32581 + Interview Questions in Mathematics

1.	What is the smallest number that when we divide by 35,56 and 91 leaves remainder in each case.
Answer» What is the smallest number that when we divide by 35,56 and 91 leaves remainder in each case.

Discussion

2.	21. Proove that one out of every 3 consecutive integers is divisible by 3.
Answer» 21. Proove that one out of every 3 consecutive integers is divisible by 3.

Discussion

3.	The polynomial P(x) = 4x3+7x2–5x+t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.
Answer» The polynomial P(x) = $4 x^{3} + 7 x^{2} - 5 x + t$ , when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.

Discussion

4.	A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate) [HOTS]
Answer» A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of $π$ as found appropriate) [HOTS]

Discussion

5.	Two coincident lines are of equal length. One of them is moved clockwise with respect to the other such that they share a common end point until they coincide again. Let A be the area swept by the line and let B be the area swept when this line makes any angle θ(θ <360) with fixed line. Then A:B is:
Answer» Two coincident lines are of equal length. One of them is moved clockwise with respect to the other such that they share a common end point until they coincide again. Let A be the area swept by the line and let B be the area swept when this line makes any angle $θ (θ < 360)$ with fixed line. Then A:B is:

Discussion

6.	Which geometrical instrument is used to make equal line segments or mark points on a line ?
Answer» Which geometrical instrument is used to make equal line segments or mark points on a line ?

Discussion

7.	sin222°+sin268°cos222°+cos268°+sin263°+cos63° sin 27°
Answer» $\{\frac{\sin^{2} 22 ° + \sin^{2} 68 °}{\cos^{2} 22 ° + \cos^{2} 68 °} + \sin^{2} 63 ° + \cos 63 ° \sin 27 °\}$

Discussion

8.	Facts or figures collected with a definite purpose is called _______.
Answer» Facts or figures collected with a definite purpose is called _______.

Discussion

9.	Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.
Answer» Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Discussion

10.	Write the common difference of an A.P. the sum of whose first n terms is P2n2+Qn
Answer» Write the common difference of an A.P. the sum of whose first n terms is $\frac{P}{2} n^{2} + Q n$

Discussion

11.	What is the perimeter of a square which circumscribes a circle of radius a cm?
Answer» What is the perimeter of a square which circumscribes a circle of radius a cm?

Discussion

12.

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number of letters 1 − 4 4 − 7 7 − 10 10 − 13 13 − 16 16 − 19 Number of surnames 6 30 40 6 4 4 Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Answer»

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters	1 − 4	4 − 7	7 − 10	10 − 13	13 − 16	16 − 19
Number of surnames	6	30	40	6	4	4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Discussion

13.	A solid metallic cuboid of dimensions 9 m × 8 m × 2 m is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed. [CBSE 2017]
Answer» A solid metallic cuboid of dimensions 9 m × 8 m × 2 m is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed. [CBSE 2017]

Discussion

14.	d/dx (cotx) = ?d/dx (secx) = ?d/dx (cosecx) = ?
Answer» d/dx (cotx) = ? d/dx (secx) = ? d/dx (cosecx) = ?

Discussion

15.	Water is leaking from a conical funnel at the rate of 5 cm2sec.If the radius of the base of the funnel is 5 cm and its altitude is 10 cm.find the rate at which the water level is dropping when it is 2.5 cm from the top
Answer» Water is leaking from a conical funnel at the rate of 5 cm2sec.If the radius of the base of the funnel is 5 cm and its altitude is 10 cm.find the rate at which the water level is dropping when it is 2.5 cm from the top

Discussion

16.	A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied?
Answer» A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied?

Discussion

17.	Short-Answer QuestionsSolve: 3x2-22x-23=0 [CBSE 2014]
Answer» Short-Answer Questions Solve: $\sqrt{3} x^{2} - 2 \sqrt{2} x - 2 \sqrt{3} = 0$ [CBSE 2014]

Discussion

18.	In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.
Answer» In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.

18.

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.

Answer»

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.

Discussion

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

Discussion

20.	Evaluate the following : (i) sin–1(sin 10) (ii) cot–1(cot 4)
Answer» Evaluate the following : (i) sin–1(sin 10) (ii) cot–1(cot 4)

Discussion

21.	In a parabola show that the tangent at any point makes equal angles with the focal radius of the point and the line parallel to the axis through the point.
Answer» In a parabola show that the tangent at any point makes equal angles with the focal radius of the point and the line parallel to the axis through the point.

Discussion

22.	Determine the nature of the roots of the following quadratic equations:(i) (ii) ,a ≠0, b≠0(iii) (iv)
Answer» Determine the nature of the roots of the following quadratic equations: (i) (ii) , $a \neq 0, b \neq 0$ (iii) (iv)

Discussion

23.	In a ∆ABC, AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm, then DC =(a) 11.3 cm(b) 2.5 cm(c) 3 : 5 cm(d) None of these
Answer» In a ∆ABC, AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm, then DC = (a) 11.3 cm (b) 2.5 cm (c) 3 : 5 cm (d) None of these

Discussion

24.	'As the new teacher saw it' (Paragraph 6). Which of the following best explains the meaning of this expression?(a) as our new teacher understood it(b) as our new teacher wanted it(c) as our new teacher was asked to ensure
Answer» 'As the new teacher saw it' (Paragraph 6). Which of the following best explains the meaning of this expression? (a) as our new teacher understood it (b) as our new teacher wanted it (c) as our new teacher was asked to ensure

24.

'As the new teacher saw it' (Paragraph 6). Which of the following best explains the meaning of this expression?(a) as our new teacher understood it(b) as our new teacher wanted it(c) as our new teacher was asked to ensure

Answer»

'As the new teacher saw it' (Paragraph 6). Which of the following best explains the meaning of this expression?

(a) as our new teacher understood it

(b) as our new teacher wanted it

(c) as our new teacher was asked to ensure

Discussion

25.	Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60∘.
Answer» Draw a pair of tangents to a circle of radius $5 c m$ which are inclined to each other at an angle of $60^{\circ}$ .

Discussion

26.	A rhombus having each side 10 cm has one of its angles as 120∘, then find the area of the rhombus.
Answer» A rhombus having each side 10 cm has one of its angles as $120^{\circ}$ , then find the area of the rhombus.

Discussion

27.	Short-Answer QuestionsSolve: x2-3+1x+3=0 [CBSE 2015]
Answer» Short-Answer Questions Solve: $x^{2} - (\sqrt{3} + 1) x + \sqrt{3} = 0$ [CBSE 2015]

Discussion

28.	The area of the bounded by the circle x2 + y2 = 1 is ______________.
Answer» The area of the bounded by the circle x² + y² = 1 is ______________.

Discussion

29.	how to find largest integral value of a solution ?What are the rules for it in wavy curve method of a equation?
Answer» how to find largest integral value of a solution ?What are the rules for it in wavy curve method of a equation?

Discussion

30.	Question 6A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
Answer» Question 6 A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Discussion

31.	The midpoints of the sides BC, CA and AB of a ΔABC are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of the vertices of the triangle. [CBSE 2017]
Answer» The midpoints of the sides BC, CA and AB of a ΔABC are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of the vertices of the triangle. [CBSE 2017]

Discussion

32.	If the radius of a sphere is 2r, then its volume is _________.
Answer» If the radius of a sphere is 2r, then its volume is _________.

Discussion

33.	Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Answer» Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Discussion

34.	Abc is an arc of circle with centre p ,if measure angle abc is 110 then abc is (major /minor) arc?
Answer» Abc is an arc of circle with centre p ,if measure angle abc is 110 then abc is (major /minor) arc?

Discussion

35.	cot θcot θ-cot 3θ+tan θtan θ-tan 3θis equal to(a) 0(b) 1(c) −1(d) 2
Answer» $\frac{\cot θ}{\cot θ - c o t 3 θ} + \frac{\tan θ}{\tan θ - \tan 3 θ}$ is equal to (a) 0 (b) 1 (c) −1 (d) 2

Discussion

36.	Water in a 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 m2) in 30 minutes, if 8 cm of standing water is needed?
Answer» Water in a 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 $m^{2}$ ) in 30 minutes, if 8 cm of standing water is needed?

Discussion

37.	ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that
Answer» ABCD is a trapezium in which AB \|\| DC and its diagonals intersect each other at the point O. Show that

Discussion

38.	In a nursery, 37 plants have been arranged in the first row, 35 in the second, 33 in the third and so on. If there are 5 plants in the last row, how many plants are there in the nursery? [3 MARKS]
Answer» In a nursery, 37 plants have been arranged in the first row, 35 in the second, 33 in the third and so on. If there are 5 plants in the last row, how many plants are there in the nursery? [3 MARKS]

Discussion

39.	If the principal is doubled, what change must be made in the rate of interest such that the interest is the same through out?
Answer» If the principal is doubled, what change must be made in the rate of interest such that the interest is the same through out?

Discussion

40.	Prove the following trigonometric identities: (1+sin θ)2+(1−sin θ)22 cos2θ=1+sin2θ1−sin2θ
Answer» Prove the following trigonometric identities: $\frac{(1 + s i n θ)^{2} + (1 - s i n θ)^{2}}{2 c o s^{2} θ} = \frac{1 + s i n^{2} θ}{1 - s i n^{2} θ}$

40.

Prove the following trigonometric identities: (1+sin θ)2+(1−sin θ)22 cos2θ=1+sin2θ1−sin2θ

Answer»

Prove the following trigonometric identities:

$\frac{(1 + s i n θ)^{2} + (1 - s i n θ)^{2}}{2 c o s^{2} θ} = \frac{1 + s i n^{2} θ}{1 - s i n^{2} θ}$

Discussion

41.	If sin 3A = cos (A − 26°), where 3A is an acute angles, find the value of A.
Answer» If sin 3A = cos (A − 26°), where 3A is an acute angles, find the value of A.

Discussion

42.	The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .
Answer» The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .

Discussion

43.	Question 97 Solve the following: Find the product of the cube of (-2) and the square of (+4).
Answer» Question 97 Solve the following: Find the product of the cube of (-2) and the square of (+4).

43.

Question 97 Solve the following: Find the product of the cube of (-2) and the square of (+4).

Answer»

Question 97

Solve the following:

Find the product of the cube of (-2) and the square of (+4).

Discussion

44.	The surface area of a sphere is 616 cm2 . Find its radius.
Answer» The surface area of a sphere is 616 cm² . Find its radius.

Discussion

45.	The measure of ∠B in the given triangle (in degrees) is
Answer» The measure of $∠ B$ in the given triangle (in degrees) is

Discussion

46.	A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.
Answer» A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.

Discussion

47.	The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of NIT Trichy college. If the red coloured portion represents the boys percentage and the total number of students be 100 then what is the probability of a student being picked at random being a girl?
Answer» The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of NIT Trichy college. If the red coloured portion represents the boys percentage and the total number of students be 100 then what is the probability of a student being picked at random being a girl?

47.

The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of NIT Trichy college. If the red coloured portion represents the boys percentage and the total number of students be 100 then what is the probability of a student being picked at random being a girl?

Answer»

The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of NIT Trichy college. If the red coloured portion represents the boys percentage and the total number of students be 100 then what is the probability of a student being picked at random being a girl?

Discussion

48.	Question 9 (ii)In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that:(ii)CAPA=BCMP
Answer» Question 9 (ii) In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that: $(i i) \frac{C A}{P A} = \frac{B C}{M P}$

Discussion

49.	A bag contains 5 red, 8 green and 7 white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?
Answer» A bag contains 5 red, 8 green and 7 white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?

Discussion

50.

Trial Balance of a business as at 31st March, 2019 is given below: Particulars Dr. (₹) Particulars Cr. (₹) Stock on 1st April, 2018 25,000 Sales 2,27,800 Furniture 8,000 Commission 500 Plant and Machinery 1,50,000 Returns Outward 1,000 Debtors 30,000 Creditors 40,000 Wages 12,000 Capital 1,50,000 Salaries 20,000 Bad Debts 1,000 Purchases 1,20,000 Electricity Charges 1,200 Telephone Charges 2,400 General Expenses 3,000 Postage Expenses 1,800 Returns Inward 900 Insurance Premium 1,500 Cash in Hand 2,500 Cash at Bank 40,000 4,19,300 4,19,300 Prepare Trading and Profit and Loss Account for the year ended 31st March, 2019 and Balance Sheet as at that date after taking into account the following adjustments:(i) Closing Stock was valued at ₹ 7,000.(ii) Outstanding liabilities for wages were ₹ 600 and salaries ₹ 1,400.(iii) Depreciation is to be provided 5% p.a. on fixed assets.(iv) Included in Plant and Machinery is a machine purchased for ₹ 10,000 on 1st October, 2018.(v) Insurance premium paid in advance ₹ 200.

Answer» Trial Balance of a business as at 31st March, 2019 is given below:


Particulars	Dr. (₹)	Particulars	Cr. (₹)
Stock on 1st April, 2018	25,000	Sales	2,27,800
Furniture	8,000	Commission	500
Plant and Machinery	1,50,000	Returns Outward	1,000
Debtors	30,000	Creditors	40,000
Wages	12,000	Capital	1,50,000
Salaries	20,000
Bad Debts	1,000
Purchases	1,20,000
Electricity Charges	1,200
Telephone Charges	2,400
General Expenses	3,000
Postage Expenses	1,800
Returns Inward	900
Insurance Premium	1,500
Cash in Hand	2,500
Cash at Bank	40,000
	4,19,300		4,19,300

Prepare Trading and Profit and Loss Account for the year ended 31st March, 2019 and Balance Sheet as at that date after taking into account the following adjustments:

(i) Closing Stock was valued at ₹ 7,000.

(ii) Outstanding liabilities for wages were ₹ 600 and salaries ₹ 1,400.

(iii) Depreciation is to be provided 5% p.a. on fixed assets.

(iv) Included in Plant and Machinery is a machine purchased for ₹ 10,000 on 1st October, 2018.

(v) Insurance premium paid in advance ₹ 200.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the smallest number that when we divide by 35,56 and 91 leaves remainder in each case.

21. Proove that one out of every 3 consecutive integers is divisible by 3.

The polynomial P(x) = 4x3+7x2–5x+t, when divided by x + 1 gives 3 as the remainder. Find the value of ‘t’.

A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate) [HOTS]

Which geometrical instrument is used to make equal line segments or mark points on a line ?

sin222°+sin268°cos222°+cos268°+sin263°+cos63° sin 27°

Facts or figures collected with a definite purpose is called _______.

Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Write the common difference of an A.P. the sum of whose first n terms is P2n2+Qn

What is the perimeter of a square which circumscribes a circle of radius a cm?

A solid metallic cuboid of dimensions 9 m × 8 m × 2 m is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed. [CBSE 2017]

d/dx (cotx) = ?d/dx (secx) = ?d/dx (cosecx) = ?

Water is leaking from a conical funnel at the rate of 5 cm2sec.If the radius of the base of the funnel is 5 cm and its altitude is 10 cm.find the rate at which the water level is dropping when it is 2.5 cm from the top

A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied?

Short-Answer QuestionsSolve: 3x2-22x-23=0 [CBSE 2014]

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.

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

Evaluate the following : (i) sin–1(sin 10) (ii) cot–1(cot 4)

In a parabola show that the tangent at any point makes equal angles with the focal radius of the point and the line parallel to the axis through the point.

Determine the nature of the roots of the following quadratic equations:(i) (ii) ,a ≠0, b≠0(iii) (iv)

In a ∆ABC, AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm, then DC =(a) 11.3 cm(b) 2.5 cm(c) 3 : 5 cm(d) None of these

'As the new teacher saw it' (Paragraph 6). Which of the following best explains the meaning of this expression?(a) as our new teacher understood it(b) as our new teacher wanted it(c) as our new teacher was asked to ensure

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60∘.

A rhombus having each side 10 cm has one of its angles as 120∘, then find the area of the rhombus.

Short-Answer QuestionsSolve: x2-3+1x+3=0 [CBSE 2015]

​The area of the bounded by the circle x2 + y2 = 1 is ______________.

how to find largest integral value of a solution ?What are the rules for it in wavy curve method of a equation?

Question 6A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

The midpoints of the sides BC, CA and AB of a ΔABC are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of the vertices of the triangle. [CBSE 2017]

If the radius of a sphere is 2r, then its volume is _________.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Abc is an arc of circle with centre p ,if measure angle abc is 110 then abc is (major /minor) arc?

cot θcot θ-cot 3θ+tan θtan θ-tan 3θis equal to(a) 0(b) 1(c) −1(d) 2

Water in a 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 m2) in 30 minutes, if 8 cm of standing water is needed?

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

In a nursery, 37 plants have been arranged in the first row, 35 in the second, 33 in the third and so on. If there are 5 plants in the last row, how many plants are there in the nursery? [3 MARKS]

If the principal is doubled, what change must be made in the rate of interest such that the interest is the same through out?

Prove the following trigonometric identities: (1+sin θ)2+(1−sin θ)22 cos2θ=1+sin2θ1−sin2θ

If sin 3A = cos (A − 26°), where 3A is an acute angles, find the value of A.

The length of the minute hand of a clock is 14cm. The area swept by the minute hand between 3: 20 and 3: 45 is __ .

Question 97 Solve the following: Find the product of the cube of (-2) and the square of (+4).

The surface area of a sphere is 616 cm2 . Find its radius.

The measure of ∠B in the given triangle (in degrees) is

A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.

Question 9 (ii)In the following figure, ABC and AMP are two right triangles, right angled at B and M respectively, prove that:(ii)CAPA=BCMP

A bag contains 5 red, 8 green and 7 white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?

The area of the bounded by the circle x2 + y2 = 1 is ______________.