32581 + Interview Questions in Mathematics

1.	Which term of the AP 3, 15, 27, 39, .... will be 132 more than its 54th term?
Answer» Which term of the AP 3, 15, 27, 39, .... will be 132 more than its $54^{t h}$ term?

Discussion

2.	If the X-coordinate of a point is twice the Y-coordinate and it is equidistant from R(2,-5) and S(-3,6) then the coordinate of point is___
Answer» If the X-coordinate of a point is twice the Y-coordinate and it is equidistant from R(2,-5) and S(-3,6) then the coordinate of point is___

Discussion

3.	In ΔABC,D and E are points AC and BC respectively such that DE \|\| AB. If AD = 2x, BE = 2x - 1, CD = x + 1 and CE = x - 1, then find the value of x.
Answer» In $Δ A B C, D$ and E are points AC and BC respectively such that DE \|\| AB. If AD = 2x, BE = 2x - 1, CD = x + 1 and CE = x - 1, then find the value of x.

Discussion

4.	Find the value of BD×DC ,if AD=5 cm.
Answer» Find the value of $B D \times D C$ ,if $A D = 5 c m$ .

Discussion

5.	A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.
Answer» A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

Discussion

6.	The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is ___.
Answer» The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is ___.

Discussion

7.	Find the sum of the roots of the equation x2–8x+2=0.
Answer» Find the sum of the roots of the equation $x^{2} - 8 x + 2 = 0$ .

Discussion

8.	Draw the graphs of the pair of linear equations x - y + 2 = 0 amd 4 x - y - 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.
Answer» Draw the graphs of the pair of linear equations x - y + 2 = 0 amd 4 x - y - 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

Discussion

9.	The sums of first n terms of two A.P’s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
Answer» The sums of first n terms of two A.P’s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5^th terms.

Discussion

10.	Two numbers such that their sum is 3 and product is 2 are _____ and ______.
Answer» Two numbers such that their sum is 3 and product is 2 are _____ and ______.

Discussion

11.	Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6), R(2,-3) and S(1,2).
Answer» Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6), R(2,-3) and S(1,2).

Discussion

12.	sinθ(cotθ+cosecθ)−sinθ(cotθ−cosecθ)=2
Answer» $\frac{s i n θ}{(c o t θ + c o s e c θ)} - \frac{s i n θ}{(c o t θ - c o s e c θ)} = 2$

Discussion

13.	The decimal expansion of pi is:
Answer» The decimal expansion of pi is:

Discussion

14.	Question 9 In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠AOB=90∘.
Answer» Question 9 In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that $∠ A O B = 90^{\circ}$ .

Discussion

15.	Without solving, examine the nature of roots of the equation. 4x2 – 4x + 1 = 0 [2 MARKS]
Answer» Without solving, examine the nature of roots of the equation. 4 $x^{2}$ – 4x + 1 = 0 [2 MARKS]

Discussion

16.	In the figure, the bisector of B and C meet at O. Then ∠ BOC is
Answer» In the figure, the bisector of B and C meet at O. Then $∠$ BOC is

16.

In the figure, the bisector of B and C meet at O. Then ∠ BOC is

Answer»

In the figure, the bisector of B and C meet at O. Then $∠$ BOC is

Discussion

17.	The point where the perpendicular bisectors of a triangle intersect is called as ____
Answer» The point where the perpendicular bisectors of a triangle intersect is called as ____

Discussion

18.	The capacity of your cousin is one roti when the radius is 4 cm. The__ of the rotis made by your mother must be 14th so that your cousin can eat 4 rotis.
Answer» The capacity of your cousin is one roti when the radius is 4 cm. The__ of the rotis made by your mother must be ${\frac{1}{4}}^{t h}$ so that your cousin can eat 4 rotis.

Discussion

19.	Show that each of the following systems of equations has a unique solution and solve it: 2x−3y=17,4x+y=13.
Answer» Show that each of the following systems of equations has a unique solution and solve it: $2 x - 3 y = 17, 4 x + y = 13.$

19.

Show that each of the following systems of equations has a unique solution and solve it: 2x−3y=17,4x+y=13.

Answer»

Show that each of the following systems of equations has a unique solution and solve it:

$2 x - 3 y = 17, 4 x + y = 13.$

Discussion

20.	In a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides. Prove it
Answer» In a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides. Prove it

Discussion

21.	Defining profitability as the ratio of net profit to sales, IVP Ltd. recorded the highest profitability in-
Answer» Defining profitability as the ratio of net profit to sales, IVP Ltd. recorded the highest profitability in-

Discussion

22.	If sinθ+cosθ=1.2 then sinθ.cosθ=___________
Answer» If sinθ+cosθ=1.2 then sinθ.cosθ=___________

Discussion

23.	A man invested Rs 45,000 in 15% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8400. Calculate the : (i) Number of shares he still holds ; (ii) Dividend due to him on these remaining shares. [3 MARKS]
Answer» A man invested Rs 45,000 in 15% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8400. Calculate the : (i) Number of shares he still holds ; (ii) Dividend due to him on these remaining shares. [3 MARKS]

Discussion

24.	A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take π=227)
Answer» A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take $π = \frac{22}{7}$ )

Discussion

25.	Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is
Answer» Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is

Discussion

26.	zero of the zero degree polynomial is
Answer» zero of the zero degree polynomial is

Discussion

27.	Which of the following is the Athletics team?
Answer» Which of the following is the Athletics team?

Discussion

28.	Construct a cyclic quadrilateral ABCD when AB = 8 cm, BC = 6 cm, ∠ABC=60∘ and AD = 5.4 cm.
Answer» Construct a cyclic quadrilateral ABCD when AB = 8 cm, BC = 6 cm, $∠ A B C = 60^{\circ}$ and AD = 5.4 cm.

Discussion

29.	For any integers a and 3, there exists unique integers q and r such that a=3q+r. Find the possible value of r.
Answer» For any integers a and 3, there exists unique integers q and r such that a=3q+r. Find the possible value of r.

Discussion

30.	Question 16 Two years ago, Salim was thrice as old as his daughter and six years later he will be four year older than twice her age. How old are they now?
Answer» Question 16 Two years ago, Salim was thrice as old as his daughter and six years later he will be four year older than twice her age. How old are they now?

Discussion

31.	When three coins are tossed simultaneously find the probability of atmost two head
Answer» When three coins are tossed simultaneously find the probability of atmost two head

Discussion

32.	Which term of the AP : 3, 8, 13, 18, . . . . is 78? ___
Answer» Which term of the AP : 3, 8, 13, 18, . . . . is 78? ___

Discussion

33.	The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.
Answer» The surface area of a solid metallic sphere is $2464 c m^{2}$ . It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.

Discussion

34.	Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and Radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which 25th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?
Answer» Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and Radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which $\frac{2}{5}$ th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

Discussion

35.	Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, ….. If the mth term is negative, then which of the following is true?
Answer» Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, ….. If the $m^{t h}$ term is negative, then which of the following is true?

35.

Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, ….. If the mth term is negative, then which of the following is true?

Answer»

Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, …..

If the $m^{t h}$ term is negative, then which of the following is true?

Discussion

36.	If three coins are tossed, find the probability of getting, at least, one tail.
Answer» If three coins are tossed, find the probability of getting, at least, one tail.

Discussion

37.	The value of 2.4¯¯¯¯¯¯¯¯178 is
Answer» The value of $2.4 ¯ ¯¯¯¯¯¯ ¯ 178$ is

Discussion

38.	The circumference of a circle is 22 cm. Find the area of its quadrant.
Answer» The circumference of a circle is 22 cm. Find the area of its quadrant.

Discussion

39.	A chord of a circle of radius 12 cm subtends an angle of 120∘ at the center. Find the area of the corresponding segment of the circle. (Use π=3.14 and √3=1.73) 1. 88.44 cm2 2. 176.88 cm2 3. 150.72 cm2 4. 75.36 cm2
Answer» A chord of a circle of radius 12 cm subtends an angle of $120^{\circ}$ at the center. Find the area of the corresponding segment of the circle. (Use $π = 3.14 a n d \sqrt{3} = 1.73)$ 1. $88.44 c m^{2}$ 2. $176.88 c m^{2}$ 3. $150.72 c m^{2}$ 4. $75.36 c m^{2}$

Discussion

40.	IF the probability fo occurrence of an event is p then the probability of non-happening of this event is (a) (p-1) (b) (1-p) (c) p (d) (1−1p)
Answer» IF the probability fo occurrence of an event is p then the probability of non-happening of this event is (a) (p-1) (b) (1-p) (c) p (d) $(1 - \frac{1}{p})$

Discussion

41.	A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm,respectively. Find the total surface area of the solid.(Use π=3.14)
Answer» A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm,respectively. Find the total surface area of the solid.(Use $π = 3.14)$

Discussion

42.	In v−t graph shown in fig. the displacement of the body in 5 seconds will be, if it starts from origin.
Answer» In $v - t$ graph shown in fig. the displacement of the body in $5$ seconds will be, if it starts from origin.

Discussion

43.	If sin A = 941, find the values of cos A and tan A,
Answer» If sin A = $\frac{9}{41}$ , find the values of cos A and tan A,

Discussion

44.	Question 42 0.5 ___ 0.7 = 0.35
Answer» Question 42 0.5 ___ 0.7 = 0.35

44.

Question 42 0.5 ___ 0.7 = 0.35

Answer»

Question 42

0.5 ___ 0.7 = 0.35

Discussion

45.	Question 3 (v) Find 23.6 ÷ 100
Answer» Question 3 (v) Find 23.6 $\div$ 100

Discussion

46.	Question 93 The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes 3.17 minutes and 3.32 minutes find the average times taken by him in the races.
Answer» Question 93 The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes 3.17 minutes and 3.32 minutes find the average times taken by him in the races.

46.

Question 93 The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes 3.17 minutes and 3.32 minutes find the average times taken by him in the races.

Answer»

Question 93

The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes 3.17 minutes and 3.32 minutes find the average times taken by him in the races.

Discussion

47.	Given graph represents _______________ pair of linear equation having _____________solution(s).
Answer» Given graph represents _______________ pair of linear equation having _____________solution(s).

47.

Given graph represents ___ pair of linear equation having _solution(s).

Answer»

Given graph represents _______________ pair of linear equation having _____________solution(s).

Discussion

48.	Question 3 (ii) Form the pair of linear equations for the following problems and find their solution by substitution method: The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Answer» Question 3 (ii) Form the pair of linear equations for the following problems and find their solution by substitution method: The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Discussion

49.	In a ∆ABC, write cos[(B+C)÷2] in terms of angle A
Answer» In a ∆ABC, write cos[(B+C)÷2] in terms of angle A

Discussion

50.	Question 11 If a sin θ+b cos θ=c, then prove that a cos θ−b sin θ=√a2+b2−c2
Answer» Question 11 If $a s i n θ + b c o s θ = c$ , then prove that $a c o s θ - b s i n θ = \sqrt{a^{2} + b^{2} - c^{2}}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Which term of the AP 3, 15, 27, 39, .... will be 132 more than its ​54th term?

If the X-coordinate of a point is twice the Y-coordinate and it is equidistant from R(2,-5) and S(-3,6) then the coordinate of point is___

In ΔABC,D and E are points AC and BC respectively such that DE || AB. If AD = 2x, BE = 2x - 1, CD = x + 1 and CE = x - 1, then find the value of x.

Find the value of BD×DC ,if AD=5 cm.

A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is ___.

Find the sum of the roots of the equation x2–8x+2=0.

Draw the graphs of the pair of linear equations x - y + 2 = 0 amd 4 x - y - 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

The sums of first n terms of two A.P’s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.

Two numbers such that their sum is 3 and product is 2 are _____ and ______.

Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6), R(2,-3) and S(1,2).

sinθ(cotθ+cosecθ)−sinθ(cotθ−cosecθ)=2

The decimal expansion of pi is:

Question 9 In Fig. 10.13, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠AOB=90∘.

Without solving, examine the nature of roots of the equation. 4x2 – 4x + 1 = 0 [2 MARKS]

In the figure, the bisector of B and C meet at O. Then ∠ BOC is

The point where the perpendicular bisectors of a triangle intersect is called as ____

The capacity of your cousin is one roti when the radius is 4 cm. The__ of the rotis made by your mother must be 14th so that your cousin can eat 4 rotis.

Show that each of the following systems of equations has a unique solution and solve it: 2x−3y=17,4x+y=13.

In a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides. Prove it

Defining profitability as the ratio of net profit to sales, IVP Ltd. recorded the highest profitability in-

If sinθ+cosθ=1.2 then sinθ.cosθ=___________

A man invested Rs 45,000 in 15% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8400. Calculate the : (i) Number of shares he still holds ; (ii) Dividend due to him on these remaining shares. [3 MARKS]

A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take π=227)

Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is

zero of the zero degree polynomial is

Which of the following is the Athletics team?

Construct a cyclic quadrilateral ABCD when AB = 8 cm, BC = 6 cm, ∠ABC=60∘ and AD = 5.4 cm.

For any integers a and 3, there exists unique integers q and r such that a=3q+r. Find the possible value of r.

Question 16 Two years ago, Salim was thrice as old as his daughter and six years later he will be four year older than twice her age. How old are they now?

When three coins are tossed simultaneously find the probability of atmost two head

Which term of the AP : 3, 8, 13, 18, . . . . is 78? ___

The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate the number of cones recast.

Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, ….. If the mth term is negative, then which of the following is true?

If three coins are tossed, find the probability of getting, at least, one tail.

The value of 2.4¯¯¯¯¯¯¯¯178 is

The circumference of a circle is 22 cm. Find the area of its quadrant.

A chord of a circle of radius 12 cm subtends an angle of 120∘ at the center. Find the area of the corresponding segment of the circle. (Use π=3.14 and √3=1.73) 1. 88.44 cm2 2. 176.88 cm2 3. 150.72 cm2 4. 75.36 cm2

IF the probability fo occurrence of an event is p then the probability of non-happening of this event is (a) (p-1) (b) (1-p) (c) p (d) (1−1p)

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm,respectively. Find the total surface area of the solid.(Use π=3.14)

In v−t graph shown in fig. the displacement of the body in 5 seconds will be, if it starts from origin.

If sin A = 941, find the values of cos A and tan A,

Question 42 0.5 ___ 0.7 = 0.35

Question 3 (v) Find 23.6 ÷ 100

Question 93 The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes 3.17 minutes and 3.32 minutes find the average times taken by him in the races.

Given graph represents _______________ pair of linear equation having _____________solution(s).

Question 3 (ii) Form the pair of linear equations for the following problems and find their solution by substitution method: The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

In a ∆ABC, write cos[(B+C)÷2] in terms of angle A

Question 11 If a sin θ+b cos θ=c, then prove that a cos θ−b sin θ=√a2+b2−c2

Which term of the AP 3, 15, 27, 39, .... will be 132 more than its 54th term?

Two numbers such that their sum is 3 and product is 2 are _ and __.

Given graph represents ___ pair of linear equation having _solution(s).