously. Find the probability of: i) obtaining a total of at least 9. ii) getting a multiple of 2 on one die and a multiple of 3 on the other die.
Answer» Two dice are rolled simultaneously. Find the probability of: i) obtaining a total of at least 9. ii) getting a multiple of 2 on one die and a multiple of 3 on the other die.

40.

Two dice are rolled simultaneously. Find the probability of: i) obtaining a total of at least 9. ii) getting a multiple of 2 on one die and a multiple of 3 on the other die.

Answer»

Two dice are rolled simultaneously. Find the probability of:

i) obtaining a total of at least 9.

ii) getting a multiple of 2 on one die and a multiple of 3 on the other die.

Discussion

41.	Question 1 (i) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. x - 3y - 3 = 0 ; 3x - 9y - 2 =0
Answer» Question 1 (i) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. x - 3y - 3 = 0 ; 3x - 9y - 2 =0

Discussion

42.	Question 12 Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.
Answer» Question 12 Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.

Discussion

43.	The angle of elevation of a tower of height m from the eye of two observers A and B on the same side of the tower are α and β. respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then, The distance between the two people is :
Answer» The angle of elevation of a tower of height m from the eye of two observers A and B on the same side of the tower are $α$ and $β$ . respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then, The distance between the two people is :

Discussion

44.	In Fig. BD and CE are two altitudes of a Δ ABC such that BD = CE. Prove that the ABC is an isoceles triangle. [2 MARKS]
Answer» In Fig. BD and CE are two altitudes of a $Δ$ ABC such that BD = CE. Prove that the ABC is an isoceles triangle. [2 MARKS]

44.

In Fig. BD and CE are two altitudes of a Δ ABC such that BD = CE. Prove that the ABC is an isoceles triangle. [2 MARKS]

Answer»

In Fig. BD and CE are two altitudes of a $Δ$ ABC such that BD = CE.

Prove that the ABC is an isoceles triangle. [2 MARKS]

Discussion

45.	The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that arc APB2 = arc BQC3 = arc CRA4. Find ∠BOA.
Answer» The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that $\frac{a r c A P B}{2} = \frac{a r c B Q C}{3} = \frac{a r c C R A}{4}$ . Find $∠ B O A .$

45.

The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that arc APB2 = arc BQC3 = arc CRA4. Find ∠BOA.

Answer»

The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that

$\frac{a r c A P B}{2} = \frac{a r c B Q C}{3} = \frac{a r c C R A}{4}$ . Find $∠ B O A .$

Discussion

46.	△ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5cm.
Answer» $△ A B C$ is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5cm.

Discussion

47.	Represent 0.353535… in a rational form. How will you verify whether the obtained fraction is reccurring or non-recurring? [4 MARKS]
Answer» Represent 0.353535… in a rational form. How will you verify whether the obtained fraction is reccurring or non-recurring? [4 MARKS]

Discussion

48.	The height of a cone is 4 cm and its base radius is 3 cm. The total surface area of the cone is:
Answer» The height of a cone is 4 cm and its base radius is 3 cm. The total surface area of the cone is:

Discussion

49.	In adjoining figure, write the names : (i) Two pairs of intersecting lines and their corresponding points of intersection (ii) Three concurrent lines and their point of intersection (iii) Three rays (iv) Two line segments
Answer» In adjoining figure, write the names : (i) Two pairs of intersecting lines and their corresponding points of intersection (ii) Three concurrent lines and their point of intersection (iii) Three rays (iv) Two line segments

49.

In adjoining figure, write the names : (i) Two pairs of intersecting lines and their corresponding points of intersection (ii) Three concurrent lines and their point of intersection (iii) Three rays (iv) Two line segments

Answer»

In adjoining figure, write the names :

(i) Two pairs of intersecting lines and their corresponding points of intersection

(ii) Three concurrent lines and their point of intersection

(iii) Three rays

(iv) Two line segments

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.

If I is a unit matrix, then 3I will be

If x+1x=2, find the value of x64+1x64

A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.

In the figure, PQRS in an isosceles trapezium. Find x and y.

In the figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD=146∘, find ∠AOB.

The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point (a) (2, 0) (b) (3, 0) (c) (0, 2) (d) (0, 3)

The diameters of two cones are equal.If their slant heights are in the ratio 5:4,find the ratio of their curved surfaces.

Question 94 In the following question, state whether the given statement is true (T) or false (F). Any two consecutive numbers are coprime.

The diagonals of a rectangle ABCD meet at O. If ∠BOC=44∘, find ∠OAD. [2 MARKS]

Using factor theorem, show that g(x) is a factor of p(x), when p(x)=7x2−4√2x−6,g(x)=x−√2

The number if planks of dimensions 4m×59cm×20cm that can be stored in a pit which is 16m long,12m wide, and 4m deep is?

A, B, C are three sets of values as given below: A : 2, 3, 7, 1, 3, 2, 3 B : 7, 5, 9, 12, 5, 3, 8 C : 4, 4, 11, 7, 2, 3, 4 Which one of the following statements is correct?

You have deposited Rs 1000.00 in the bank. The rate of interest is 7% per annum(simple interest). How much money will you have after 5 years?

In the figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram. 3

A sphere and a cube have same surface area. Show that the ratio of the volume of sphere to that of cube is √6:√π.

Angle between hour and minute hand of a clock at 12:30 p.m. (in degrees) is ______________.

If ∆ABC ≅ ∆PQR then which of the following is true:

A polynomial of degree 3 is called a __ polynomial

If abscissa of a point is zero, on which axis do the point lies

What is componendo dividends?

A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source. Find the intensity 10 m away from it?

If x=5-2root6,find x^2+1/x^2

Factorise 3x^2-x-4

Area of a square whose perimeter is 36 cm is

What is a terminating number?

Find 3 rational no between root2 and root3

If a10 = b4 = c6 = 4a−3b+9cx. Find the value of x.82

Factor theorem

Question 1 (ii) ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that ΔABP≅ΔACP

The base of a prism is a right-angled triangle having its base and altitude as 10 cm and 24 cm respectively. If the height of prism is 30 cm, what will be the lateral surface area ?

How many equations are required to obtain a unique solution for a linear equation in two variables? ___

If log 2 = 0.3010 and log 3 = 0.4771, the value of log5512 is:

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Prove that in a triangle, other than an equilateral triangle, angle opposite to the longest side is greater than 2/3 of a right angle.

The volume of hemisphere with total surface area 115.62 cm2 is approximately (Take π= 22/7)

In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ABC.

The volume of cuboid is given by the expression x3 + 2x2 – x -2 . The dimension of the cuboid for x = 5 is:

A base of a triangle QR touches a circle at S. The other two sides PQ and QR of ∆PQR is extended such a way that they touch the circle at T and U respectively .If the perimeter of ∆PQR is 10 cm, then length of PT is

Two dice are rolled simultaneously. Find the probability of: i) obtaining a total of at least 9. ii) getting a multiple of 2 on one die and a multiple of 3 on the other die.

Question 1 (i) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. x - 3y - 3 = 0 ; 3x - 9y - 2 =0

Question 12 Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.

In Fig. BD and CE are two altitudes of a Δ ABC such that BD = CE. Prove that the ABC is an isoceles triangle. [2 MARKS]

The circumference of a circle with centre O is divided into three arcs APB, BQC and CRA such that arc APB2 = arc BQC3 = arc CRA4. Find ∠BOA.

△ABC is right angled at B and the perpendicular drawn to the opposite side bisects it at D. BD = ___ cm if AD = DC = 5cm.

Represent 0.353535… in a rational form. How will you verify whether the obtained fraction is reccurring or non-recurring? [4 MARKS]

The height of a cone is 4 cm and its base radius is 3 cm. The total surface area of the cone is:

In adjoining figure, write the names : (i) Two pairs of intersecting lines and their corresponding points of intersection (ii) Three concurrent lines and their point of intersection (iii) Three rays (iv) Two line segments

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