32581 + Interview Questions in Mathematics

1.	In a survey of 300 android mobile users, who make video calls, 65 people said they use only viber, 35 use only skype and 100 people use both. The number of persons who use neither viber nor skype is __.
Answer» In a survey of 300 android mobile users, who make video calls, 65 people said they use only viber, 35 use only skype and 100 people use both. The number of persons who use neither viber nor skype is __.

Discussion

2.	Find the discriminant of the quadratic equation 3x2–5x+2=0 and hence, find the nature of the roots.
Answer» Find the discriminant of the quadratic equation $3 x^{2} - 5 x + 2 = 0$ and hence, find the nature of the roots.

Discussion

3.	The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.
Answer» The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

Discussion

4.	Question 5 What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.
Answer» Question 5 What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ? Perform the division to check your answer.

Discussion

5.	PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA=35∘, then find ∠POB.
Answer» $PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠ O P A = 35^{\circ}, then find ∠ P O B .$

Discussion

6.	If the 3rd and 9th term of an AP are 4 and -8 respectively, which term of this AP is zero? [2 MARKS]
Answer» If the $3^{r d}$ and $9^{t h}$ term of an AP are 4 and -8 respectively, which term of this AP is zero? [2 MARKS]

Discussion

7.	Question 1 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Answer» Question 1 2 cubes each of volume 64 $c m^{3}$ are joined end to end. Find the surface area of the resulting cuboid.

Discussion

8.	The above figure is a square. The value of x1+y1+x2+y2+x3+y3 is
Answer» The above figure is a square. The value of $x_{1} + y_{1} + x_{2} + y_{2} + x_{3} + y_{3}$ is

Discussion

9.	Find the value of k for which x2–4x+k=0 has coincident roots.
Answer» Find the value of $k$ for which $x^{2} - 4 x + k = 0$ has coincident roots.

Discussion

10.	Solve : −3+x<2,x ϵ N.
Answer» Solve : $- 3 + x < 2, x ϵ N .$

Discussion

11.	Select the statements that are true for the given figure.
Answer» Select the statements that are true for the given figure.

11.

Select the statements that are true for the given figure.

Answer»

Select the statements that are true for the given figure.

Discussion

12.	If A=[1389], find the sum of the principal diagonal elements of A2−A.2
Answer» If $A = [\begin{matrix} 1 & 3 8 & 9 \end{matrix}]$ , find the sum of the principal diagonal elements of $A^{2} - A . 2$

Discussion

13.	A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656 cm3. Find the height of the toy. Also , find the cost of painting the hemispherical part of the toy at the rate of Rs 10per cm2. Use π=227
Answer» A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656 cm3. Find the height of the toy. Also , find the cost of painting the hemispherical part of the toy at the rate of Rs $10 p e r c m^{2}$ . Use $π = \frac{22}{7}$

Discussion

14.	You are given an Ellingham diagram (deliberately not shown). It is given that for almost all practically achievable temperatures, the Fe→Fe2O3 line lies above the Al→Al2O3 line and ΔfG∘ for both Al2O3 and Fe2O3 are negative. Which of the following statements is/are true?
Answer» You are given an Ellingham diagram (deliberately not shown). It is given that for almost all practically achievable temperatures, the $F e \to F e_{2} O_{3}$ line lies above the $A l \to A l_{2} O_{3}$ line and $Δ_{f} G^{\circ}$ for both $A l_{2} O_{3}$ and $F e_{2} O_{3}$ are negative. Which of the following statements is/are true?

Discussion

15.	I take a cone of Base radius r1 and height h1. I cut the cone on a plane parallel to its base. The cut is made at a height h from the base. After the cut I remove the cone. What is the name of the figure left out? What is the radius of its top surface?
Answer» I take a cone of Base radius $r_{1}$ and height $h_{1}$ . I cut the cone on a plane parallel to its base. The cut is made at a height h from the base. After the cut I remove the cone. What is the name of the figure left out? What is the radius of its top surface?

Discussion

16.	The sum to n terms of the series 22+42+62+..........is
Answer» The sum to n terms of the series $2^{2} + 4^{2} + 6^{2} + . . . . . . . . . . i s$

Discussion

17.	What is Expansion of (x−y)3?
Answer» What is Expansion of $(x - y)^{3}$ ?

Discussion

18.	When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.
Answer» When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.

Discussion

19.	Prove that √5 is irrational.
Answer» Prove that $\sqrt{5}$ is irrational.

Discussion

20.	x−y=0 is a line which is
Answer» $x - y = 0$ is a line which is

Discussion

21.	Give the meaning of arithmetic average.
Answer» Give the meaning of arithmetic average.

Discussion

22.	−5x3+1<23 Solve for x
Answer» $- \frac{5 x}{3} + 1 < \frac{2}{3}$ Solve for x

Discussion

23.	Directions:- Study the following information carefully to answer the question given below. Twelve persons are sitting in two rows containing six people, each in such a way that there is an equal distance between adjacent persons. In row 1 - A, B, C, D, E and F are seated and all of them are facing South but not necessarily in the same order. In row 2 - P, Q, R, S, T and V are seated and all of them are facing West but not necessarily in the same order. D sits third to the right of B. Either D or B sits at one of the extreme ends of the line. The one who is adjacent to B sits second to the right of T. Two persons sit between Q and V. Neither Q nor V sits at the extreme end of the line. The immediate neighbour of Q is eighth left of A. C and E are immediate neighbours of each other. R sits second to the left of T. E is fourth to the left of the immediate neighbour of S. Which of the following is true?
Answer» Directions:- Study the following information carefully to answer the question given below. Twelve persons are sitting in two rows containing six people, each in such a way that there is an equal distance between adjacent persons. In row 1 - A, B, C, D, E and F are seated and all of them are facing South but not necessarily in the same order. In row 2 - P, Q, R, S, T and V are seated and all of them are facing West but not necessarily in the same order. D sits third to the right of B. Either D or B sits at one of the extreme ends of the line. The one who is adjacent to B sits second to the right of T. Two persons sit between Q and V. Neither Q nor V sits at the extreme end of the line. The immediate neighbour of Q is eighth left of A. C and E are immediate neighbours of each other. R sits second to the left of T. E is fourth to the left of the immediate neighbour of S. Which of the following is true?

Discussion

24.	Enter the following transactions in the Purchase Journal (Book) of M/s Gupta Traders of July 2010. 1- Bought from Rahul Traders as per invoice no 20041 40 Registers 60 each 80 Gel Pens 15 each 50 notebooks Rs. 20 each Trade discount 10% 15- Bought from Global Stationers as per invoice no 1132 40 Ink Pads Rs.8 each 50 Files Rs. 10 each 20 Colour Books Rs. 20 each Trade Discount 5% 23- Purchased from Lamba Furniture as per invoice no 3201 2 Chairs 600 per chair 1 Table 1,000 per table 25- Bought from Mumbai Traders as per invoice no 1111 10 Paper Rim Rs. 100 per rim 400 Drawing Sheets Rs.3 each 20 Packet Water Colour Rs. 40 per packet
Answer» Enter the following transactions in the Purchase Journal (Book) of M/s Gupta Traders of July 2010. 1- Bought from Rahul Traders as per invoice no 20041 40 Registers 60 each 80 Gel Pens 15 each 50 notebooks Rs. 20 each Trade discount 10% 15- Bought from Global Stationers as per invoice no 1132 40 Ink Pads Rs.8 each 50 Files Rs. 10 each 20 Colour Books Rs. 20 each Trade Discount 5% 23- Purchased from Lamba Furniture as per invoice no 3201 2 Chairs 600 per chair 1 Table 1,000 per table 25- Bought from Mumbai Traders as per invoice no 1111 10 Paper Rim Rs. 100 per rim 400 Drawing Sheets Rs.3 each 20 Packet Water Colour Rs. 40 per packet

24.

Enter the following transactions in the Purchase Journal (Book) of M/s Gupta Traders of July 2010. 1- Bought from Rahul Traders as per invoice no 20041 40 Registers 60 each 80 Gel Pens 15 each 50 notebooks Rs. 20 each Trade discount 10% 15- Bought from Global Stationers as per invoice no 1132 40 Ink Pads Rs.8 each 50 Files Rs. 10 each 20 Colour Books Rs. 20 each Trade Discount 5% 23- Purchased from Lamba Furniture as per invoice no 3201 2 Chairs 600 per chair 1 Table 1,000 per table 25- Bought from Mumbai Traders as per invoice no 1111 10 Paper Rim Rs. 100 per rim 400 Drawing Sheets Rs.3 each 20 Packet Water Colour Rs. 40 per packet

Answer»

Enter the following transactions in the Purchase Journal (Book) of M/s Gupta Traders of July 2010.

1- Bought from Rahul Traders as per invoice no 20041
40 Registers 60 each
80 Gel Pens 15 each
50 notebooks Rs. 20 each
Trade discount 10%

15- Bought from Global Stationers as per invoice no 1132
40 Ink Pads Rs.8 each
50 Files Rs. 10 each
20 Colour Books Rs. 20 each
Trade Discount 5%

23- Purchased from Lamba Furniture as per invoice no 3201
2 Chairs 600 per chair
1 Table 1,000 per table

25- Bought from Mumbai Traders as per invoice no 1111
10 Paper Rim Rs. 100 per rim
400 Drawing Sheets Rs.3 each
20 Packet Water Colour Rs. 40 per packet

Discussion

25.	I got a viral question, kindly help me with it 6÷2(1+2)
Answer» I got a viral question, kindly help me with it 6÷2(1+2)

Discussion

26.	The relation R ={(x, √x):x is a natural number less than 100; √x is an integer }. Write the relation in roster form.
Answer» The relation R ={(x, $\sqrt{x}$ ):x is a natural number less than 100; $\sqrt{x}$ is an integer }. Write the relation in roster form.

Discussion

27.	The LCM of (x−3)(x−5) and (x−5)(x−7) is:
Answer» The LCM of $(x - 3) (x - 5) a n d (x - 5) (x - 7)$ is:

Discussion

28.	give an example in which remainder is greater than divisor
Answer» give an example in which remainder is greater than divisor

Discussion

29.	A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.
Answer» A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.

29.

A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.

Answer»

A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.

Discussion

30.	If pth,qth,rth terms of an A.P. are a,b,c respectively, then the value of a(q−r)+b(r−p)+c(p−q) is
Answer» If $p^{t h}, q^{t h}, r^{t h}$ terms of an A.P. are $a, b, c$ respectively, then the value of $a (q - r) + b (r - p) + c (p - q)$ is

Discussion

31.	Solve for x :1(x−1)(x−2)+1(x−2)(x−3) = 23,x≠1,2,3
Answer» Solve for x : $\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)}$ = $\frac{2}{3}, x \neq 1, 2, 3$

Discussion

32.	Solve each of the following quadratic equations: (4x−32x+1)−10(2x+14x−3)=3,x≠−12,34
Answer» Solve each of the following quadratic equations: $(\frac{4 x - 3}{2 x + 1}) - 10 (\frac{2 x + 1}{4 x - 3}) = 3, x \neq \frac{- 1}{2}, \frac{3}{4}$

Discussion

33.	In a class text, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of his marks, would have been 180. Find his marks in the two subjects.
Answer» In a class text, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of his marks, would have been 180. Find his marks in the two subjects.

Discussion

34.	In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB=120∘, then the correct relation is-
Answer» In the adjoining figure, if BC = a, AC = b, AB = c and $∠ C A B = 120^{\circ}$ , then the correct relation is-

34.

In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB=120∘, then the correct relation is-

Answer»

In the adjoining figure, if BC = a, AC = b, AB = c and $∠ C A B = 120^{\circ}$ , then the correct relation is-

Discussion

35.	Question 9 The point which divides the line segment joining points (7, - 6) and (3,4) in ratio 1:2 internally lies in the (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant
Answer» Question 9 The point which divides the line segment joining points (7, - 6) and (3,4) in ratio 1:2 internally lies in the (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Discussion

36.	Write the value of sec2 θ (1+sin θ)(1−sin θ).
Answer» Write the value of $s e c^{2} θ (1 + s i n θ) (1 - s i n θ)$ .

Discussion

37.	Solve the following quadratic equation for x. 4x2−4a2x+(a4−b4)=0
Answer» Solve the following quadratic equation for x. $4 x^{2} - 4 a^{2} x + (a^{4} - b^{4}) = 0$

Discussion

38.	The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.
Answer» The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Discussion

39.	Question 20 In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? [Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2×5+2×(5+3)]
Answer» Question 20 In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? [Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is $2 \times 5 + 2 \times (5 + 3)]$

Discussion

40.	A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completly. Find the diameter of the cylindrical vessel.
Answer» A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completly. Find the diameter of the cylindrical vessel.

Discussion

41.	From the given table, find (i) the agerage (Mean) wage of a worker. (ii) the model class.
Answer» From the given table, find (i) the agerage (Mean) wage of a worker. (ii) the model class.

41.

From the given table, find (i) the agerage (Mean) wage of a worker. (ii) the model class.

Answer»

From the given table, find (i) the agerage (Mean) wage of a worker. (ii) the model class.

Discussion

42.	For what value of 'K' will the system of equations: 3x + y = 1, (2K - 1) x + (K - 1) y = 2K + 1 have no solution?
Answer» For what value of 'K' will the system of equations: 3x + y = 1, (2K - 1) x + (K - 1) y = 2K + 1 have no solution?

42.

For what value of 'K' will the system of equations: 3x + y = 1, (2K - 1) x + (K - 1) y = 2K + 1 have no solution?

Answer»

For what value of 'K' will the system of equations:

3x + y = 1, (2K - 1) x + (K - 1) y = 2K + 1 have no solution?

Discussion

43.	The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be
Answer» The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be

Discussion

44.	Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Answer» Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

Discussion

45.	Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.
Answer» Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Discussion

46.	Question 4 (viii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (viii) −12,−12,−12,−12……
Answer» Question 4 (viii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (viii) $- \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2} \dots \dots$

Discussion

47.	A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
Answer» A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

Discussion

48.	In an A.P., if the first erm is 22, the common difference is -4 and the sum to n terms is -650, find n.
Answer» In an A.P., if the first erm is 22, the common difference is -4 and the sum to n terms is -650, find n.

Discussion

49.	A point P is at a distance of 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.
Answer» A point $P$ is at a distance of $25 c m$ from the centre of a circle. The radius of the circle is $7 c m$ and length of the tangent drawn from $P$ to the circle is $x c m .$ The value of $x$ is ___ $c m .$

Discussion

50.	The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m. then at what time will they again change simultaneously.
Answer» The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m. then at what time will they again change simultaneously.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In a survey of 300 android mobile users, who make video calls, 65 people said they use only viber, 35 use only skype and 100 people use both. The number of persons who use neither viber nor skype is __.

Find the discriminant of the quadratic equation 3x2–5x+2=0 and hence, find the nature of the roots.

The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

Question 5 What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.

PA and PB are the two tangents drawn to the circle. O is the center of the circle. A and B are the points of contact of the tangents PA and PB with the circle. If ∠OPA=35∘, then find ∠POB.

If the 3rd and 9th term of an AP are 4 and -8 respectively, which term of this AP is zero? [2 MARKS]

Question 1 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

The above figure is a square. The value of x1+y1+x2+y2+x3+y3 is

Find the value of k for which x2–4x+k=0 has coincident roots.

Solve : −3+x&lt;2,x ϵ N.

Select the statements that are true for the given figure.

If A=[1389], find the sum of the principal diagonal elements of A2−A.2

You are given an Ellingham diagram (deliberately not shown). It is given that for almost all practically achievable temperatures, the Fe→Fe2O3 line lies above the Al→Al2O3 line and ΔfG∘ for both Al2O3 and Fe2O3 are negative. Which of the following statements is/are true?

I take a cone of Base radius r1 and height h1. I cut the cone on a plane parallel to its base. The cut is made at a height h from the base. After the cut I remove the cone. What is the name of the figure left out? What is the radius of its top surface?

The sum to n terms of the series 22+42+62+..........is

What is Expansion of (x−y)3?

When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.

Prove that √5 is irrational.

x−y=0 is a line which is

Give the meaning of arithmetic average.

−5x3+1&lt;23 Solve for x

I got a viral question, kindly help me with it 6÷2(1+2)

The relation R ={(x, √x):x is a natural number less than 100; √x is an integer }. Write the relation in roster form.

The LCM of (x−3)(x−5) and (x−5)(x−7) is:

give an example in which remainder is greater than divisor

A(2, 20), B(x,20), C (40,y), and D(10,6) are vertices of parallelogram taken in order, find x and y.

If pth,qth,rth terms of an A.P. are a,b,c respectively, then the value of a(q−r)+b(r−p)+c(p−q) is

Solve for x :1(x−1)(x−2)+1(x−2)(x−3) = 23,x≠1,2,3

Solve each of the following quadratic equations: (4x−32x+1)−10(2x+14x−3)=3,x≠−12,34

In a class text, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of his marks, would have been 180. Find his marks in the two subjects.

In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB=120∘, then the correct relation is-

Question 9 The point which divides the line segment joining points (7, - 6) and (3,4) in ratio 1:2 internally lies in the (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Write the value of sec2 θ (1+sin θ)(1−sin θ).

Solve the following quadratic equation for x. 4x2−4a2x+(a4−b4)=0

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completly. Find the diameter of the cylindrical vessel.

From the given table, find (i) the agerage (Mean) wage of a worker. (ii) the model class.

For what value of 'K' will the system of equations: 3x + y = 1, (2K - 1) x + (K - 1) y = 2K + 1 have no solution?

The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Question 4 (viii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (viii) −12,−12,−12,−12……

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

In an A.P., if the first erm is 22, the common difference is -4 and the sum to n terms is -650, find n.

A point P is at a distance of 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x is ___ cm.

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m. then at what time will they again change simultaneously.

Solve : −3+x<2,x ϵ N.

−5x3+1<23 Solve for x