32581 + Interview Questions in Mathematics

1.	How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?
Answer» How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?

Discussion

2.	Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.
Answer» Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.

Discussion

3.	Find the probability that the month of January may have 5 Mondays in (I) a leap year (II) a non leap year.
Answer» Find the probability that the month of January may have 5 Mondays in (I) a leap year (II) a non leap year.

3.

Find the probability that the month of January may have 5 Mondays in (I) a leap year (II) a non leap year.

Answer»

Find the probability that the month of January may have 5 Mondays in

(I) a leap year

(II) a non leap year.

Discussion

4.	Question 7 A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Answer» Question 7 A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per $m^{2}$ . (Note that the base of the tent will not be covered with canvas.)

Discussion

5.	If the solutions of the equation x2+3x−18=0 are -6, 3 then the roots of the equation 2(x2+3x−18)=0 are
Answer» If the solutions of the equation $x^{2} + 3 x - 18 = 0$ are -6, 3 then the roots of the equation $2 (x^{2} + 3 x - 18) = 0$ are

Discussion

6.	A bank’s function of providing locker facility to its customers for the safe custody of their valuables is a/an
Answer» A bank’s function of providing locker facility to its customers for the safe custody of their valuables is a/an

Discussion

7.	Draw the graph of y=x2+x−12 and hence solve x2+2x+2=0.
Answer» Draw the graph of $y = x^{2} + x - 12$ and hence solve $x^{2} + 2 x + 2 = 0$ .

Discussion

8.	Two points on the circumference of a circle result in the formation of two arcs. The arc of shorter length is called the ___ arc.
Answer» Two points on the circumference of a circle result in the formation of two arcs. The arc of shorter length is called the ___ arc.

Discussion

9.	Find the equation of a straight line whose y intercept is −4 and is parallel to the line joining the points (3,−2) and (1,4).
Answer» Find the equation of a straight line whose y intercept is $- 4$ and is parallel to the line joining the points $(3, - 2)$ and $(1, 4)$ .

Discussion

10.	4 + 44 + 444 + .................upto n terms = __
Answer» 4 + 44 + 444 + .................upto $n$ terms = __

Discussion

11.	The LCM of 6(4x2−4x+1) and 9(2x2−7x+3) is:
Answer» $The LCM of 6 (4 x^{2} - 4 x + 1) and 9 (2 x^{2} - 7 x + 3) is :$

Discussion

12.	Which of the following has a non terminating decimal expansion?
Answer» Which of the following has a non terminating decimal expansion?

Discussion

13.	Question 15 If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is (A) 4πr2 (B) 6πr2 (C) 3πr2 (D) 8πr2
Answer» Question 15 If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is (A) $4 π r^{2}$ (B) $6 π r^{2}$ (C) $3 π r^{2}$ (D) $8 π r^{2}$

Discussion

14.	In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.
Answer» In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

Discussion

15.	The median of the observations 50 , 54 , 56 , 58 , (2x + 1) , 66 , 72 , 74 , 78 arranged in ascending order is 63. Find the value of x
Answer» The median of the observations 50 , 54 , 56 , 58 , (2x + 1) , 66 , 72 , 74 , 78 arranged in ascending order is 63. Find the value of x

Discussion

16.	The expansion of the algebraic identity ( x + a ) ( x + b ) is:
Answer» The expansion of the algebraic identity ( x + a ) ( x + b ) is:

Discussion

17.	Which of the following points does not lie on the line 2x + 4y = 8?
Answer» Which of the following points does not lie on the line 2x + 4y = 8?

Discussion

18.	Question 5 In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.
Answer» Question 5 In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.

Discussion

19.	Find the acute angle (θ) at which sin θ and tan θ are equal?
Answer» Find the acute angle $(θ)$ at which $s i n θ a n d t a n θ are equal?$

Discussion

20.	There are 60 students in a class among which 30 are boys. In another class, there are 50 students among which 25 of them are boys. If one from each class is selected, What is the probability of both being girls?
Answer» There are 60 students in a class among which 30 are boys. In another class, there are 50 students among which 25 of them are boys. If one from each class is selected, What is the probability of both being girls?

Discussion

21.	If the sum of the first "n" natural numbers is 351, which of the following is the value of "n" ?
Answer» If the sum of the first "n" natural numbers is 351, which of the following is the value of "n" ?

Discussion

22.	Simplify sin θ×cosec θ×cot θ.
Answer» Simplify $s i n θ \times c o s e c θ \times c o t θ .$

Discussion

23.	Match the volume of the cone of radius 'r', height 'h' and slant height 'l' in each case (all meaures in cm).
Answer» Match the volume of the cone of radius 'r', height 'h' and slant height 'l' in each case (all meaures in cm).

Discussion

24.	i) Using step-deviation method, calculate the mean marks of the following distribution. ii) State the modal class. Class intervalFrequency50−55555−602060−651065−701070−75975−80680−851285−908 [4 MARKS]
Answer» i) Using step-deviation method, calculate the mean marks of the following distribution. ii) State the modal class. $\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 50 - 55 & 5 55 - 60 & 20 60 - 65 & 10 65 - 70 & 10 70 - 75 & 9 75 - 80 & 6 80 - 85 & 12 85 - 90 & 8 \end{matrix}$ [4 MARKS]

Discussion

25.	A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
Answer» A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Discussion

26.	Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: (i) y = x,y = 2x and y + x = 6 (ii) y = x, 3y = x, x + y = 8
Answer» Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: (i) y = x,y = 2x and y + x = 6 (ii) y = x, 3y = x, x + y = 8

26.

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: (i) y = x,y = 2x and y + x = 6 (ii) y = x, 3y = x, x + y = 8

Answer»

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are:

(i) y = x,y = 2x and y + x = 6

(ii) y = x, 3y = x, x + y = 8

Discussion

27.	A die is rolled once. Find the probability of getting: i) a perfect square ii) an even prime number iii) a number < 5 iv) not an even number. [4 MARKS]
Answer» A die is rolled once. Find the probability of getting: i) a perfect square ii) an even prime number iii) a number < 5 iv) not an even number. [4 MARKS]

Discussion

28.	In order to get a head at least once with probability ≥0.9, the minimum number of times a unbiased coin needs to be tossed is
Answer» In order to get a head at least once with probability $\geq 0.9,$ the minimum number of times a unbiased coin needs to be tossed is

Discussion

29.	The following arrow diagram of the function f : A → A be defined as
Answer» The following arrow diagram of the function f : A → A be defined as

29.

The following arrow diagram of the function f : A → A be defined as

Answer»

The following arrow diagram of the function f : A → A be defined as

Discussion

30.	The relationship between Mean, Median and Mode is
Answer» The relationship between Mean, Median and Mode is

Discussion

31.	When we construct a triangle similar to a triangle or when we divide a line segment in some ratio, why do we make a ray downwards of an acute angle? Can't we make it of 90 degrees or obtuse?
Answer» When we construct a triangle similar to a triangle or when we divide a line segment in some ratio, why do we make a ray downwards of an acute angle? Can't we make it of 90 degrees or obtuse?

Discussion

32.	A manufacuturer marks an article for Rs 5,000. He sells it to a wholesaler at a discount of 25% on the marked price and the wholesaler sells it to a retailer at a discount of 15% on the marked price. The retailer sells it to a consumer at the marked price and at each stage the VAT is 8%. Calculate the amount of VAT received by the Government from : (i) The wholesaler (ii) The retailer [4 MARKS]
Answer» A manufacuturer marks an article for Rs 5,000. He sells it to a wholesaler at a discount of 25% on the marked price and the wholesaler sells it to a retailer at a discount of 15% on the marked price. The retailer sells it to a consumer at the marked price and at each stage the VAT is 8%. Calculate the amount of VAT received by the Government from : (i) The wholesaler (ii) The retailer [4 MARKS]

Discussion

33.	Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2
Answer» Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2

33.

Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2

Answer»

Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2

Discussion

34.	A big iron boiler tank has a cylindrical structure which is open from the top. Its height is 10 m and radius is 7 m. It gets painted at a rate of 3 m2 per day. Then find the number of days in which the tank gets painted completely? (Take π=227)
Answer» A big iron boiler tank has a cylindrical structure which is open from the top. Its height is 10 m and radius is 7 m. It gets painted at a rate of 3 m $^{2}$ per day. Then find the number of days in which the tank gets painted completely? (Take $π = \frac{22}{7}$ )

Discussion

35.	The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm, find: (iii) curved surface area of the cone. [Assume π=227]
Answer» The volume of a right circular cone is $9856 c m^{3}$ . If the diameter of the base is 28cm, find: (iii) curved surface area of the cone. $[A s s u m e π = \frac{22}{7}]$

35.

The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm, find: (iii) curved surface area of the cone. [Assume π=227]

Answer»

The volume of a right circular cone is $9856 c m^{3}$ . If the diameter of the base is 28cm, find:
(iii) curved surface area of the cone.
$[A s s u m e π = \frac{22}{7}]$

Discussion

36.	A model of an aeroplane is made to a scale of 1:400. Then what is the length, in cm, of the model; if the length of the aeroplane is 40 m and what is the length, in m, of the aeroplane, if the length of its model is 16 cm?
Answer» A model of an aeroplane is made to a scale of 1:400. Then what is the length, in cm, of the model; if the length of the aeroplane is 40 m and what is the length, in m, of the aeroplane, if the length of its model is 16 cm?

Discussion

37.	The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the lateral edge is 50 cm. What is its lateral surface area?
Answer» The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the lateral edge is $50 c m$ . What is its lateral surface area?

Discussion

38.	Find the value of x and y from the pair of linear equations, using cross-multiplication method. 15 (x – 2) = 14(1 – y) 26x + 3y + 4 = 0
Answer» Find the value of x and y from the pair of linear equations, using cross-multiplication method. $\frac{1}{5}$ (x – 2) = $\frac{1}{4}$ (1 – y) 26x + 3y + 4 = 0

38.

Find the value of x and y from the pair of linear equations, using cross-multiplication method. 15 (x – 2) = 14(1 – y) 26x + 3y + 4 = 0

Answer»

Find the value of x and y from the pair of linear equations, using cross-multiplication method.

$\frac{1}{5}$ (x – 2) = $\frac{1}{4}$ (1 – y)

26x + 3y + 4 = 0

Discussion

39.	The money required to buy 100, ₹ 15 shares at a premium of ₹ 5 is _________
Answer» The money required to buy 100, ₹ 15 shares at a premium of ₹ 5 is _________

Discussion

40.	The vertices of a ΔABC are A(4, 6), B (1, 5) and (7, 2) A line is drawn to intersected sides AB and AC at D and E respectively, such that ADAB=AEAC=14. Calculate the area of the ΔADE and compare it with the area of ΔABC. .
Answer» The vertices of a $Δ A B C$ are A(4, 6), B (1, 5) and (7, 2) A line is drawn to intersected sides AB and AC at D and E respectively, such that $\frac{A D}{A B} = \frac{A E}{A C} = \frac{1}{4} .$ Calculate the area of the $Δ A D E$ and compare it with the area of $Δ A B C .$ .

Discussion

41.	Deepa has a 4-year recurring deposit account in a bank and deposits Rs 1,800 per month. If she gets Rs 1,08,450 at the time of maturity, find the rate of interest.
Answer» Deepa has a 4-year recurring deposit account in a bank and deposits Rs 1,800 per month. If she gets Rs 1,08,450 at the time of maturity, find the rate of interest.

Discussion

42.	A cake weighing 2 pounds is divided equally between 3 children. What weight of the cake does each student get?0.66
Answer» A cake weighing 2 pounds is divided equally between 3 children. What weight of the cake does each student get? 0.66

Discussion

43.	If the sum of 1+2+22+................+2n−1 is 255. find the value of n.
Answer» If the sum of $1 + 2 + 2^{2} + . . . . . . . . . . . . . . . . + 2^{n - 1}$ is 255. find the value of n.

Discussion

44.	Calculate the ratio in which the line joining A (6, 5) and B (4, –3) is divided by the line = 2.
Answer» Calculate the ratio in which the line joining A (6, 5) and B (4, –3) is divided by the line = 2.

Discussion

45.	Hwo many numbers are there between 101 and 999, which are divisible by both 2 and 5?
Answer» Hwo many numbers are there between 101 and 999, which are divisible by both 2 and 5?

Discussion

46.	Draw a circle with centre O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.
Answer» Draw a circle with centre O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.

Discussion

47.	How many terms of the AP: 21, 18, 15, ... must be added to get the sum 0?
Answer» How many terms of the AP: 21, 18, 15, ... must be added to get the sum 0?

Discussion

48.	Solve each of the following systems of equations graphically: 3x+2y=4,2x−3y=7.
Answer» Solve each of the following systems of equations graphically: $3 x + 2 y = 4, 2 x - 3 y = 7.$

48.

Solve each of the following systems of equations graphically: 3x+2y=4,2x−3y=7.

Answer»

Solve each of the following systems of equations graphically:

$3 x + 2 y = 4, 2 x - 3 y = 7.$

Discussion

49.	In a 2D plane, what does x > 2 represent?
Answer» In a 2D plane, what does x > 2 represent?

Discussion

50.	Given A=[04630−1] B=⎡⎢⎣01−12−5−6⎤⎥⎦ is the following possible: (i) AB (ii) BA (iii) A2
Answer» Given A $= [\begin{matrix} 0 & 4 & 6 3 & 0 & - 1 \end{matrix}]$ $B = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 - 1 & 2 - 5 & - 6 \end{matrix} ⎤ ⎥ ⎦$ is the following possible: (i) AB (ii) BA (iii) $A^{2}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How many coins 1.75 cm in diameter &amp; 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?

Line L passes through the points (4, -5) and (3, 7). Find the slope of a line perpendicular to L.

Find the probability that the month of January may have 5 Mondays in (I) a leap year (II) a non leap year.

If the solutions of the equation x2+3x−18=0 are -6, 3 then the roots of the equation 2(x2+3x−18)=0 are

A bank’s function of providing locker facility to its customers for the safe custody of their valuables is a/an

Draw the graph of y=x2+x−12 and hence solve x2+2x+2=0.

Two points on the circumference of a circle result in the formation of two arcs. The arc of shorter length is called the ___ arc.

Find the equation of a straight line whose y intercept is −4 and is parallel to the line joining the points (3,−2) and (1,4).

4 + 44 + 444 + .................upto n terms = __

The LCM of 6(4x2−4x+1) and 9(2x2−7x+3) is:

Which of the following has a non terminating decimal expansion?

Question 15 If two solid hemispheres of same base radius r are joined together along their bases the curved surface area of this new solid is (A) 4πr2 (B) 6πr2 (C) 3πr2 (D) 8πr2

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC =7.5 cm, find the radius of the circle.

The median of the observations 50 , 54 , 56 , 58 , (2x + 1) , 66 , 72 , 74 , 78 arranged in ascending order is 63. Find the value of x

The expansion of the algebraic identity ( x + a ) ( x + b ) is:

Which of the following points does not lie on the line 2x + 4y = 8?

Question 5 In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.

Find the acute angle (θ) at which sin θ and tan θ are equal?

There are 60 students in a class among which 30 are boys. In another class, there are 50 students among which 25 of them are boys. If one from each class is selected, What is the probability of both being girls?

If the sum of the first "n" natural numbers is 351, which of the following is the value of "n" ?

Simplify sin θ×cosec θ×cot θ.

Match the volume of the cone of radius 'r', height 'h' and slant height 'l' in each case (all meaures in cm).

i) Using step-deviation method, calculate the mean marks of the following distribution. ii) State the modal class. Class intervalFrequency50−55555−602060−651065−701070−75975−80680−851285−908 [4 MARKS]

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: (i) y = x,y = 2x and y + x = 6 (ii) y = x, 3y = x, x + y = 8

A die is rolled once. Find the probability of getting: i) a perfect square ii) an even prime number iii) a number < 5 iv) not an even number. [4 MARKS]

In order to get a head at least once with probability ≥0.9, the minimum number of times a unbiased coin needs to be tossed is

The following arrow diagram of the function f : A → A be defined as

The relationship between Mean, Median and Mode is

When we construct a triangle similar to a triangle or when we divide a line segment in some ratio, why do we make a ray downwards of an acute angle? Can't we make it of 90 degrees or obtuse?

Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2 ​​​

A big iron boiler tank has a cylindrical structure which is open from the top. Its height is 10 m and radius is 7 m. It gets painted at a rate of 3 m2 per day. Then find the number of days in which the tank gets painted completely? (Take π=227)

The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm, find: (iii) curved surface area of the cone. [Assume π=227]

A model of an aeroplane is made to a scale of 1:400. Then what is the length, in cm, of the model; if the length of the aeroplane is 40 m and what is the length, in m, of the aeroplane, if the length of its model is 16 cm?

The lateral surface area of a square pyramid comprises of equilateral triangles and the length of the lateral edge is 50 cm. What is its lateral surface area?

Find the value of x and y from the pair of linear equations, using cross-multiplication method. 15 (x – 2) = 14(1 – y) 26x + 3y + 4 = 0

The money required to buy 100, ₹ 15 shares at a premium of ₹ 5 is _________

The vertices of a ΔABC are A(4, 6), B (1, 5) and (7, 2) A line is drawn to intersected sides AB and AC at D and E respectively, such that ADAB=AEAC=14. Calculate the area of the ΔADE and compare it with the area of ΔABC. .

Deepa has a 4-year recurring deposit account in a bank and deposits Rs 1,800 per month. If she gets Rs 1,08,450 at the time of maturity, find the rate of interest.

A cake weighing 2 pounds is divided equally between 3 children. What weight of the cake does each student get?0.66

If the sum of 1+2+22+................+2n−1 is 255. find the value of n.

Calculate the ratio in which the line joining A (6, 5) and B (4, –3) is divided by the line = 2.

Hwo many numbers are there between 101 and 999, which are divisible by both 2 and 5?

Draw a circle with centre O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.

How many terms of the AP: 21, 18, 15, ... must be added to get the sum 0?

Solve each of the following systems of equations graphically: 3x+2y=4,2x−3y=7.

In a 2D plane, what does x &gt; 2 represent?

Given A=[04630−1] B=⎡⎢⎣01−12−5−6⎤⎥⎦ is the following possible: (i) AB (ii) BA (iii) A2

How many coins 1.75 cm in diameter & 2 mm thick must be melted to form a cuboid 11 cm x 10 cm x 7 cm?

Find the zeros of the polynomial 2x^4 + 7x^3 - 19x^2 - 14x + 30. If two of its zeros are square root of 2 and. - square root of 2

In a 2D plane, what does x > 2 represent?