24740 + Interview Questions in Mathematics

1.	The height of a conical tent is 14 m and its floor area is 346.5 m2. The length of canvas, 1.1 m wide, required for it is:
Answer» The height of a conical tent is $14 m$ and its floor area is $346.5 m^{2}$ . The length of canvas, $1.1 m$ wide, required for it is:

Discussion

2.	If the ratio of volume and total surface area of a solid sphere is 8 : 1, then the value of radius = _____ cm.24
Answer» If the ratio of volume and total surface area of a solid sphere is 8 : 1, then the value of radius = _____ cm. 24

Discussion

3.	Factorisea12 – b12
Answer» Factorise a¹² – b¹²

Discussion

4.	Find the value of x of the following proportion:14∶x=7∶9
Answer» Find the value of x of the following proportion: 14∶x=7∶9

Discussion

5.	If A is a symmetric and B is skew-symmetric matrix and (A+B) is non-singular and C=(A+B)−1(A−B), then which of the following options is/are correct
Answer» If $A$ is a symmetric and $B$ is skew-symmetric matrix and $(A + B)$ is non-singular and $C = (A + B)^{- 1} (A - B)$ , then which of the following options is/are correct

Discussion

6.	A rhombus sheet whose perimeter = 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per m2. Find the cost of painting.
Answer» A rhombus sheet whose perimeter = 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per $m^{2}$ . Find the cost of painting.

Discussion

7.	In a circle, the major arc is 3 times the minor arc. The corresponding centre angles and the degree measures of two arcs are
Answer» In a circle, the major arc is 3 times the minor arc. The corresponding centre angles and the degree measures of two arcs are

Discussion

8.	Question 7In the figure, ABCDE is any pentagon, BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (ΔAPQ).
Answer» Question 7 In the figure, ABCDE is any pentagon, BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar ( $Δ$ APQ).

Discussion

9.	In the given figure, AB \|\| CD \|\| EF and GH \|\| KL. Find the ∠HKL.
Answer» In the given figure, AB \|\| CD \|\| EF and GH \|\| KL. Find the ∠HKL.

Discussion

10.	A point D is taken on the side BC of a △ABC such that BD = 2DC. Prove that ar (△ABD)=2ar(△ADC)
Answer» A point D is taken on the side BC of a $△ A B C$ such that BD = 2DC. Prove that ar $(△ A B D) = 2 a r (△ A D C)$

Discussion

11.	Find the amount of water displaced by a solid spherical ball of diameter(i) 28 cm (ii) 0.21 m
Answer» Find the amount of water displaced by a solid spherical ball of diameter (i) 28 cm (ii) 0.21 m

11.

Find the amount of water displaced by a solid spherical ball of diameter(i) 28 cm (ii) 0.21 m

Answer»

Find the amount of water displaced by a solid spherical ball of diameter

(i) 28 cm (ii) 0.21 m

Discussion

12.	In a grass land, a horse is tethered by a rope of 5 m length. Find the maximum area that the horse can graze.
Answer» In a grass land, a horse is tethered by a rope of $5 m$ length. Find the maximum area that the horse can graze.

Discussion

13.	The value of the dot product of the eigen vectors corresponding to any pair of different eigen values of a 4 x 4 symmetric positive definite matrix is .
Answer» The value of the dot product of the eigen vectors corresponding to any pair of different eigen values of a 4 x 4 symmetric positive definite matrix is .

Discussion

14.	Find the centre of mass of a uniform semicircular disc of radius R
Answer» Find the centre of mass of a uniform semicircular disc of radius R

Discussion

15.	Factorise:9x2 – 3x – 20
Answer» Factorise: 9x² – 3x – 20

Discussion

16.	In the given figure, AB is the diameter of the circle. Find the value of x.
Answer» In the given figure, AB is the diameter of the circle. Find the value of $x$ .

16.

In the given figure, AB is the diameter of the circle. Find the value of x.

Answer»

In the given figure, AB is the diameter of the circle. Find the value of $x$ .

Discussion

17.	Now prepare a graph based on the students' response to the survey you conducted in C.2. Then write a report for the newspaper taking the help of B.5, C.3 and C.6.
Answer» Now prepare a graph based on the students' response to the survey you conducted in C.2. Then write a report for the newspaper taking the help of B.5, C.3 and C.6.

Discussion

18.	Which one of the following can also be written in form of 3x = 4y + 123?
Answer» Which one of the following can also be written in form of 3x = 4y + 123?

Discussion

19.	Evaluate: arcsec(Cosec (pi/8))
Answer» Evaluate: arcsec(Cosec (pi/8))

Discussion

20.	In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =(a) 3 cm(b) 3.5 cm(c) 2.5 cm(d) 5 cm
Answer» In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF = (a) 3 cm (b) 3.5 cm (c) 2.5 cm (d) 5 cm

Discussion

21.	ABCD is a square, X and Y are points on sides AD and BC respectively such that AY= BX. Prove that BY = AX and ∠BAY = ∠ABX.
Answer» ABCD is a square, X and Y are points on sides AD and BC respectively such that AY= BX. Prove that BY = AX and ∠BAY = ∠ABX.

Discussion

22.	Identify the solutions for the given equation 4x + y = 16.
Answer» Identify the solutions for the given equation 4x + y = 16.

Discussion

23.	24.The number of ways of painting the faces of a cube with 6 different colors is?
Answer» 24.The number of ways of painting the faces of a cube with 6 different colors is?

Discussion

24.	Fill in the BlanksQuestion 17The distance of any point from the Y-axis is the ___ coordinate.
Answer» Fill in the Blanks Question 17 The distance of any point from the Y-axis is the ___ coordinate.

Discussion

25.	Question 6In covering a distance s m , a circular wheel of radius r m makes s2πr revolution. Is this statement true ? why?
Answer» Question 6 In covering a distance s m , a circular wheel of radius r m makes $\frac{s}{2 π r}$ revolution. Is this statement true ? why?

Discussion

26.	If α and β are the zeros of the polynomial f(x)=5x2−7x+1, find the value of (1α+1β)..
Answer» If $α$ and $β$ are the zeros of the polynomial $f (x) = 5 x^{2} - 7 x + 1$ , find the value of $(\frac{1}{α} + \frac{1}{β}) .$ .

Discussion

27.	is neither a positive nor a negative integer.
Answer» is neither a positive nor a negative integer.

Discussion

28.	Question 152 (iii)A rectangle MORE is shown below.Answer the following questions by giving an appropriate reason.Is ∠MOY = ∠REX?
Answer» Question 152 (iii) A rectangle MORE is shown below. Answer the following questions by giving an appropriate reason. Is ∠MOY = ∠REX?

Discussion

29.	Construct ∆XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.
Answer» Construct $∆$ XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.

Discussion

30.	Which angle has a large measure? First estimate and then measure.Measure of angle A = Measure of angle B =
Answer» Which angle has a large measure? First estimate and then measure. Measure of angle A = Measure of angle B =

30.

Which angle has a large measure? First estimate and then measure.Measure of angle A = Measure of angle B =

Answer»

Which angle has a large measure? First estimate and then measure.

Measure of angle A =

Measure of angle B =

Discussion

31.	Question 16In the given figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.
Answer» Question 16 In the given figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Discussion

32.	The least area of a circle circumscribing any right triangle of area S is a
Answer» The least area of a circle circumscribing any right triangle of area S is a

Discussion

33.	Question 1 (ii) State whether the following statement is true or false. Justify your answer. Every point on the number line is of the form √m, where m is a natural number.
Answer» Question 1 (ii) State whether the following statement is true or false. Justify your answer. Every point on the number line is of the form $\sqrt{m}$ , where m is a natural number.

33.

Question 1 (ii) State whether the following statement is true or false. Justify your answer. Every point on the number line is of the form √m, where m is a natural number.

Answer»

Question 1 (ii)
State whether the following statement is true or false. Justify your answer.

Every point on the number line is of the form $\sqrt{m}$ , where m is a natural number.

Discussion

34.	Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.
Answer» Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.

Discussion

35.	Find the value of 4x2+y2+25z2+4xy−10yz−20zx when x = 4, y = 3 and z = 2.
Answer» Find the value of $4 x^{2} + y^{2} + 25 z^{2} + 4 x y - 10 y z - 20 z x$ when x = 4, y = 3 and z = 2.

Discussion

36.	If one angle of parallelogram is 90∘,then all the other angles are equal to .
Answer» $If one angle of parallelogram is 90^{\circ}, then all the other angles are equal to$ .

Discussion

37.	The histogram below represents the Mathematics marks of the students.Find the total number of students with total marks more than or equal to 40 and less than 70.
Answer» The histogram below represents the Mathematics marks of the students. Find the total number of students with total marks more than or equal to 40 and less than 70.

37.

The histogram below represents the Mathematics marks of the students.Find the total number of students with total marks more than or equal to 40 and less than 70.

Answer»

The histogram below represents the Mathematics marks of the students.

Find the total number of students with total marks more than or equal to 40 and less than 70.

Discussion

38.	In the given figure, ∠BAD=75∘,∠DCF=x∘ and ∠DEF=y∘. Find the values of x and y.
Answer» In the given figure, $∠ B A D = 75^{\circ}, ∠ D C F = x^{\circ} a n d ∠ D E F = y^{\circ}$ . Find the values of x and y.

38.

In the given figure, ∠BAD=75∘,∠DCF=x∘ and ∠DEF=y∘. Find the values of x and y.

Answer»

In the given figure, $∠ B A D = 75^{\circ}, ∠ D C F = x^{\circ} a n d ∠ D E F = y^{\circ}$ . Find the values of x and y.

Discussion

39.	What is area of triangle formed by 3x – 2y = 4, x + y – 3 = 0 and y = 0
Answer» What is area of triangle formed by 3x – 2y = 4, x + y – 3 = 0 and y = 0

Discussion

40.	Question 4ABCD is a trapezium in which AB \|\| DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F ( See the given figure). Show that F is the mid - point of BC.
Answer» Question 4 ABCD is a trapezium in which AB \|\| DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F ( See the given figure). Show that F is the mid - point of BC.

Discussion

41.	Draw the graph of 2x + y = 3.
Answer» Draw the graph of 2x + y = 3.

Discussion

42.	If the decimal is shifted 2 places to the left in the decimal , 312749.563738 what will be the digit at the thousand's position?
Answer» If the decimal is shifted 2 places to the left in the decimal , 312749.563738 what will be the digit at the thousand's position?

Discussion

43.	What is the radius of the circle in which a central angle of 60o intercepts an arc length of 48.4 cm?
Answer» What is the radius of the circle in which a central angle of 60^o intercepts an arc length of 48.4 cm?

Discussion

44.	In the given figure, if AB \|\| CD \|\| EF, PQ \|\| RS, ∠RQD=25∘ and ∠CQP=60∘, then the measure of ∠ARS.
Answer» In the given figure, if AB \|\| CD \|\| EF, PQ \|\| RS, $∠ R Q D = 25^{\circ}$ and $∠ C Q P = 60^{\circ}$ , then the measure of $∠ A R S$ .

Discussion

45.	In a ABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects FE at Q. Prove that AQ = QP.
Answer» In a ABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects FE at Q. Prove that AQ = QP.

Discussion

46.	The value of tan A +sin A=M and tan A – sin A=N . The value of (M2−N2)(MN)0.5
Answer» The value of tan A +sin A=M and tan A – sin A=N . The value of $\frac{(M^{2} - N^{2})}{(M N)^{0.5}}$

46.

The value of tan A +sin A=M and tan A – sin A=N . The value of (M2−N2)(MN)0.5

Answer»

The value of tan A +sin A=M and tan A – sin A=N .

The value of $\frac{(M^{2} - N^{2})}{(M N)^{0.5}}$

Discussion

47.	Use the following information to answer the next question. How many diagonals containing point B or point D can be drawn in the given polygon?
Answer» Use the following information to answer the next question. How many diagonals containing point B or point D can be drawn in the given polygon?

47.

Use the following information to answer the next question. How many diagonals containing point B or point D can be drawn in the given polygon?

Answer»

Use the following information to answer the next question.

How many diagonals containing point B or point D can be drawn in the given polygon?

Discussion

48.	Simplify the expressions below(i) (ii) (iii) (iv) (v) (vi) (vii) (viii)
Answer» Simplify the expressions below (i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

48.

Simplify the expressions below(i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

Answer»

Simplify the expressions below

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Discussion

49.	The graph of every linear equation in two variables is --------------.
Answer» The graph of every linear equation in two variables is --------------.

Discussion

50.	In triangle ABC ,D is the midpoint of AB. P IS ANY POINT OF BC. CQ \|\| PD meets AB in Q . Show that ar ( ∆BPQ) = ½(∆ABC)
Answer» In triangle ABC ,D is the midpoint of AB. P IS ANY POINT OF BC. CQ \|\| PD meets AB in Q . Show that ar ( ∆BPQ) = ½(∆ABC)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The height of a conical tent is 14 m and its floor area is 346.5 m2. The length of canvas, 1.1 m wide, required for it is:

If the ratio of volume and total surface area of a solid sphere is 8 : 1, then the value of radius = _____ cm.24

Factorisea12 – b12

Find the value of x of the following proportion:14∶x=7∶9

If A is a symmetric and B is skew-symmetric matrix and (A+B) is non-singular and C=(A+B)−1(A−B), then which of the following options is/are correct

A rhombus sheet whose perimeter = 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs. 5 per m2. Find the cost of painting.

In a circle, the major arc is 3 times the minor arc. The corresponding centre angles and the degree measures of two arcs are

Question 7In the figure, ABCDE is any pentagon, BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (ΔAPQ).

In the given figure, AB || CD || EF and GH || KL. Find the ∠HKL.

A point D is taken on the side BC of a △ABC such that BD = 2DC. Prove that ar (△ABD)=2ar(△ADC)

Find the amount of water displaced by a solid spherical ball of diameter(i) 28 cm (ii) 0.21 m

In a grass land, a horse is tethered by a rope of 5 m length. Find the maximum area that the horse can graze.

The value of the dot product of the eigen vectors corresponding to any pair of different eigen values of a 4 x 4 symmetric positive definite matrix is .

Find the centre of mass of a uniform semicircular disc of radius R

Factorise:9x2 – 3x – 20

In the given figure, AB is the diameter of the circle. Find the value of x.

Now prepare a graph based on the students' response to the survey you conducted in C.2. Then write a report for the newspaper taking the help of B.5, C.3 and C.6.

Which one of the following can also be written in form of 3x = 4y + 123?

Evaluate: arcsec(Cosec (pi/8))

In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =(a) 3 cm(b) 3.5 cm(c) 2.5 cm(d) 5 cm

ABCD is a square, X and Y are points on sides AD and BC respectively such that AY= BX. Prove that BY = AX and ∠BAY = ∠ABX.

Identify the solutions for the given equation 4x + y = 16.

24.The number of ways of painting the faces of a cube with 6 different colors is?

Fill in the BlanksQuestion 17The distance of any point from the Y-axis is the ___ coordinate.

Question 6In covering a distance s m , a circular wheel of radius r m makes s2πr revolution. Is this statement true ? why?

If α and β are the zeros of the polynomial f(x)=5x2−7x+1, find the value of (1α+1β)..

is neither a positive nor a negative integer.

Question 152 (iii)A rectangle MORE is shown below.Answer the following questions by giving an appropriate reason.Is ∠MOY = ∠REX?

Construct ∆XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.

Which angle has a large measure? First estimate and then measure.Measure of angle A = Measure of angle B =

Question 16In the given figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

The least area of a circle circumscribing any right triangle of area S is a

Question 1 (ii) State whether the following statement is true or false. Justify your answer. Every point on the number line is of the form √m, where m is a natural number.

Find the surface area (in sq. cm.) of a cylindrical container with radius 4 cm and height 10 cm, assuming it has an open top and a closed bottom.

Find the value of 4x2+y2+25z2+4xy−10yz−20zx when x = 4, y = 3 and z = 2.

If one angle of parallelogram is 90∘,then all the other angles are equal to .

The histogram below represents the Mathematics marks of the students.Find the total number of students with total marks more than or equal to 40 and less than 70.

In the given figure, ∠BAD=75∘,∠DCF=x∘ and ∠DEF=y∘. Find the values of x and y.

What is area of triangle formed by 3x – 2y = 4, x + y – 3 = 0 and y = 0

Question 4ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F ( See the given figure). Show that F is the mid - point of BC.

Draw the graph of 2x + y = 3.

If the decimal is shifted 2 places to the left in the decimal , 312749.563738 what will be the digit at the thousand's position?

What is the radius of the circle in which a central angle of 60o intercepts an arc length of 48.4 cm?

In the given figure, if AB || CD || EF, PQ || RS, ∠RQD=25∘ and ∠CQP=60∘, then the measure of ∠ARS.

In a ABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects FE at Q. Prove that AQ = QP.

The value of tan A +sin A=M and tan A – sin A=N . The value of (M2−N2)(MN)0.5

Use the following information to answer the next question. How many diagonals containing point B or point D can be drawn in the given polygon?

Simplify the expressions below(i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

The graph of every linear equation in two variables is --------------.

In triangle ABC ,D is the midpoint of AB. P IS ANY POINT OF BC. CQ || PD meets AB in Q . Show that ar ( ∆BPQ) = ½(∆ABC)