32581 + Interview Questions in Mathematics

1.	Solve:- x2 + 14x – 32 = 0
Answer» Solve:- $x^{2}$ + 14x – 32 = 0

Discussion

2.	Show graphically that each of the following given systems of equations has infinitely many solutions: 3x−y=5,6x−2y=10.
Answer» Show graphically that each of the following given systems of equations has infinitely many solutions: $3 x - y = 5, 6 x - 2 y = 10.$

Discussion

3.	A sum of 700 is to be issued to give seven cash prizes to students of a school for their overall academic performance, If each prize is Rs.20 less than its preceding prize, Find the value for each prize.
Answer» A sum of 700 is to be issued to give seven cash prizes to students of a school for their overall academic performance, If each prize is Rs.20 less than its preceding prize, Find the value for each prize.

Discussion

4.	Construct a triangle ABC in which BC is 5 cm, Angle B is 120∘ and AB+AC=17cm
Answer» Construct a triangle ABC in which BC is 5 cm, Angle B is $120^{\circ}$ and AB+AC=17cm

Discussion

5.	Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ?
Answer» Water in a canal, $5.4$ m wide and $1.8$ m deep, is flowing with a speed of $25$ km/hour. How much area can it irrigate in $40$ minutes, if $10$ cm of standing water is required for irrigation ?

Discussion

6.	A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the are PRQ.
Answer» A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the are PRQ.

Discussion

7.	Find the value of x, if the distance between the points (x, –1) and (3, 2) is 5. [2 MARKS]
Answer» Find the value of x, if the distance between the points (x, –1) and (3, 2) is 5. [2 MARKS]

Discussion

8.	Question 8 (i) Justify whether it is true to say that the following are the nth terms of an AP. 2n – 3
Answer» Question 8 (i) Justify whether it is true to say that the following are the nth terms of an AP. 2n – 3

Discussion

9.	Find the Mean of the following frequency table by step - deviation method : Class IntervalFrequency10−151015−20520−25625−30830−35435−407
Answer» Find the Mean of the following frequency table by step - deviation method : $\begin{matrix} Class Interval & Frequency 10 - 15 & 10 15 - 20 & 5 20 - 25 & 6 25 - 30 & 8 30 - 35 & 4 35 - 40 & 7 \end{matrix}$

9.

Find the Mean of the following frequency table by step - deviation method : Class IntervalFrequency10−151015−20520−25625−30830−35435−407

Answer»

Find the Mean of the following frequency table by step - deviation method :

$\begin{matrix} Class Interval & Frequency 10 - 15 & 10 15 - 20 & 5 20 - 25 & 6 25 - 30 & 8 30 - 35 & 4 35 - 40 & 7 \end{matrix}$

Discussion

10.	In the figure, AB = √ units __
Answer» In the figure, AB = $\sqrt{} u n i t s$ __

10.

In the figure, AB = √ units __

Answer»

In the figure, AB = $\sqrt{} u n i t s$

__

Discussion

11.	Find the mode of the following distribution: Class interval 10−1414−1818−2222−2626−3030−3434−3838−42Frequency8611202522104
Answer» Find the mode of the following distribution: $\begin{matrix} Class interval & 10 - 14 & 14 - 18 & 18 - 22 & 22 - 26 & 26 - 30 & 30 - 34 & 34 - 38 & 38 - 42 Frequency & 8 & 6 & 11 & 20 & 25 & 22 & 10 & 4 \end{matrix}$

Discussion

12.	If the nth term of a progression is (4n-10) show that it is an AP. Find its (i) first term (ii) common difference, and (iii) 16th term.
Answer» If the nth term of a progression is (4n-10) show that it is an AP. Find its (i) first term (ii) common difference, and (iii) 16th term.

Discussion

13.	Question 16 A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?
Answer» Question 16 A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Discussion

14.	In an A.P., if the 5th and 12th terms are 30 and 65 respecitvely, what is the sum of first 20 terms?
Answer» In an A.P., if the 5th and 12th terms are 30 and 65 respecitvely, what is the sum of first 20 terms?

Discussion

15.	Find the value of k for which the equation x2+k(2x+k-1)+2 has real and equal roots.
Answer» Find the value of k for which the equation x²+k(2x+k-1)+2 has real and equal roots.

Discussion

16.	If ABCD is a cyclic quadrilateral, then x = ___.
Answer» If ABCD is a cyclic quadrilateral, then $x$ = ___.

16.

If ABCD is a cyclic quadrilateral, then x = ___.

Answer»

If ABCD is a cyclic quadrilateral, then $x$ = ___.

Discussion

17.	A and B undertake to do a piece of work for Rs. 200. A alone can do it in 6 days and B in 8 days. With the help of C they finish it in 3 days. How much is paid to C?
Answer» A and B undertake to do a piece of work for Rs. 200. A alone can do it in 6 days and B in 8 days. With the help of C they finish it in 3 days. How much is paid to C?

Discussion

18.	An iron spherical ball of radius 21cm is melted and it is re casted in hemispherical balls of radius 7cm. How many such balls will be formed? ___
Answer» An iron spherical ball of radius 21cm is melted and it is re casted in hemispherical balls of radius 7cm. How many such balls will be formed? ___

Discussion

19.	Excuse me ....how to write theta with keypad...can i write O in place of theta because there is no symbol provided in keypad for theta
Answer» Excuse me ....how to write theta with keypad...can i write O in place of theta because there is no symbol provided in keypad for theta

Discussion

20.	Question 17 A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.
Answer» Question 17 A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Discussion

21.	Find the value of k if (2x−3) is a factor of 2x3−9x2+x+k.
Answer» Find the value of $k$ if $(2 x - 3)$ is a factor of $2 x^{3} - 9 x^{2} + x + k .$

Discussion

22.	Express the hcf of 234 and 111 as 234x + 111y , where x and y are integers.
Answer» Express the hcf of 234 and 111 as 234x + 111y , where x and y are integers.

Discussion

23.	If arc ABC=110∘ and arc CDE=120∘, then the measure of arc ACE is equal to?
Answer» If $a r c A B C = 110^{\circ}$ and $a r c C D E = 120^{\circ},$ then the measure of arc ACE is equal to?

Discussion

24.	What's the constant of an equation which passes through origin?
Answer» What's the constant of an equation which passes through origin?

Discussion

25.	Hemakshi reshaped a cone of height h cm and radius of its base r cm into a sphere. Then, which of the following option is always correct?
Answer» Hemakshi reshaped a cone of height h cm and radius of its base r cm into a sphere. Then, which of the following option is always correct?

Discussion

26.	Question 5 Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4m Find the distance between the first and the last sapling.
Answer» Question 5 Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4m Find the distance between the first and the last sapling.

Discussion

27.	Show that the points (-3 ,3), (3, 3) and (−3√3,3√3 ) are the vertices of an equilateral triangle.
Answer» Show that the points (-3 ,3), (3, 3) and $(- 3 \sqrt{3}, 3 \sqrt{3}$ ) are the vertices of an equilateral triangle.

Discussion

28.	If the mean of the data is 60, find the value of p Class intervalfrequency25−351235−451645−55p55−651565−75875−851985−9513 [2 MARKS]
Answer» If the mean of the data is 60, find the value of p $\begin{matrix} C l a s s i n t e r v a l & f r e q u e n c y 25 - 35 & 12 35 - 45 & 16 45 - 55 & p 55 - 65 & 15 65 - 75 & 8 75 - 85 & 19 85 - 95 & 13 \end{matrix}$ [2 MARKS]

Discussion

29.	Match the equations A, B, C and D with the lines L1,L2,L3 and L4, whose graphs are roughly drawn in the given diagram. A ≡ y = 2x; B ≡ y - 2x + 2 = 0; C ≡ 3x + 2y = 6; D ≡ y = 2
Answer» Match the equations A, B, C and D with the lines $L_{1}, L_{2}, L_{3} a n d L_{4}$ , whose graphs are roughly drawn in the given diagram. A $\equiv$ y = 2x; B $\equiv$ y - 2x + 2 = 0; C $\equiv$ 3x + 2y = 6; D $\equiv$ y = 2

29.

Match the equations A, B, C and D with the lines L1,L2,L3 and L4, whose graphs are roughly drawn in the given diagram. A ≡ y = 2x; B ≡ y - 2x + 2 = 0; C ≡ 3x + 2y = 6; D ≡ y = 2

Answer»

Match the equations A, B, C and D with the lines $L_{1}, L_{2}, L_{3} a n d L_{4}$ , whose graphs are roughly drawn in the given diagram.

A $\equiv$ y = 2x; B $\equiv$ y - 2x + 2 = 0;

C $\equiv$ 3x + 2y = 6; D $\equiv$ y = 2

Discussion

30.	Question 3 The points (0,5), (0,-9) and (3,6) are collinear.
Answer» Question 3 The points (0,5), (0,-9) and (3,6) are collinear.

Discussion

31.	Suppose f(x)=(x+1)2 for x≥−1. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y = x, then g(x) equals.
Answer» Suppose $f (x) = (x + 1)^{2}$ for $x \geq - 1$ . If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y = x, then g(x) equals.

Discussion

32.	Which of the following rational numbers is in the standard form?
Answer» Which of the following rational numbers is in the standard form?

Discussion

33.	Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract?
Answer» Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract?

Discussion

34.	Determine which of the following polynomials have (x+2) as a factor:
Answer» Determine which of the following polynomials have $(x + 2)$ as a factor:

Discussion

35.	Find the single discount equivalent to two successive discounts 25% and 8%.
Answer» Find the single discount equivalent to two successive discounts 25% and 8%.

Discussion

36.	If √x/y + √y/x = 10/3, then find xy.
Answer» If √x/y + √y/x = 10/3, then find xy.

Discussion

37.	A man buys an article for Rs. 12000 and pays 8% tax. He sells the same article for Rs. 14000 and charges 10% tax. The VAT paid by the man is
Answer» A man buys an article for Rs. 12000 and pays 8% tax. He sells the same article for Rs. 14000 and charges 10% tax. The VAT paid by the man is

Discussion

38.	Explain why 13121110+12 and 23293137+37 are composite numbers?
Answer» Explain why 13121110+12 and 23293137+37 are composite numbers?

Discussion

39.	Find the factors of the expression x3−5x2+8x−4
Answer» Find the factors of the expression $x^{3} - 5 x^{2} + 8 x - 4$

Discussion

40.	Rohan bought pop corn in a theater which is given in a paper cone. He ate it and came to home with empty cone, which has height 9 cm and radius 7 cm. Find the approximate volume of pop corn he ate.
Answer» Rohan bought pop corn in a theater which is given in a paper cone. He ate it and came to home with empty cone, which has height 9 cm and radius 7 cm. Find the approximate volume of pop corn he ate.

Discussion

41.	Mohan deposited Rs 300 per month in a cumulative deposit for 2 years. The bank pays him Rs 9000 on maturity. Find the rate of interest. [4 MARKS]
Answer» Mohan deposited Rs 300 per month in a cumulative deposit for 2 years. The bank pays him Rs 9000 on maturity. Find the rate of interest. [4 MARKS]

Discussion

42.	√3+√5 prove it is irrational
Answer» √3+√5 prove it is irrational

Discussion

43.	Which of the following can be said about the roots of 2x2–6x+8=0?
Answer» Which of the following can be said about the roots of $2 x^{2} - 6 x + 8 = 0$ ?

Discussion

44.	What are the conditions under which the logarithm log2x(x2−1) is defined ?
Answer» What are the conditions under which the logarithm ${log}_{2 x} (x^{2} - 1)$ is defined ?

Discussion

45.	One says,"give me a hundred,friend! I shallthen become twice as rich as you".The other replies,"If you give me ten,I shall be as rich as you".Tell me what is the amount of their(respective)capital?
Answer» One says,"give me a hundred,friend! I shallthen become twice as rich as you".The other replies,"If you give me ten,I shall be as rich as you".Tell me what is the amount of their(respective)capital?

Discussion

46.	Show that the square of an odd positive integer is of the form 8m+1, for some whole number m
Answer» Show that the square of an odd positive integer is of the form 8m+1, for some whole number m

Discussion

47.	If the numbers 5,x,125 are in G.P. what is the value of x?
Answer» If the numbers $5, x, 125$ are in G.P. what is the value of $x$ ?

Discussion

48.	The sum of the three numbers in an AP is 21 and the product of the first and third number of the sequence is 45. What are the three numbers?
Answer» The sum of the three numbers in an AP is 21 and the product of the first and third number of the sequence is 45. What are the three numbers?

Discussion

49.	What are the coordinates of the centre of the circle x2+y2−2x−2y+1=0.
Answer» What are the coordinates of the centre of the circle $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ .

Discussion

50.	Graph of the quadratic equation ax2 + bx + c = 0 , with a > 0 , D < 0 is
Answer» Graph of the quadratic equation ax² + bx + c = 0 , with a > 0 , D < 0 is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve:- x2 + 14x – 32 = 0

Show graphically that each of the following given systems of equations has infinitely many solutions: 3x−y=5,6x−2y=10.

A sum of 700 is to be issued to give seven cash prizes to students of a school for their overall academic performance, If each prize is Rs.20 less than its preceding prize, Find the value for each prize.

Construct a triangle ABC in which BC is 5 cm, Angle B is 120∘ and AB+AC=17cm

Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ?

A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the are PRQ.

Find the value of x, if the distance between the points (x, –1) and (3, 2) is 5. [2 MARKS]

Question 8 (i) Justify whether it is true to say that the following are the nth terms of an AP. 2n – 3

Find the Mean of the following frequency table by step - deviation method : Class IntervalFrequency10−151015−20520−25625−30830−35435−407

In the figure, AB = √ units __

Find the mode of the following distribution: Class interval 10−1414−1818−2222−2626−3030−3434−3838−42Frequency8611202522104

If the nth term of a progression is (4n-10) show that it is an AP. Find its (i) first term (ii) common difference, and (iii) 16th term.

Question 16 A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

In an A.P., if the 5th and 12th terms are 30 and 65 respecitvely, what is the sum of first 20 terms?

Find the value of k for which the equation x​​​​​​2+k(2x+k-1)+2 has real and equal roots. ​​​

If ABCD is a cyclic quadrilateral, then x = ___.

A and B undertake to do a piece of work for Rs. 200. A alone can do it in 6 days and B in 8 days. With the help of C they finish it in 3 days. How much is paid to C?

An iron spherical ball of radius 21cm is melted and it is re casted in hemispherical balls of radius 7cm. How many such balls will be formed? ___

Excuse me ....how to write theta with keypad...can i write O in place of theta because there is no symbol provided in keypad for theta

Question 17 A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Find the value of k if (2x−3) is a factor of 2x3−9x2+x+k.

Express the hcf of 234 and 111 as 234x + 111y , where x and y are integers.

If arc ABC=110∘ and arc CDE=120∘, then the measure of arc ACE is equal to?

What's the constant of an equation which passes through origin?

Hemakshi reshaped a cone of height h cm and radius of its base r cm into a sphere. Then, which of the following option is always correct?

Question 5 Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4m Find the distance between the first and the last sapling.

Show that the points (-3 ,3), (3, 3) and (−3√3,3√3 ) are the vertices of an equilateral triangle.

If the mean of the data is 60, find the value of p Class intervalfrequency25−351235−451645−55p55−651565−75875−851985−9513 [2 MARKS]

Match the equations A, B, C and D with the lines L1,L2,L3 and L4, whose graphs are roughly drawn in the given diagram. A ≡ y = 2x; B ≡ y - 2x + 2 = 0; C ≡ 3x + 2y = 6; D ≡ y = 2

Question 3 The points (0,5), (0,-9) and (3,6) are collinear.

Suppose f(x)=(x+1)2 for x≥−1. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line y = x, then g(x) equals.

Which of the following rational numbers is in the standard form?

Three companies are bidding on a contract. Company A is twice as likely to win as Company B, and Company B is three times as likely to win as Company C. What is the probability of each company winning the contract?

Determine which of the following polynomials have (x+2) as a factor:

Find the single discount equivalent to two successive discounts 25% and 8%.

If √x/y + √y/x = 10/3, then find xy.

A man buys an article for Rs. 12000 and pays 8% tax. He sells the same article for Rs. 14000 and charges 10% tax. The VAT paid by the man is

Explain why 13*12*11*10+12 and 23*29*31*37+37 are composite numbers?

Find the factors of the expression x3−5x2+8x−4

Rohan bought pop corn in a theater which is given in a paper cone. He ate it and came to home with empty cone, which has height 9 cm and radius 7 cm. Find the approximate volume of pop corn he ate.

Mohan deposited Rs 300 per month in a cumulative deposit for 2 years. The bank pays him Rs 9000 on maturity. Find the rate of interest. [4 MARKS]

√3+√5 prove it is irrational

Which of the following can be said about the roots of 2x2–6x+8=0?

What are the conditions under which the logarithm log2x(x2−1) is defined ?

One says,"give me a hundred,friend! I shallthen become twice as rich as you".The other replies,"If you give me ten,I shall be as rich as you".Tell me what is the amount of their(respective)capital?

Show that the square of an odd positive integer is of the form 8m+1, for some whole number m

If the numbers 5,x,125 are in G.P. what is the value of x?

The sum of the three numbers in an AP is 21 and the product of the first and third number of the sequence is 45. What are the three numbers?

What are the coordinates of the centre of the circle x2+y2−2x−2y+1=0.

Graph of the quadratic equation ax2 + bx + c = 0 , with a &gt; 0 , D &lt; 0 is

Find the value of k for which the equation x2+k(2x+k-1)+2 has real and equal roots.

Explain why 13121110+12 and 23293137+37 are composite numbers?

Graph of the quadratic equation ax2 + bx + c = 0 , with a > 0 , D < 0 is