24740 + Interview Questions in Mathematics

1.	Solve the following pair of equations. 5x−1+1y−2=2 6x−1−3y−2=1 Here, x ≠ 1 and y ≠ 2
Answer» Solve the following pair of equations. $\frac{5}{x - 1} + \frac{1}{y - 2} = 2$ $\frac{6}{x - 1} - \frac{3}{y - 2} = 1$ Here, x $\neq$ 1 and y $\neq$ 2

1.

Solve the following pair of equations. 5x−1+1y−2=2 6x−1−3y−2=1 Here, x ≠ 1 and y ≠ 2

Answer»

Solve the following pair of equations.

$\frac{5}{x - 1} + \frac{1}{y - 2} = 2$

$\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

Here, x $\neq$ 1 and y $\neq$ 2

2.	Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Answer» Father is aged three times more than his son Ronit. After $8$ years, he would be two and a half times of Ronit's age. After further $8$ years, how many times would he be of Ronit's age?

Discussion

3.	The area of a triangle of sides 7 m, 8 m and 9 m is equal to m2.
Answer» The area of a triangle of sides 7 m, 8 m and 9 m is equal to $m^{2}$ .

Discussion

4.	Find one irrational number between 0.2101 and 0.2222?
Answer» Find one irrational number between 0.2101 and 0.2222?

Discussion

5.	Construct the angles of the following measurements:(i) 30°(ii) 75°(iii) 105°(iv) 135°(v) 15°(vi) 2212°
Answer» Construct the angles of the following measurements: (i) 30° (ii) 75° (iii) 105° (iv) 135° (v) 15° (vi) $22 {\frac{1}{2}}^{°}$

Discussion

6.	An electrician has to repair an electric falut on a pole of height 4 metres, He needs to reach a point 1 metre below the top of pole to undertake the repair work. What should be the length of the ladder that the should use, which when inclined at an angle of 60∘ to the horizontal would enable him to reach the required position ? [Use √3=1.732.]
Answer» An electrician has to repair an electric falut on a pole of height 4 metres, He needs to reach a point 1 metre below the top of pole to undertake the repair work. What should be the length of the ladder that the should use, which when inclined at an angle of $60^{\circ}$ to the horizontal would enable him to reach the required position ? [Use $\sqrt{3} = 1.732.$ ]

Discussion

7.	Simplify: (2√2+5√5)(4√2+3√5)
Answer» Simplify: $(2 \sqrt{2} + 5 \sqrt{5})$ $(4 \sqrt{2} + 3 \sqrt{5})$

Discussion

8.	Which of the following can be the equation for the line plotted in the graph below?
Answer» Which of the following can be the equation for the line plotted in the graph below?

Discussion

9.	An equilateral ABC is inscribed in a circle with centre O. Then measure of ∠BOC is
Answer» An equilateral ABC is inscribed in a circle with centre O. Then measure of $∠ B O C$ is

Discussion

10.	Solve the equations for x and y.2x−3y=75x+y=9
Answer» Solve the equations for $x$ and $y$ . $2 x - 3 y = 7$ $5 x + y = 9$

10.

Solve the equations for x and y.2x−3y=75x+y=9

Answer»

Solve the equations for $x$ and $y$ .

$2 x - 3 y = 7$

$5 x + y = 9$

Discussion

11.	Sort the decimals in ascending order.
Answer» Sort the decimals in ascending order.

Discussion

12.	Arc BCD is known as
Answer» Arc BCD is known as

12.

Arc BCD is known as

Answer»

Arc BCD is known as

Discussion

13.	The semi perimeter of an equilateral triangle having side 10 cm is __.
Answer» The semi perimeter of an equilateral triangle having side 10 cm is __.

Discussion

14.	Question 10The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that AB=29AC.
Answer» Question 10 The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that $A B = \frac{2}{9} A C .$

Discussion

15.	In the given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR.
Answer» In the given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR.

Discussion

16.	45. The volume of a vesselbin the form of right circular cylinder is 448πcm3 and its height is 7cm . Find radiys of its base and also lateral surface area and total surface area.
Answer» 45. The volume of a vesselbin the form of right circular cylinder is 448πcm3 and its height is 7cm . Find radiys of its base and also lateral surface area and total surface area.

Discussion

17.	Given n observations x1, x2 ......xn and their central tendency a. Find the mean deviation about a.
Answer» Given n observations x₁, x₂ ......x_n and their central tendency a. Find the mean deviation about a.

Discussion

18.	2. If median of an equilateral triangle is x cm long then triangle area is?
Answer» 2. If median of an equilateral triangle is x cm long then triangle area is?

Discussion

19.	The volume of metal in a metallic cylinder pipe is 748cm3 , its length is 14cm and its external radius is 9cm. Find its thickness.
Answer» The volume of metal in a metallic cylinder pipe is $748 c m^{3}$ , its length is $14 c m$ and its external radius is $9 c m$ . Find its thickness.

Discussion

20.	Factorise: a2(b+c)−(b+c)3
Answer» Factorise: $a^{2} (b + c) - (b + c)^{3}$

Discussion

21.	86.A quadrilateral inscribed in the circle has side lengths 20,99,22 and 97 in the order taking =22/7 if the area of the circle is a/b where a and b are co-prime then find a-70b
Answer» 86.A quadrilateral inscribed in the circle has side lengths 20,99,22 and 97 in the order taking =22/7 if the area of the circle is a/b where a and b are co-prime then find a-70b

Discussion

22.	Match the following with their answers.
Answer» Match the following with their answers.

Discussion

23.	23. Find the equation of the circle which touches the coordinate axes and whose centre lies on the line x-2y=3.[ explain all posiblities]
Answer» 23. Find the equation of the circle which touches the coordinate axes and whose centre lies on the line x-2y=3.[ explain all posiblities]

Discussion

24.	In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to
Answer» In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

24.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

Answer»

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

Discussion

25.	Classify the following as linear, quadratic and cubic polynomial:(i) (ii) (iii) (iv) (v) (vi) (vii)
Answer» Classify the following as linear, quadratic and cubic polynomial: (i) (ii) (iii) (iv) (v) (vi) (vii)

25.

Classify the following as linear, quadratic and cubic polynomial:(i) (ii) (iii) (iv) (v) (vi) (vii)

Answer»

Classify the following as linear, quadratic and cubic polynomial:

(i) (ii) (iii) (iv) (v)

(vi) (vii)

Discussion

26.	Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
Answer» Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Discussion

27.	Factorize (x square - 4x) (x square - 4x -1).- 20
Answer» Factorize (x square - 4x) (x square - 4x -1).- 20

27.

Factorize (x square - 4x) (x square - 4x -1).- 20

Answer»

Factorize

(x square - 4x) (x square - 4x -1).- 20

Discussion

28.	A survey was conducted to find out which brands of computer mouse different people used. The data collected from a 100 people is as follows: BrandFrequencyLogitech32Microsoft26Dell23Others19 Find the probability that a person (i) uses Dell or Microsoft (ii) does not use either Logitech, Dell or Microsoft. [3 MARKS]
Answer» A survey was conducted to find out which brands of computer mouse different people used. The data collected from a 100 people is as follows: $\begin{matrix} B r a n d & F r e q u e n c y L o g i t e c h & 32 M i c r o s o f t & 26 D e l l & 23 O t h e r s & 19 \end{matrix}$ Find the probability that a person (i) uses Dell or Microsoft (ii) does not use either Logitech, Dell or Microsoft. [3 MARKS]

28.

A survey was conducted to find out which brands of computer mouse different people used. The data collected from a 100 people is as follows: BrandFrequencyLogitech32Microsoft26Dell23Others19 Find the probability that a person (i) uses Dell or Microsoft (ii) does not use either Logitech, Dell or Microsoft. [3 MARKS]

Answer»

A survey was conducted to find out which brands of computer mouse different people used. The data collected from a 100 people is as follows:

$\begin{matrix} B r a n d & F r e q u e n c y L o g i t e c h & 32 M i c r o s o f t & 26 D e l l & 23 O t h e r s & 19 \end{matrix}$

Find the probability that a person
(i) uses Dell or Microsoft
(ii) does not use either Logitech, Dell or Microsoft. [3 MARKS]

Discussion

29.	The boat goes 30 km upstream and 44 km downstream in 10 hours . In 13 hours, it can go 40km upstream and 55 km downstream .Determine the speed of stream and that of the boat instill water.
Answer» The boat goes 30 km upstream and 44 km downstream in 10 hours . In 13 hours, it can go 40 km upstream and 55 km downstream .Determine the speed of stream and that of the boat in still water.

Discussion

30.	Using a suitable identity, evaluate the following:(69.3)2−(30.7)2
Answer» Using a suitable identity, evaluate the following: $(69.3)^{2} - (30.7)^{2}$

30.

Using a suitable identity, evaluate the following:(69.3)2−(30.7)2

Answer»

Using a suitable identity, evaluate the following:

$(69.3)^{2} - (30.7)^{2}$

Discussion

31.	Question 8 (ii)ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:Diagonal BD bisects ∠B as well as ∠D.
Answer» Question 8 (ii) ABCD is a rectangle in which diagonal AC bisects $∠ A$ as well as $∠ C$ . Show that: Diagonal BD bisects $∠ B$ as well as $∠ D$ .

Discussion

32.	The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is
Answer» The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is

Discussion

33.	in the given figure,AB\|\|CD and EFis a transversal, cutting them at G and H respectively. if ∠EGB=35∘and QP⊥EF,find the measure of ∠PQH.
Answer» $in the given figure, A B \| \| C D a n d E F is a transversal, cutting them at G and H respectively. if ∠ E G B = 35^{\circ} a n d Q P ⊥ E F, find the measure of ∠ P Q H .$

33.

in the given figure,AB||CD and EFis a transversal, cutting them at G and H respectively. if ∠EGB=35∘and QP⊥EF,find the measure of ∠PQH.

Answer»

$in the given figure, A B | | C D a n d E F is a transversal, cutting them at G and H respectively. if ∠ E G B = 35^{\circ} a n d Q P ⊥ E F, find the measure of ∠ P Q H .$

Discussion

34.	ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, find ∠BAC.
Answer» ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If $∠ A D C = 130^{\circ}$ , find $∠ B A C$ .

Discussion

35.	Find the value of k inx^2+5x+6+k=0
Answer» Find the value of k in x^2+5x+6+k=0

Discussion

36.	In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q.Prove that, ∠ PRQ + ∠ PSQ = 180°
Answer» In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q. Prove that, ∠ PRQ + ∠ PSQ = 180°

Discussion

37.	Find the value of x.3(x + 2) = 7
Answer» Find the value of x. 3(x + 2) = 7

Discussion

38.

Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory: Wages (in Rs) 110-130 130-150 150-170 170-190 190-210 210-230 230-250 No. of workers 3 4 5 6 5 4 3 A worker is selected at random. Find the probability that his wages are:(i) less than Rs 150(ii) at least Rs 210(iii) more than or equal to 150 but less than Rs 210.

Answer» Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:

Wages (in Rs)	110-130	130-150	150-170	170-190	190-210	210-230	230-250
No. of workers	3	4	5	6	5	4	3

A worker is selected at random. Find the probability that his wages are:

(i) less than Rs 150

(ii) at least Rs 210

(iii) more than or equal to 150 but less than Rs 210.

Discussion

39.	Mark the correct alternative in each of the following:The probability of an impossible event is(a) 1(b) 0(c) less than 0(d) greater than 1
Answer» Mark the correct alternative in each of the following: The probability of an impossible event is (a) 1 (b) 0 (c) less than 0 (d) greater than 1

Discussion

40.	Question 87 Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?
Answer» Question 87 Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?

Discussion

41.	There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.
Answer» There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.

Discussion

42.	The linear equation 2x – 5y = x – 2 has
Answer» The linear equation 2x – 5y = x – 2 has

Discussion

43.	Find the value of 13−√8−1√8−√7+1√7−√6−1√6−√5+1√5−2 .
Answer» Find the value of $\frac{1}{3 - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2}$ .

Discussion

44.	If x= 9+4√5 then find the value of √x-1/√x
Answer» If x= 9+4√5 then find the value of √x-1/√x

Discussion

45.	The ages of Hari and Harry are in the ratio 5:7. Four years from now, the ratio of their ages will be 3:4. Find their present ages.
Answer» The ages of Hari and Harry are in the ratio $5 : 7$ . Four years from now, the ratio of their ages will be $3 : 4$ . Find their present ages.

Discussion

46.	If 63√2−2√3=3√2−x√6,then the value of x is
Answer» $If \frac{6}{3 \sqrt{2} - 2 \sqrt{3}} = 3 \sqrt{2} - x \sqrt{6}, then the value of x is$

Discussion

47.	The following table shows the marks obtained by 5 students in a class. Find the average marks of the class. MarksFrequency981651882541
Answer» The following table shows the marks obtained by 5 students in a class. Find the average marks of the class. $\begin{matrix} M a r k s & F r e q u e n c y 98 & 1 65 & 1 88 & 2 54 & 1 \end{matrix}$

47.

The following table shows the marks obtained by 5 students in a class. Find the average marks of the class. MarksFrequency981651882541

Answer»

The following table shows the marks obtained by 5 students in a class. Find the average marks of the class.

$\begin{matrix} M a r k s & F r e q u e n c y 98 & 1 65 & 1 88 & 2 54 & 1 \end{matrix}$

Discussion

48.	The area of a figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is
Answer» The area of a figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is

Discussion

49.	There were two sacks containing numbers, sack A contained the set of positive integers while sack B contained the set of whole numbers. Which sack contains more numbers?
Answer» There were two sacks containing numbers, sack A contained the set of positive integers while sack B contained the set of whole numbers. Which sack contains more numbers?

Discussion

50.	If ΔABC≅ΔPQR and it is given that ∠A=60∘, ∠B=70∘. Then the value of ∠R is___ ∘.
Answer» $If Δ A B C ≅ Δ P Q R and it is given that ∠ A = 60^{\circ}, ∠ B = 70^{\circ} . Then the value of ∠ R is$ ___ $^{\circ}$ .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following pair of equations. 5x−1+1y−2=2 6x−1−3y−2=1 Here, x ≠ 1 and y ≠ 2

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

The area of a triangle of sides 7 m, 8 m and 9 m is equal to m2.

Find one irrational number between 0.2101 and 0.2222?

Construct the angles of the following measurements:(i) 30°(ii) 75°(iii) 105°(iv) 135°(v) 15°(vi) 2212°

Simplify: (2√2+5√5)(4√2+3√5)

Which of the following can be the equation for the line plotted in the graph below?

An equilateral ABC is inscribed in a circle with centre O. Then measure of ∠BOC is

Solve the equations for x and y.2x−3y=75x+y=9

Sort the decimals in ascending order.

Arc BCD is known as

The semi perimeter of an equilateral triangle having side 10 cm is __.

Question 10The point A(-6, 10), B(-4,6) and C(3,-8) are collinear such that AB=29AC.

In the given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR.

45. The volume of a vesselbin the form of right circular cylinder is 448πcm3 and its height is 7cm . Find radiys of its base and also lateral surface area and total surface area.

Given n observations x1, x2 ......xn and their central tendency a. Find the mean deviation about a.

2. If median of an equilateral triangle is x cm long then triangle area is?

The volume of metal in a metallic cylinder pipe is 748cm3 , its length is 14cm and its external radius is 9cm. Find its thickness.

Factorise: a2(b+c)−(b+c)3

86.A quadrilateral inscribed in the circle has side lengths 20,99,22 and 97 in the order taking =22/7 if the area of the circle is a/b where a and b are co-prime then find a-70b

Match the following with their answers.

23. Find the equation of the circle which touches the coordinate axes and whose centre lies on the line x-2y=3.[ explain all posiblities]

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

Classify the following as linear, quadratic and cubic polynomial:(i) (ii) (iii) (iv) (v) (vi) (vii)

Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Factorize (x square - 4x) (x square - 4x -1).- 20

The boat goes 30 km upstream and 44 km downstream in 10 hours . In 13 hours, it can go 40km upstream and 55 km downstream .Determine the speed of stream and that of the boat instill water.

Using a suitable identity, evaluate the following:(69.3)2−(30.7)2

Question 8 (ii)ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:Diagonal BD bisects ∠B as well as ∠D.

The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class limit of the highest class is

in the given figure,AB||CD and EFis a transversal, cutting them at G and H respectively. if ∠EGB=35∘and QP⊥EF,find the measure of ∠PQH.

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, find ∠BAC.

Find the value of k inx^2+5x+6+k=0

In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q.Prove that, ∠ PRQ + ∠ PSQ = 180°

Find the value of x.3(x + 2) = 7

Mark the correct alternative in each of the following:The probability of an impossible event is(a) 1(b) 0(c) less than 0(d) greater than 1

Question 87 Draw a figure that represents your mathematics textbook. What is the name of this figure? Is it a prism?

There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.

The linear equation 2x – 5y = x – 2 has

Find the value of 13−√8−1√8−√7+1√7−√6−1√6−√5+1√5−2 .

If x= 9+4√5 then find the value of √x-1/√x

The ages of Hari and Harry are in the ratio 5:7. Four years from now, the ratio of their ages will be 3:4. Find their present ages.

If 63√2−2√3=3√2−x√6,then the value of x is

The following table shows the marks obtained by 5 students in a class. Find the average marks of the class. MarksFrequency981651882541

The area of a figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is

There were two sacks containing numbers, sack A contained the set of positive integers while sack B contained the set of whole numbers. Which sack contains more numbers?

If ΔABC≅ΔPQR and it is given that ∠A=60∘, ∠B=70∘. Then the value of ∠R is___ ∘.