32581 + Interview Questions in Mathematics

1.	A bag contains 5 red , 4 green and 3 blue balls. If a ball is drawn at random, what is the probability of getting a red ball
Answer» A bag contains 5 red , 4 green and 3 blue balls. If a ball is drawn at random, what is the probability of getting a red ball

Discussion

2.	Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the center
Answer» Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the center

Discussion

3.	Question 17 If the points A(2,9), B(a,5) and C(5,5) are the vertices of a Δ ABC right angled at B, then find the values of a and hence the area of Δ ABC.
Answer» Question 17 If the points A(2,9), B(a,5) and C(5,5) are the vertices of a $Δ$ ABC right angled at B, then find the values of a and hence the area of $Δ$ ABC.

Discussion

4.	If two circles intersect at two points, then prove that their centers lie on the perpendicular bisector of the common chord. [2 MARKS]
Answer» If two circles intersect at two points, then prove that their centers lie on the perpendicular bisector of the common chord. [2 MARKS]

Discussion

5.	Saloni deposited Rs 150 per month in her bank account for eight months under the Recurring Deposit scheme. What will be the maturity value of her deposit, if the rate of interest is 8% per anum and the interest is calculated at the end of every month? [3 MARKS]
Answer» Saloni deposited Rs 150 per month in her bank account for eight months under the Recurring Deposit scheme. What will be the maturity value of her deposit, if the rate of interest is 8% per anum and the interest is calculated at the end of every month? [3 MARKS]

Discussion

6.	What is the value of a is degree of polynomial X ^ 3 + X ^ a - 4 + X ^ 2 + 1 is 4
Answer» What is the value of a is degree of polynomial X ^ 3 + X ^ a - 4 + X ^ 2 + 1 is 4

Discussion

7.	Question 2 (i) Find the sum of those integers between 1 and 500 which are multiple of 2 as well as of 5.
Answer» Question 2 (i) Find the sum of those integers between 1 and 500 which are multiple of 2 as well as of 5.

Discussion

8.	Which constant must be added and subtracted to solve the quadratic equation 9x2+34x−2=0 by the method of completing the square?
Answer» Which constant must be added and subtracted to solve the quadratic equation $9 x^{2} + \frac{3}{4} x - 2 = 0$ by the method of completing the square?

8.

Which constant must be added and subtracted to solve the quadratic equation 9x2+34x−2=0 by the method of completing the square?

Answer»

Which constant must be added and subtracted to solve the quadratic equation $9 x^{2} + \frac{3}{4} x - 2 = 0$ by the method of completing the square?

Discussion

9.	The sum of 3 numbers which are in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Answer» The sum of 3 numbers which are in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

Discussion

10.	Question 15 Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
Answer» Question 15 Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Discussion

11.	If p(x) = 2x2 + 2x + 5 is divided by (2x − 1), then the remainder is ________.
Answer» If $p (x) = 2 x^{2} + 2 x + 5$ is divided by $(2 x - 1)$ , then the remainder is ________.

Discussion

12.	A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the cylinder is 20 cm.
Answer» A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the cylinder is 20 cm.

Discussion

13.	A card is selected from a pack of 52 cards. How many points are there in the sample space?
Answer» A card is selected from a pack of 52 cards. How many points are there in the sample space?

Discussion

14.	Find the distance between the points (i) P(-6, 7) and Q(-1, -5) (ii) R(a + b, a - b) and S(a - b, - a - b)
Answer» Find the distance between the points (i) P(-6, 7) and Q(-1, -5) (ii) R(a + b, a - b) and S(a - b, - a - b)

Discussion

15.	For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?
Answer» For the given linear equation $y - 3 x + 1 = 0,$ what are the values of $y$ if $x = [3, - 4, 2]$ ?

Discussion

16.	What is the sum of the first n terms of the AP a, 3a, 5a,..
Answer» What is the sum of the first n terms of the AP a, 3a, 5a,..

Discussion

17.	If a circle is drawn with centre 'C' (0,4) and radius 5 cm as shown in figure then the coordinates of R and S are___
Answer» If a circle is drawn with centre 'C' (0,4) and radius 5 cm as shown in figure then the coordinates of R and S are___

17.

If a circle is drawn with centre 'C' (0,4) and radius 5 cm as shown in figure then the coordinates of R and S are___

Answer»

If a circle is drawn with centre 'C' (0,4) and radius 5 cm as shown in figure then the coordinates of R and S are___

Discussion

18.	A piece of cloth costs ₹200.if the piece was 5m longer and each metre of cloth costs ₹2 less , the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?
Answer» A piece of cloth costs ₹200.if the piece was 5m longer and each metre of cloth costs ₹2 less , the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?

Discussion

19.	If pth,qth and rth term of an A.P. are a,b,c respectively ,then show that: a(q-r)+b(r-p)+c(p-q)=0
Answer» If pth,qth and rth term of an A.P. are a,b,c respectively ,then show that: a(q-r)+b(r-p)+c(p-q)=0

Discussion

20.	Find the quadratic polynomial whose zeros are √2+3 &√2-3
Answer» Find the quadratic polynomial whose zeros are √2+3 &√2-3

Discussion

21.	Anam's age 3 times his son's age 10years ago he was his son's age find there present age
Answer» Anam's age 3 times his son's age 10years ago he was his son's age find there present age

Discussion

22.	The distance of point Q is twice as far from (-2,-8) as it is from (13, 5). If it lies on the line segment joining the two, what are the coordinates of Q?
Answer» The distance of point Q is twice as far from (-2,-8) as it is from (13, 5). If it lies on the line segment joining the two, what are the coordinates of Q?

Discussion

23.	Question 102 State whether the statement is True or False. a÷(−b)=−(a÷b)
Answer» Question 102 State whether the statement is True or False. $a \div (- b) = - (a \div b)$

23.

Question 102 State whether the statement is True or False. a÷(−b)=−(a÷b)

Answer»

Question 102

State whether the statement is True or False.

$a \div (- b) = - (a \div b)$

Discussion

24.	Write the negation of the following compound statement. 'Square of an integer is positive or negative'.
Answer» Write the negation of the following compound statement. 'Square of an integer is positive or negative'.

24.

Write the negation of the following compound statement. 'Square of an integer is positive or negative'.

Answer»

Write the negation of the following compound statement.

'Square of an integer is positive or negative'.

Discussion

25.	Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.
Answer» Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.

Discussion

26.	The expression 4x3−bx2+x−c leaves remainders 0 and 30 when divided by x+1 and 2x-3 respectively. Calculate the values of b and c hence, factorize the expression completely.
Answer» The expression $4 x^{3} - b x^{2} + x - c$ leaves remainders 0 and 30 when divided by x+1 and 2x-3 respectively. Calculate the values of b and c hence, factorize the expression completely.

Discussion

27.	If a:b is the reciprocal ratio of 10:9, then a:b is ____
Answer» If a:b is the reciprocal ratio of 10:9, then a:b is ____

Discussion

28.	ABCD is a parallelogram. The circle through A,B and C intersect CD (produced if necessary) at E. Prove that AE=AD.
Answer» $A B C D$ is a parallelogram. The circle through $A, B$ and $C$ intersect $C D$ (produced if necessary) at $E$ . Prove that $A E = A D$ .

Discussion

29.	If the (p+q)th term of a G.P. is m and (p−q)th term is n, then pth term will be _____.
Answer» If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

Discussion

30.	Which of the following money may not be acceptable by the public?
Answer» Which of the following money may not be acceptable by the public?

Discussion

31.	Which of the following revenues of the government pays the interest and principal amount?
Answer» Which of the following revenues of the government pays the interest and principal amount?

Discussion

32.	Question 3 (iv) For the following A.P.S, write the first term and the common difference. (iv) 0.6, 1.7, 2.8, 3.9 …
Answer» Question 3 (iv) For the following A.P.S, write the first term and the common difference. (iv) 0.6, 1.7, 2.8, 3.9 …

Discussion

33.	If a, b, c, are in H.P. then
Answer» If a, b, c, are in H.P. then

Discussion

34.	Question 2 tan A1+sec A−tan A1−sec A=2 cosec A
Answer» Question 2 $\frac{t a n A}{1 + s e c A} - \frac{t a n A}{1 - s e c A} = 2 c o s e c A$

Discussion

35.	Question 9 The value of 2 sin θ can be a+1a, where a is a positive number and a≠1.
Answer» Question 9 The value of $2 s i n θ$ can be $a + \frac{1}{a}$ , where a is a positive number and $a \neq 1$ .

Discussion

36.	The first term of an AP is 5 ,the last term is 45,sum of all its term is 400. find the number of terms and the common difference.
Answer» The first term of an AP is 5 ,the last term is 45,sum of all its term is 400. find the number of terms and the common difference.

Discussion

37.	If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then
Answer» If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

Discussion

38.	The expression that should be added to the polynomial f(x) = x4 + 2x3 – 2x2 + x + 1, so that it should be exactly divisible by (x2 + 2x – 3) is
Answer» The expression that should be added to the polynomial f(x) = x⁴ + 2x³ – 2x² + x + 1, so that it should be exactly divisible by (x² + 2x – 3) is

Discussion

39.	If the equation 2x2 + 2(c – 20) x + (c – 20) = 0 has equal roots then, the value of c is
Answer» If the equation 2x2 + 2(c – 20) x + (c – 20) = 0 has equal roots then, the value of c is

Discussion

40.	Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30∘ and 45∘ respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Answer» Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are $30^{\circ}$ and $45^{\circ}$ respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Discussion

41.	The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.
Answer» The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.

Discussion

42.	What number must be added to each of the numbers 6, 15, 20 & 43 so that the remainders are in proportion?
Answer» What number must be added to each of the numbers 6, 15, 20 & 43 so that the remainders are in proportion?

Discussion

43.	MN is a tangent to the circle at the point of contact C. Identify the angle that is equal to x.
Answer» MN is a tangent to the circle at the point of contact C. Identify the angle that is equal to x.

Discussion

44.	Find the sum of 2n terms of the series 1^2-2^2+3^2-4^2+5^2-6^2...
Answer» Find the sum of 2n terms of the series 1^2-2^2+3^2-4^2+5^2-6^2...

Discussion

45.	Question 2 (v) Are the following statements ‘True’ or False’? Justify your answer. v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Answer» Question 2 (v) Are the following statements ‘True’ or False’? Justify your answer. v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

Discussion

46.	Question 3 (i) For the following A.Ps, write the first term and the common difference. (i) 3, 1, - 1, - 3 …
Answer» Question 3 (i) For the following A.Ps, write the first term and the common difference. (i) 3, 1, - 1, - 3 …

Discussion

47.	The value of tan 45∘ is
Answer» The value of $tan$ $45^{\circ}$ is

Discussion

48.	In the given figure, ∠x=20∘,∠y=160∘,∠w=105∘,∠z=75∘ Which of the following is correct?
Answer» In the given figure, $∠ x = 20^{\circ}, ∠ y = 160^{\circ}, ∠ w = 105^{\circ}, ∠ z = 75^{\circ}$ Which of the following is correct?

Discussion

49.	Railway Half Ticket costs half the full fare but the reservation are same for half and full Ticket. one reserved first class ticket from station A to B costs 2350 rupees. Also one first class ticket and one reserved first class half ticket from A to B cost rupees 3810 . find the full first class fare from station a to b and also a reservation charge for a ticket.
Answer» Railway Half Ticket costs half the full fare but the reservation are same for half and full Ticket. one reserved first class ticket from station A to B costs 2350 rupees. Also one first class ticket and one reserved first class half ticket from A to B cost rupees 3810 . find the full first class fare from station a to b and also a reservation charge for a ticket.

Discussion

50.	The following table shows the class mark and frequency. Convert the table in the class interval Class MarkFrequency558656751885259512
Answer» The following table shows the class mark and frequency. Convert the table in the class interval $\begin{matrix} Class Mark & Frequency 55 & 8 65 & 6 75 & 18 85 & 25 95 & 12 \end{matrix}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A bag contains 5 red , 4 green and 3 blue balls. If a ball is drawn at random, what is the probability of getting a red ball

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the center

Question 17 If the points A(2,9), B(a,5) and C(5,5) are the vertices of a Δ ABC right angled at B, then find the values of a and hence the area of Δ ABC.

If two circles intersect at two points, then prove that their centers lie on the perpendicular bisector of the common chord. [2 MARKS]

Saloni deposited Rs 150 per month in her bank account for eight months under the Recurring Deposit scheme. What will be the maturity value of her deposit, if the rate of interest is 8% per anum and the interest is calculated at the end of every month? [3 MARKS]

What is the value of a is degree of polynomial X ^ 3 + X ^ a - 4 + X ^ 2 + 1 is 4

Question 2 (i) Find the sum of those integers between 1 and 500 which are multiple of 2 as well as of 5.

Which constant must be added and subtracted to solve the quadratic equation 9x2+34x−2=0 by the method of completing the square?

The sum of 3 numbers which are in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

Question 15 Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

If p(x) = 2x2 + 2x + 5 is divided by (2x − 1), then the remainder is ________.

A card is selected from a pack of 52 cards. How many points are there in the sample space?

Find the distance between the points (i) P(-6, 7) and Q(-1, -5) (ii) R(a + b, a - b) and S(a - b, - a - b)

For the given linear equation y−3x+1=0, what are the values of y if x=[3,−4,2]?

What is the sum of the first n terms of the AP a, 3a, 5a,..

If a circle is drawn with centre 'C' (0,4) and radius 5 cm as shown in figure then the coordinates of R and S are___

A piece of cloth costs ₹200.if the piece was 5m longer and each metre of cloth costs ₹2 less , the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?

If pth,qth and rth term of an A.P. are a,b,c respectively ,then show that: a(q-r)+b(r-p)+c(p-q)=0

Find the quadratic polynomial whose zeros are √2+3 &amp;√2-3

Anam's age 3 times his son's age 10years ago he was his son's age find there present age

The distance of point Q is twice as far from (-2,-8) as it is from (13, 5). If it lies on the line segment joining the two, what are the coordinates of Q?

Question 102 State whether the statement is True or False. a÷(−b)=−(a÷b)

Write the negation of the following compound statement. 'Square of an integer is positive or negative'.

Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.

The expression 4x3−bx2+x−c leaves remainders 0 and 30 when divided by x+1 and 2x-3 respectively. Calculate the values of b and c hence, factorize the expression completely.

If a:b is the reciprocal ratio of 10:9, then a:b is ____

ABCD is a parallelogram. The circle through A,B and C intersect CD (produced if necessary) at E. Prove that AE=AD.

If the (p+q)th term of a G.P. is m and (p−q)th term is n, then pth term will be _____.

Which of the following money may not be acceptable by the public?

Which of the following revenues of the government pays the interest and principal amount?

Question 3 (iv) For the following A.P.S, write the first term and the common difference. (iv) 0.6, 1.7, 2.8, 3.9 …

If a, b, c, are in H.P. then

Question 2 tan A1+sec A−tan A1−sec A=2 cosec A

Question 9 The value of 2 sin θ can be a+1a, where a is a positive number and a≠1.

The first term of an AP is 5 ,the last term is 45,sum of all its term is 400. find the number of terms and the common difference.

If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

The expression that should be added to the polynomial f(x) = x4 + 2x3 – 2x2 + x + 1, so that it should be exactly divisible by (x2 + 2x – 3) is

If the equation 2x2 + 2(c – 20) x + (c – 20) = 0 has equal roots then, the value of c is

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30∘ and 45∘ respectively. If the lighthouse is 100 m high, the distance between the two ships is:

The coordinate of the mid-point of the line segment joining the points (2,1) and (1,-3) is ____.

What number must be added to each of the numbers 6, 15, 20 &amp; 43 so that the remainders are in proportion?

MN is a tangent to the circle at the point of contact C. Identify the angle that is equal to x.

Find the sum of 2n terms of the series 1^2-2^2+3^2-4^2+5^2-6^2...

Question 2 (v) Are the following statements ‘True’ or False’? Justify your answer. v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

Question 3 (i) For the following A.Ps, write the first term and the common difference. (i) 3, 1, - 1, - 3 …

The value of tan 45∘ is

In the given figure, ∠x=20∘,∠y=160∘,∠w=105∘,∠z=75∘ Which of the following is correct?

The following table shows the class mark and frequency. Convert the table in the class interval Class MarkFrequency558656751885259512

Find the quadratic polynomial whose zeros are √2+3 &√2-3

What number must be added to each of the numbers 6, 15, 20 & 43 so that the remainders are in proportion?