32581 + Interview Questions in Mathematics

1.	Find the weight of a hollow sphere of metal having internal and external diameters as 20 cm and 22 cm, respectively if 1m3 of metal weighs 21g.
Answer» Find the weight of a hollow sphere of metal having internal and external diameters as 20 cm and 22 cm, respectively if 1m³ of metal weighs 21g.

Discussion

2.	Draw a triangle of sides 4, 5, 6 centimetres and draw its incircle.
Answer» Draw a triangle of sides 4, 5, 6 centimetres and draw its incircle.

Discussion

3.	Show that the points A (1, 0), B (5, 3), C (2, 7) and D(-2, 4) are the vertices of a parallelogram.
Answer» Show that the points A (1, 0), B (5, 3), C (2, 7) and D(-2, 4) are the vertices of a parallelogram.

Discussion

4.	Evaluate each of the following4 (sin4 60° + cos4 30°) − 3 (tan2 60° − tan2 45°) + 5 cos2 45°
Answer» Evaluate each of the following 4 (sin⁴60° + cos⁴ 30°) − 3 (tan² 60° − tan² 45°) + 5 cos² 45°

Discussion

5.	A sector of 56° cut out from a circle contains area 4.4 cm2. Find the radius of the circle.
Answer» A sector of 56° cut out from a circle contains area 4.4 cm². Find the radius of the circle.

Discussion

6.	Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Answer» Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Discussion

7.	A person standing on the top of a cliff, 171 ft high, has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend with a speed of 15.0 ft/s, how short will the packet fall? Give g = 32 ft/s2.
Answer» A person standing on the top of a cliff, $171 f t$ high, has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend with a speed of $15.0 f t / s$ , how short will the packet fall? Give $g$ = $32 f t / s^{2}$ .

Discussion

8.	If the vertices of a triangle are (2,0) (0,2) (4,6), then the equation of the median through the vertex (2,0) is
Answer» If the vertices of a triangle are (2,0) (0,2) (4,6), then the equation of the median through the vertex (2,0) is

Discussion

9.	Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.
Answer» Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.

Discussion

10.	Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed?
Answer» Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed?

Discussion

11.	An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed in km/hr.300
Answer» An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed in km/hr. 300

Discussion

12.	If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is(a) 1 : 2(b) 1: 4(c) 1 : 6(d) 1 : 8
Answer» If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is (a) 1 : 2 (b) 1: 4 (c) 1 : 6 (d) 1 : 8

Discussion

13.	cos 60° =
Answer» cos 60° =

Discussion

14.	Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.
Answer» Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

14.

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

Answer»

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

Discussion

15.	Question 3Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.
Answer» Question 3 Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}} a n d - \sqrt{\frac{5}{3}}$ .

Discussion

16.	If 'n' things are arranged at random in a row then the probability that 'm' particular things are never together is?
Answer» If 'n' things are arranged at random in a row then the probability that 'm' particular things are never together is?

Discussion

17.	Find the total surface area of the given cuboid.
Answer» Find the total surface area of the given cuboid.

Discussion

18.	In the given figure, PA and PB are two tangents to a circle with centre O, If ∠APB = 60∘ then find the measure of ∠OAB
Answer» In the given figure, PA and PB are two tangents to a circle with centre O, If ∠APB = 60^∘ then find the measure of ∠OAB

Discussion

19.	y=2x+4 and are parallel lines.
Answer» $y = 2 x + 4$ and are parallel lines.

Discussion

20.	A spherical ball is divided into two halves. If the curved surface of each half is 56.57 cm2, find the volume of the spherical ball.
Answer» A spherical ball is divided into two halves. If the curved surface of each half is $56.57 c m^{2}$ , find the volume of the spherical ball.

Discussion

21.	Total surface area of a cone of radius 5 cm and slant height 10 cm is .(Take π=3.14)
Answer» Total surface area of a cone of radius 5 cm and slant height 10 cm is . $(T a k e π = 3.14)$

Discussion

22.	Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.
Answer» Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.

Discussion

23.	Find the value of tan(90−A)cot(90−A)
Answer» Find the value of $\frac{t a n (90 - A)}{c o t (90 - A)}$

23.

Find the value of tan(90−A)cot(90−A)

Answer»

Find the value of

$\frac{t a n (90 - A)}{c o t (90 - A)}$

Discussion

24.	Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.
Answer» Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Discussion

25.	Two traffic sign boards are placed beside a highway. They look like two isosceles triangles. Find the ratio of ABXY.
Answer» Two traffic sign boards are placed beside a highway. They look like two isosceles $triangles. Find the ratio of \frac{A B}{X Y} .$

Discussion

26.	The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is(a) 60π cm2(b) 68π cm2(c) 120π cm2(d) 136π cm2
Answer» The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is (a) 60π cm² (b) 68π cm² (c) 120π cm² (d) 136π cm²

Discussion

27.	Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.
Answer» Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.

Discussion

28.	12 identical balls are to be placed in 3 boxes. Probability that one of the box contains exactly 3 balls
Answer» 12 identical balls are to be placed in 3 boxes. Probability that one of the box contains exactly 3 balls

Discussion

29.	If α & β are the zeros of 6x2−x−2 , then αβ+βα=?
Answer» If $α & β$ are the zeros of $6 x^{2} - x - 2$ , then $\frac{α}{β} + \frac{β}{α} = ?$

Discussion

30.	Two dice are thrown simultaneously. The probability of getting a pair of aces is(a) 1/36(b) 1/3(c) 1/6(d) none of these
Answer» Two dice are thrown simultaneously. The probability of getting a pair of aces is (a) 1/36 (b) 1/3 (c) 1/6 (d) none of these

Discussion

31.	Find the domain of the given function.
Answer» Find the domain of the given function.

Discussion

32.	Q41.If mcosecx + ncotx =2 and (m^2.cosec^2x)-(n^2.cot^2x)=5 then (81/m^2)-(1/n^2) is equal to
Answer» Q41.If mcosecx + ncotx =2 and (m^2.cosec^2x)-(n^2.cot^2x)=5 then (81/m^2)-(1/n^2) is equal to

Discussion

33.	If cos 2θ = sin 4θ, where 2θ and 4θ are acute angles, find the value of θ.
Answer» If cos 2θ = sin 4θ, where 2θ and 4θ are acute angles, find the value of θ.

Discussion

34.	A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3:4
Answer» A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3:4

Discussion

35.	Water in canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. how much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Answer» Water in canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. how much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Discussion

36.	Question 4 (iv)hich of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:2x - 2y - 2 = 0, 4x - 4y - 5 = 0
Answer» Question 4 (iv) hich of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically: 2x - 2y - 2 = 0, 4x - 4y - 5 = 0

Discussion

37.	40. Out of 15 persons sitting around a round table 4 persons A B C D are chosen at random. The chance that no 2 of these 4 are sitting next to one another
Answer» 40. Out of 15 persons sitting around a round table 4 persons A B C D are chosen at random. The chance that no 2 of these 4 are sitting next to one another

Discussion

38.	Find the mean age in years from the frequency distribution given below:Class interval of age in yearsFrequency(fi)25−29430−341435−392240−441645−49650−54555−593Total70
Answer» Find the mean age in years from the frequency distribution given below: $\begin{matrix} Class interval of age in years & Frequency (f_{i}) 25 - 29 & 4 30 - 34 & 14 35 - 39 & 22 40 - 44 & 16 45 - 49 & 6 50 - 54 & 5 55 - 59 & 3 Total & 70 \end{matrix}$

Discussion

39.	A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.
Answer» A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

40.	The probability of picking the letter K from the word TREKKING is x4. Then find the value of x.
Answer» The probability of picking the letter K from the word TREKKING is $\frac{x}{4}$ . Then find the value of x.

Discussion

41.	Two poles of equal heights are standing opposite each other on either side of the road,90 m wide . From a point between them on the road, the angles of elevation of the top of the poles are 60∘ and 30∘, respectively. Find the distances of the point from the poles.
Answer» Two poles of equal heights are standing opposite each other on either side of the road,90 m wide . From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ , respectively. Find the distances of the point from the poles.

Discussion

42.	Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.
Answer» Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.

42.

Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.

Answer»

Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.

Discussion

43.	The following are the marks (out of 100) of 60 students in Mathematics.16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35,72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55,26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.Construct a grouped frequency distribution table with width 10 of each class starting from 0 - 9.
Answer» The following are the marks (out of 100) of 60 students in Mathematics. 16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30. Construct a grouped frequency distribution table with width 10 of each class starting from 0 - 9.

Discussion

44.	How many three- digit numbers are divisible by 87 ?
Answer» How many three- digit numbers are divisible by 87 ?

Discussion

45.	35. The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x+2y=16 is:- (1)2x-5y+11=0 (2)2x+5y-11=0 (3)2x+5y+11=0 (4)none of these
Answer» 35. The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x+2y=16 is:- (1)2x-5y+11=0 (2)2x+5y-11=0 (3)2x+5y+11=0 (4)none of these

Discussion

46.	Select the option that contains the factor of 4x3+4x2−x−1
Answer» Select the option that contains the factor of $4 x^{3} + 4 x^{2} - x - 1$

Discussion

47.	In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.
Answer» In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.

Discussion

48.	(sinA+cosecA)2−(sinA−cosecA)2=
Answer» $(s i n A + c o s e c A)^{2} - (s i n A - c o s e c A)^{2} =$

Discussion

49.	Simplify : (2√45+3√20)2√5
Answer» Simplify : $\frac{(2 \sqrt{45} + 3 \sqrt{20})}{2 \sqrt{5}}$

Discussion

50.	If P(A) = 0.15, then P(not A)
Answer» If P(A) = 0.15, then P(not A)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the weight of a hollow sphere of metal having internal and external diameters as 20 cm and 22 cm, respectively if 1m3 of metal weighs 21g.

Draw a triangle of sides 4, 5, 6 centimetres and draw its incircle.

Show that the points A (1, 0), B (5, 3), C (2, 7) and D(-2, 4) are the vertices of a parallelogram.

Evaluate each of the following4 (sin4 60° + cos4 30°) − 3 (tan2 60° − tan2 45°) + 5 cos2 45°

A sector of 56° cut out from a circle contains area 4.4 cm2. Find the radius of the circle.

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

A person standing on the top of a cliff, 171 ft high, has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend with a speed of 15.0 ft/s, how short will the packet fall? Give g = 32 ft/s2.

If the vertices of a triangle are (2,0) (0,2) (4,6), then the equation of the median through the vertex (2,0) is

Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.

Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed?

An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed in km/hr.300

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is(a) 1 : 2(b) 1: 4(c) 1 : 6(d) 1 : 8

cos 60° =

Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.

Question 3Obtain all other zeroes of 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

If 'n' things are arranged at random in a row then the probability that 'm' particular things are never together is?

Find the total surface area of the given cuboid.

In the given figure, PA and PB are two tangents to a circle with centre O, If ∠APB = 60∘ then find the measure of ∠OAB

y=2x+4 and are parallel lines.

A spherical ball is divided into two halves. If the curved surface of each half is 56.57 cm2, find the volume of the spherical ball.

Total surface area of a cone of radius 5 cm and slant height 10 cm is .(Take π=3.14)

Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.

Find the value of tan(90−A)cot(90−A)

Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Two traffic sign boards are placed beside a highway. They look like two isosceles triangles. Find the ratio of ABXY.

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is(a) 60π cm2(b) 68π cm2(c) 120π cm2(d) 136π cm2

Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.

12 identical balls are to be placed in 3 boxes. Probability that one of the box contains exactly 3 balls

If α &amp; β are the zeros of 6x2−x−2 , then αβ+βα=?

Two dice are thrown simultaneously. The probability of getting a pair of aces is(a) 1/36(b) 1/3(c) 1/6(d) none of these

Find the domain of the given function.

Q41.If mcosecx + ncotx =2 and (m^2.cosec^2x)-(n^2.cot^2x)=5 then (81/m^2)-(1/n^2) is equal to

If cos 2θ = sin 4θ, where 2θ and 4θ are acute angles, find the value of θ.

A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3:4

Water in canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. how much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Question 4 (iv)hich of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:2x - 2y - 2 = 0, 4x - 4y - 5 = 0

40. Out of 15 persons sitting around a round table 4 persons A B C D are chosen at random. The chance that no 2 of these 4 are sitting next to one another

Find the mean age in years from the frequency distribution given below:Class interval of age in yearsFrequency(fi)25−29430−341435−392240−441645−49650−54555−593Total70

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.

The probability of picking the letter K from the word TREKKING is x4. Then find the value of x.

Two poles of equal heights are standing opposite each other on either side of the road,90 m wide . From a point between them on the road, the angles of elevation of the top of the poles are 60∘ and 30∘, respectively. Find the distances of the point from the poles.

Volume of a cylinder is 4400 cc and diameter is 20 cm. Find the height of the cylinder.

How many three- digit numbers are divisible by 87 ?

35. The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x+2y=16 is:- (1)2x-5y+11=0 (2)2x+5y-11=0 (3)2x+5y+11=0 (4)none of these

Select the option that contains the factor of 4x3+4x2−x−1

In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.

(sinA+cosecA)2−(sinA−cosecA)2=

Simplify : (2√45+3√20)2√5

If P(A) = 0.15, then P(not A)

If α & β are the zeros of 6x2−x−2 , then αβ+βα=?