32581 + Interview Questions in Mathematics

1.	In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options. At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (5)?
Answer» In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options. At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (5)?

Discussion

2.	On tossing three coins simultaneously, find the probability of getting atleast a head and a tail.
Answer» On tossing three coins simultaneously, find the probability of getting atleast a head and a tail.

Discussion

3.	Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Answer» Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.

Discussion

4.	23.The mid points of the sides of a triangle are (5,0),(5,12) and (0,12), then orthocentre of this triangle is:- ?
Answer» 23.The mid points of the sides of a triangle are (5,0),(5,12) and (0,12), then orthocentre of this triangle is:- ?

Discussion

5.	Two ships are there in the sea on either side of a light house in such away that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are 60∘ and 45∘ respectively. If the height of the light house is 200 m, find the distance between the two ships. (Use √3=1.73)
Answer» Two ships are there in the sea on either side of a light house in such away that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are $60^{\circ}$ and $45^{\circ}$ respectively. If the height of the light house is 200 m, find the distance between the two ships. (Use $\sqrt{3} = 1.73)$

Discussion

6.	If a is an odd number, b is not divisible by 3 and LCM of a and b is p. What is the LCM of 3a and 2b ?
Answer» If a is an odd number, b is not divisible by 3 and LCM of a and b is p. What is the LCM of 3a and 2b ?

Discussion

7.	Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
Answer» Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.

Discussion

8.	A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the inside surface area of the dome, [Assume π=227]
Answer» A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the inside surface area of the dome, $[A s s u m e π = \frac{22}{7}]$

Discussion

9.	Find the area and perimeter of an isosceles right-angled triangle, each of whose equal sides measures 10 cm. [Given: 2 = 1.41]
Answer» Find the area and perimeter of an isosceles right-angled triangle, each of whose equal sides measures 10 cm. [Given: $\sqrt{2}$ = 1.41]

Discussion

10.	A man buys ₹ 20 share at a premium of ₹ 10 share. If the company pays 9% dividend, find the percentage return on his investment in buying 200 shares.
Answer» A man buys ₹ 20 share at a premium of ₹ 10 share. If the company pays $9 %$ dividend, find the percentage return on his investment in buying 200 shares.

Discussion

11.	banu is 20 years older than binu.in 5 years banu will be twice as old as binu. find their present age
Answer» banu is 20 years older than binu.in 5 years banu will be twice as old as binu. find their present age

Discussion

12.	Solve the following quadratic equations by factorization:1x-1-1x+5=67, x≠1, -5
Answer» Solve the following quadratic equations by factorization: $\frac{1}{x - 1} - \frac{1}{x + 5} = \frac{6}{7}, x \neq 1, - 5$

Discussion

13.	The radius of a circle and the tangent are perpendicular at the point of ___ .
Answer» The radius of a circle and the tangent are perpendicular at the point of ___ .

Discussion

14.	the altitude of a triangle are 12; 15 ; 20 . find the largest angle in degree
Answer» the altitude of a triangle are 12; 15 ; 20 . find the largest angle in degree

Discussion

15.	why we have to multiply area \ast2 to find total change in area of hollow sphere and not in circl?
Answer» why we have to multiply area \ast2 to find total change in area of hollow sphere and not in circl?

Discussion

16.	The 4th term of the AP√8,√18,√32.... is ____.
Answer» The 4th term of the $A P \sqrt{8}, \sqrt{18}, \sqrt{32}$ .... is ____.

Discussion

17.	All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a (i) face card (ii) red card (iii) black card (iv) king
Answer» All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a (i) face card (ii) red card (iii) black card (iv) king

17.

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a (i) face card (ii) red card (iii) black card (iv) king

Answer»

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a

(i) face card (ii) red card (iii) black card (iv) king

Discussion

18.	Find the numbers such that the square of number is 15 lesser than twice the number.
Answer» Find the numbers such that the square of number is 15 lesser than twice the number.

Discussion

19.	A number when divided by 88 gives the remainder 8. What will be the remainder when this number is divided by 11?
Answer» A number when divided by 88 gives the remainder 8. What will be the remainder when this number is divided by 11?

Discussion

20.	In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.
Answer» In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Discussion

21.	Verify whether the following are true or false.(i) -3 is a zero of x - 3(ii) −13 is a zero of 3x + 1(iii) −45 is a zero of 4 - 5y(iv) 0 and 2 are the zeroes of t2–t
Answer» Verify whether the following are true or false. (i) -3 is a zero of x - 3 (ii) $- \frac{1}{3}$ is a zero of 3x + 1 (iii) $- \frac{4}{5}$ is a zero of 4 - 5y (iv) 0 and 2 are the zeroes of $t^{2} - t$

Discussion

22.	If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =(a) a2 b2(b) ab(c) a4 b4(d) a2 + b2
Answer» If x = a cos θ and y = b sin θ, then b²x² + a²y² = (a) a² b² (b) ab (c) a⁴ b⁴ (d) a² + b²

Discussion

23.	Two isosceles triangles have equal vertical angles and their areas are in the ratio 36.25 Find the ratio of their corresponding heights.
Answer» Two isosceles triangles have equal vertical angles and their areas are in the ratio 36.25 Find the ratio of their corresponding heights.

Discussion

24.	What is a segment?
Answer» What is a segment?

Discussion

25.	Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
Answer» Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.

Discussion

26.	The equation of two sides of triangle are 3x−2y+6=0 and 4x+5y=20 and orthocentre is (1,1), then the equation of third side is
Answer» The equation of two sides of triangle are $3 x - 2 y + 6 = 0$ and $4 x + 5 y = 20$ and orthocentre is $(1, 1)$ , then the equation of third side is

Discussion

27.	If the three equations x2+ax+12=0, x2+bx+15=0, x2+(a+b)x+36=0 have a common positive root. Then, the sum of roots is
Answer» If the three equations $x^{2} + a x + 12 = 0,$ $x^{2} + b x + 15 = 0,$ $x^{2} + (a + b) x + 36 = 0$ have a common positive root. Then, the sum of roots is

Discussion

28.	Very-Short-Answer QuestionsIf the quadratic equation px2-25px+15=0 has two equal roots then find the value of p. [CBSE 2015]
Answer» Very-Short-Answer Questions If the quadratic equation $p x^{2} - 2 \sqrt{5} p x + 15 = 0$ has two equal roots then find the value of p. [CBSE 2015]

Discussion

29.	Solve the following system of equations by using the method of cross-multiplication:ax-by=0ab2x+a2by=a2+b2, where x≠0 and y≠0
Answer» Solve the following system of equations by using the method of cross-multiplication: $\frac{a}{x} - \frac{b}{y} = 0 \frac{a b^{2}}{x} + \frac{a^{2} b}{y} = a^{2} + b^{2}, where x \neq 0 and y \neq 0$

Discussion

30.	If the difference between the circumference and radius of a circle is 37 cm then the circumference of the circle is?
Answer» If the difference between the circumference and radius of a circle is 37 cm then the circumference of the circle is?

Discussion

31.	The mode for the given data is ___ . IQ60−7070−8080−9090−100100−110110−120120−130No. of pupils2351614137
Answer» The mode for the given data is ___ . $\begin{matrix} IQ & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 No. of pupils & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

Discussion

32.	A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.
Answer» A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.

Discussion

33.	Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36th term.
Answer» Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36^th term.

Discussion

34.	According to theoretical probability approach, what is the probability of getting a head in tossing of a coin?
Answer» According to theoretical probability approach, what is the probability of getting a head in tossing of a coin?

Discussion

35.	Question 7Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as shown in figure). She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Answer» Question 7 Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as shown in figure). She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

35.

Question 7Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as shown in figure). She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Answer»

Question 7

Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as shown in figure). She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Discussion

36.	If 3+5+7+……+upto n terms5+8+11+……upto 10 terms=7, then find the value of n.
Answer» If $\frac{3 + 5 + 7 + \dots \dots + upto n terms}{5 + 8 + 11 + \dots \dots upto 10 terms} = 7$ , then find the value of n.

Discussion

37.	A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width. [CBSE 2013]
Answer» A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width. [CBSE 2013]

Discussion

38.	For 2 triangles, if the ratio of bases is 3:2 and the ratio of their corresponding altitudes is 2:3, then the ratio of their areas will be
Answer» For 2 triangles, if the ratio of bases is 3:2 and the ratio of their corresponding altitudes is 2:3, then the ratio of their areas will be

Discussion

39.	The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m².
Answer» The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m².

Discussion

40.	The king, queen and jack are removed from a deck of 52 playing cards and then shuffled. One card is selected from the remaining cards. Find the probability of getting an ace.
Answer» The king, queen and jack are removed from a deck of 52 playing cards and then shuffled. One card is selected from the remaining cards. Find the probability of getting an ace.

Discussion

41.	If secθ+tanθ=p, prove thati secθ=12p+1p ii tanθ=12p-1p iii sinθ=p2-1p2+1
Answer» If $\sec θ + \tan θ = p$ , prove that $(i) \sec θ = \frac{1}{2} (p + \frac{1}{p}) (ii) \tan θ = \frac{1}{2} (p - \frac{1}{p}) (iii) \sin θ = \frac{p^{2} - 1}{p^{2} + 1}$

Discussion

42.	One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .
Answer» One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .

Discussion

43.	Arrange the polynomials in the increasing order of their degree (bottom to top).
Answer» Arrange the polynomials in the increasing order of their degree (bottom to top).

Discussion

44.	In the figures given below, ∠ABC= and ∠DEF=
Answer» In the figures given below, $∠ A B C =$ and $∠ D E F =$

Discussion

45.	Using the distance formula, show that the given points are collinear: (i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)
Answer» Using the distance formula, show that the given points are collinear: (i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

45.

Using the distance formula, show that the given points are collinear: (i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

Answer»

Using the distance formula, show that the given points are collinear:

(i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

Discussion

46.	If one root of the equation 2x2+ax+6=0 is 3, then the value of a is ___________.
Answer» If one root of the equation $2 x^{2} + a x + 6 = 0$ is 3, then the value of a is ___________.

Discussion

47.	A man on a cliff observes a boat, at an angle of depression 30∘, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60∘. Assuming that the boat sails at a uniform speed, determine : (i) how much more time it will take to reach the shore ? (ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.
Answer» A man on a cliff observes a boat, at an angle of depression $30^{\circ}$ , which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be $60^{\circ}$ . Assuming that the boat sails at a uniform speed, determine : (i) how much more time it will take to reach the shore ? (ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.

47.

A man on a cliff observes a boat, at an angle of depression 30∘, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60∘. Assuming that the boat sails at a uniform speed, determine : (i) how much more time it will take to reach the shore ? (ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.

Answer»

A man on a cliff observes a boat, at an angle of depression $30^{\circ}$ , which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be $60^{\circ}$ . Assuming that the boat sails at a uniform speed, determine :

(i) how much more time it will take to reach the shore ?

(ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.

Discussion

48.	Which number comes next in the Arithmetic progression: 4, 8, 12, 16, ...?
Answer» Which number comes next in the Arithmetic progression: 4, 8, 12, 16, ...?

Discussion

49.	The sum of a natural number and its reciprocal is 658. Find the number.
Answer» The sum of a natural number and its reciprocal is $\frac{65}{8}$ . Find the number.

Discussion

50.	A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60∘. From another point 40 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30∘. Find the height of the tower and the width of the canal.
Answer» A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From another point 40 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the canal.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

On tossing three coins simultaneously, find the probability of getting atleast a head and a tail.

Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.

23.The mid points of the sides of a triangle are (5,0),(5,12) and (0,12), then orthocentre of this triangle is:- ?

If a is an odd number, b is not divisible by 3 and LCM of a and b is p. What is the LCM of 3a and 2b ?

Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2 per square meter, find the inside surface area of the dome, [Assume π=227]

Find the area and perimeter of an isosceles right-angled triangle, each of whose equal sides measures 10 cm. [Given: 2 = 1.41]

A man buys ₹ 20 share at a premium of ₹ 10 share. If the company pays 9% dividend, find the percentage return on his investment in buying 200 shares.

banu is 20 years older than binu.in 5 years banu will be twice as old as binu. find their present age

Solve the following quadratic equations by factorization:1x-1-1x+5=67, x≠1, -5

The radius of a circle and the tangent are perpendicular at the point of ___ .

the altitude of a triangle are 12; 15 ; 20 . find the largest angle in degree

why we have to multiply area \ast2 to find total change in area of hollow sphere and not in circl?

The 4th term of the AP√8,√18,√32.... is ____.

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a (i) face card (ii) red card (iii) black card (iv) king

Find the numbers such that the square of number is 15 lesser than twice the number.

A number when divided by 88 gives the remainder 8. What will be the remainder when this number is divided by 11?

In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14 cm, BC = 8 cm and CA = 12 cm. Find the lengths AD, BE and CF.

Verify whether the following are true or false.(i) -3 is a zero of x - 3(ii) −13 is a zero of 3x + 1(iii) −45 is a zero of 4 - 5y(iv) 0 and 2 are the zeroes of t2–t

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =(a) a2 b2(b) ab(c) a4 b4(d) a2 + b2

Two isosceles triangles have equal vertical angles and their areas are in the ratio 36.25 Find the ratio of their corresponding heights.

What is a segment?

Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.

The equation of two sides of triangle are 3x−2y+6=0 and 4x+5y=20 and orthocentre is (1,1), then the equation of third side is

If the three equations x2+ax+12=0, x2+bx+15=0, x2+(a+b)x+36=0 have a common positive root. Then, the sum of roots is

Very-Short-Answer QuestionsIf the quadratic equation px2-25px+15=0 has two equal roots then find the value of p. [CBSE 2015]

Solve the following system of equations by using the method of cross-multiplication:ax-by=0ab2x+a2by=a2+b2, where x≠0 and y≠0

If the difference between the circumference and radius of a circle is 37 cm then the circumference of the circle is?

The mode for the given data is ___ . IQ60−7070−8080−9090−100100−110110−120120−130No. of pupils2351614137

A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.

Find the term of the arithmetic progression 9, 12, 15, 18, ... which is 39 more than its 36th term.

According to theoretical probability approach, what is the probability of getting a head in tossing of a coin?

Question 7Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as shown in figure). She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

If 3+5+7+……+upto n terms5+8+11+……upto 10 terms=7, then find the value of n.

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width. [CBSE 2013]

For 2 triangles, if the ratio of bases is 3:2 and the ratio of their corresponding altitudes is 2:3, then the ratio of their areas will be

The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. Find the length of each side knowing that the area of the triangle is 24 m².

The king, queen and jack are removed from a deck of 52 playing cards and then shuffled. One card is selected from the remaining cards. Find the probability of getting an ace.

If secθ+tanθ=p, prove thati secθ=12p+1p ii tanθ=12p-1p iii sinθ=p2-1p2+1

One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .

Arrange the polynomials in the increasing order of their degree (bottom to top).

In the figures given below, ∠ABC= and ∠DEF=

Using the distance formula, show that the given points are collinear: (i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

If one root of the equation 2x2+ax+6=0 is 3, then the value of a is ___________.

Which number comes next in the Arithmetic progression: 4, 8, 12, 16, ...?

The sum of a natural number and its reciprocal is 658. Find the number.