32581 + Interview Questions in Mathematics

1.	If the rate of sales tax is 5%, ‘A’ has to pay Rs 7,140 for steel cup board. What amount he has to pay if the sales tax is increased by 2%.
Answer» If the rate of sales tax is 5%, ‘A’ has to pay Rs 7,140 for steel cup board. What amount he has to pay if the sales tax is increased by 2%.

Discussion

2.	Question 3 In the following figure, if LM \|\| CB and LN \|\| CD, prove that AMAB=ANAD.
Answer» Question 3 In the following figure, if LM \|\| CB and LN \|\| CD, prove that $\frac{A M}{A B} = \frac{A N}{A D}$ .

Discussion

3.	Question 1 (ii) Write111 in decimal form and say what kind of decimal expansion it has.
Answer» Question 1 (ii) Write $\frac{1}{11}$ in decimal form and say what kind of decimal expansion it has.

Discussion

4.	Question 1 (iv) For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization. iv) =−32√5,−12
Answer» Question 1 (iv) For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization. iv) $= \frac{- 3}{2 \sqrt{5}}, - \frac{1}{2}$

Discussion

5.	Question 2 Find the points on the X-axis which are at a distance of 2√5 from the point (7, -4). How many such points are there?
Answer» Question 2 Find the points on the X-axis which are at a distance of $2 \sqrt{5}$ from the point (7, -4). How many such points are there?

Discussion

6.	Question 1 (ii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (ii) 3x2+4x–4
Answer» Question 1 (ii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (ii) $3 x^{2} + 4 x - 4$

Discussion

7.	Question 1 (ii) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4s2−4s+1
Answer» Question 1 (ii) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. $4 s^{2} - 4 s + 1$

7.

Question 1 (ii) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4s2−4s+1

Answer»

Question 1 (ii)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$4 s^{2} - 4 s + 1$

Discussion

8.	If A(-4 , 3) & B(8 , -6) have respective coordinates a) find the length of AB, b) the ratio in which the – axis divides AB.
Answer» If A(-4 , 3) & B(8 , -6) have respective coordinates a) find the length of AB, b) the ratio in which the – axis divides AB.

8.

If A(-4 , 3) & B(8 , -6) have respective coordinates a) find the length of AB, b) the ratio in which the – axis divides AB.

Answer»

If A(-4 , 3) & B(8 , -6) have respective coordinates

a) find the length of AB,

b) the ratio in which the – axis divides AB.

Discussion

9.	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

10.	For the AP –3, –7, –11,… can we find directly a30−a20 without actually finding a30 and a20? Give the reason for your answer.
Answer» For the AP –3, –7, –11,… can we find directly $a_{30} - a_{20}$ without actually finding $a_{30} a n d a_{20}$ ? Give the reason for your answer.

Discussion

11.	Question 9 Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
Answer» Question 9 Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Discussion

12.	The sum of the terms of an infinite G.P whose first term is 6 and common ratio is 1/3 is ___.
Answer» The sum of the terms of an infinite G.P whose first term is 6 and common ratio is 1/3 is ___.

Discussion

13.	Which of the following are the factors of x2+3x+2 ?
Answer» Which of the following are the factors of $x^{2} + 3 x + 2$ ?

Discussion

14.	Factorise the following using appropriate identities: [4 MARKS] 1)9x2+6xy+y2 2)4y2−4y+1
Answer» Factorise the following using appropriate identities: [4 MARKS] $1) 9 x^{2} + 6 x y + y^{2}$ $2) 4 y^{2} - 4 y + 1$

Discussion

15.	A shopkeeper buys a number of books for ₹ 80. If he had bought 4 more books for the same amount, each book would have cost ₹ 1 less. He bought ___ books.
Answer» A shopkeeper buys a number of books for ₹ 80. If he had bought 4 more books for the same amount, each book would have cost ₹ 1 less. He bought ___ books.

Discussion

16.	Question 3 (iii) For the following A.Ps, write the first term and the common difference. (iii) 13,53,93,133……
Answer» Question 3 (iii) For the following A.Ps, write the first term and the common difference. (iii) $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3} \dots \dots$

Discussion

17.	Question 4 How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?
Answer» Question 4 How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?

Discussion

18.	On simplifying the expression √45−3√20+3√5 we get ___.
Answer» On simplifying the expression $\sqrt{45} - 3 \sqrt{20} + 3 \sqrt{5}$ we get ___.

Discussion

19.	If xg+1xa is a polynomial, what could be the value of a?
Answer» If $x^{g} + \frac{1}{x^{a}}$ is a polynomial, what could be the value of $a$ ?

Discussion

20.	The formula to find out the nth term of an AP is
Answer» The formula to find out the $n^{t h}$ term of an AP is

Discussion

21.	Solve the pair of equations using the method of substitution 3x-y = 8 ,5x+y = 0 [2 MARKS]
Answer» Solve the pair of equations using the method of substitution 3x-y = 8 ,5x+y = 0 [2 MARKS]

Discussion

22.	Form the polynomial whose zeroes are 6+√33,6−√33
Answer» Form the polynomial whose zeroes are $\frac{6 + \sqrt{3}}{3}, \frac{6 - \sqrt{3}}{3}$

Discussion

23.	If x=23 is a solution of the quadratic equation 7x2+mx−3=0, find the value of m.
Answer» If $x = \frac{2}{3}$ is a solution of the quadratic equation $7 x^{2} + m x - 3 = 0$ , find the value of m.

Discussion

24.	In Fig. 7.35, state if PQ \|\| EF.
Answer» In Fig. 7.35, state if PQ \|\| EF.

24.

In Fig. 7.35, state if PQ || EF.

Answer»

In Fig. 7.35, state if PQ || EF.

Discussion

25.	If the diagonals of a rhombus are 24 cm and 10 cm, then its perimeter =__________________cm
Answer» If the diagonals of a rhombus are 24 cm and 10 cm, then its perimeter =__________________cm

Discussion

26.	The owner of a milk store finds that he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs.17 / litre?
Answer» The owner of a milk store finds that he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs.17 / litre?

Discussion

27.	Condition for ax2 + bx + c = 0 to be a quadratic equation is
Answer» Condition for a $x^{2}$ + bx + c = 0 to be a quadratic equation is

Discussion

28.	Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8.
Answer» Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8.

Discussion

29.	The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ. Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm. Calculate the length of AP.
Answer» The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ. Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm. Calculate the length of AP.

29.

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ. Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm. Calculate the length of AP.

Answer»

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ.

Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm.

Calculate the length of AP.

Discussion

30.	1/3y+ y + 1/3x-y=3/4 1/2(3x+y)-1/2(3x-y)=-1/8 Solve for x and y
Answer» 1/3y+ y + 1/3x-y=3/4 1/2(3x+y)-1/2(3x-y)=-1/8 Solve for x and y

30.

1/3y+ y + 1/3x-y=3/4 1/2(3x+y)-1/2(3x-y)=-1/8 Solve for x and y

Answer»

1/3y+ y + 1/3x-y=3/4

1/2(3x+y)-1/2(3x-y)=-1/8

Solve for x and y

Discussion

31.	A quadratic equation whose roots are 2+1√2 and 2−1√2 is:
Answer» A quadratic equation whose roots are $2 + \frac{1}{\sqrt{2}}$ and $2 - \frac{1}{\sqrt{2}}$ is:

Discussion

32.	A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:
Answer» A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

Discussion

33.	What are the inferences that you can get from the given figure?
Answer» What are the inferences that you can get from the given figure?

33.

What are the inferences that you can get from the given figure?

Answer»

What are the inferences that you can get from the given figure?

Discussion

34.	A two digit number is 3 more than 4 times the sum of the digit. If 18 is added to the number the digits are reversed. Find the number.
Answer» A two digit number is 3 more than 4 times the sum of the digit. If 18 is added to the number the digits are reversed. Find the number.

Discussion

35.	Find the integral value of x such that 3x+1x+1+x+13x+1=52
Answer» $F i n d t h e i n t e g r a l v a l u e o f x s u c h t h a t \frac{3 x + 1}{x + 1} + \frac{x + 1}{3 x + 1} = \frac{5}{2}$

Discussion

36.	If (3x + 5y)/(3x – 5y) = 7/3, find x:y.
Answer» If (3x + 5y)/(3x – 5y) = 7/3, find x:y.

Discussion

37.	Rohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class?
Answer» Rohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class?

Discussion

38.	Question 2 In figure, if ∠AOB=125∘. Then ∠ COD is equal to (A) 62.5° (B) 45° (C) 35° (D) 55°
Answer» Question 2 In figure, if $∠ A O B = 125^{\circ}$ . Then $∠$ COD is equal to (A) 62.5° (B) 45° (C) 35° (D) 55°

Discussion

39.	Which of the following option does not belong to the construction of a circumcircle?
Answer» Which of the following option does not belong to the construction of a circumcircle?

Discussion

40.	Prove the ideintity: sec θ+1+tan θsec θ+1−tan θ=1+sin θcos θ [4 MARKS]
Answer» Prove the ideintity: $\frac{s e c θ + 1 + t a n θ}{s e c θ + 1 - t a n θ} = \frac{1 + s i n θ}{c o s θ}$ [4 MARKS]

Discussion

41.	Describe the locus for questions 1 to 13 given below: The locus of the door-handle, as the door opens.
Answer» Describe the locus for questions 1 to 13 given below: The locus of the door-handle, as the door opens.

41.

Describe the locus for questions 1 to 13 given below: The locus of the door-handle, as the door opens.

Answer»

Describe the locus for questions 1 to 13 given below:

The locus of the door-handle, as the door opens.

Discussion

42.	Shyam is on top of a building of 80m height waving at his friend Ram who is 60m away from the building. what is the direct distance between Ram and Shyam?
Answer» Shyam is on top of a building of 80m height waving at his friend Ram who is 60m away from the building. what is the direct distance between Ram and Shyam?

Discussion

43.	The slope of a line passing through points (1,2) and (10,20) is ___.
Answer» The slope of a line passing through points $(1, 2)$ and $(10, 20)$ is ___.

Discussion

44.	If a, b, c are pth, qth, and mth terms of a G.P., then (cb)p(ba)m(ac)q is equal to
Answer» If a, b, c are $p^{t h}$ , $q^{t h}$ , and $m^{t h}$ terms of a G.P., then $(\frac{c}{b})^{p} (\frac{b}{a})^{m} (\frac{a}{c})^{q}$ is equal to

Discussion

45.

A weather station recorded the temperatures of a place over a period of 7 days as follows: Day Temperature (in ∘C ) Monday 45 Tuesday 38 Wednesday 40 Thursday 42 Friday 41 Saturday 37 Sunday 36 Find the probability of a day having a temperature of more than 40 ∘ C.

Answer»

A weather station recorded the temperatures of a place over a period of 7 days as follows:

Day	Temperature (in $^{\circ}$ C )
Monday	45
Tuesday	38
Wednesday	40
Thursday	42
Friday	41
Saturday	37
Sunday	36

Find the probability of a day having a temperature of more than 40

^{\circ}

C.

Discussion

46.	For what values of p are the roots of the equations 4x2+px+3=0 real and equal?
Answer» For what values of p are the roots of the equations $4 x^{2} + p x + 3 = 0$ real and equal?

Discussion

47.	The cumulative frequency table is useful in determining the (a) mean (b) median (c) mode (d) all of these
Answer» The cumulative frequency table is useful in determining the (a) mean (b) median (c) mode (d) all of these

47.

The cumulative frequency table is useful in determining the (a) mean (b) median (c) mode (d) all of these

Answer»

The cumulative frequency table is useful in determining the

(a) mean (b) median

(c) mode (d) all of these

Discussion

48.	A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Answer» A well with $14 m$ diameter is dug $8 m$ deep. The earth taken out of it has been evenly spread all around it to a width of $21 m$ to form an embankment. Find the height of the embankment.

Discussion

49.	The slope of the line 5x+6y+3=0 is
Answer» The slope of the line $5 x + 6 y + 3 = 0$ is

Discussion

50.	A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.
Answer» A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the rate of sales tax is 5%, ‘A’ has to pay Rs 7,140 for steel cup board. What amount he has to pay if the sales tax is increased by 2%.

Question 3 In the following figure, if LM || CB and LN || CD, prove that AMAB=ANAD.

Question 1 (ii) Write111 in decimal form and say what kind of decimal expansion it has.

Question 1 (iv) For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization. iv) =−32√5,−12

Question 2 Find the points on the X-axis which are at a distance of 2√5 from the point (7, -4). How many such points are there?

Question 1 (ii) Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials (ii) 3x2+4x–4

Question 1 (ii) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 4s2−4s+1

If A(-4 , 3) &amp; B(8 , -6) have respective coordinates a) find the length of AB, b) the ratio in which the – axis divides AB.

For the AP –3, –7, –11,… can we find directly a30−a20 without actually finding a30 and a20? Give the reason for your answer.

Question 9 Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

The sum of the terms of an infinite G.P whose first term is 6 and common ratio is 1/3 is ___.

Which of the following are the factors of x2+3x+2 ?

Factorise the following using appropriate identities: [4 MARKS] 1)9x2+6xy+y2 2)4y2−4y+1

A shopkeeper buys a number of books for ₹ 80. If he had bought 4 more books for the same amount, each book would have cost ₹ 1 less. He bought ___ books.

Question 3 (iii) For the following A.Ps, write the first term and the common difference. (iii) 13,53,93,133……

Question 4 How many terms of the AP 9, 17, 25 … must be taken to give a sum of 636?

On simplifying the expression √45−3√20+3√5 we get ___.

If xg+1xa is a polynomial, what could be the value of a?

The formula to find out the nth term of an AP is

Solve the pair of equations using the method of substitution 3x-y = 8 ,5x+y = 0 [2 MARKS]

Form the polynomial whose zeroes are 6+√33,6−√33

If x=23 is a solution of the quadratic equation 7x2+mx−3=0, find the value of m.

In Fig. 7.35, state if PQ || EF.

If the diagonals of a rhombus are 24 cm and 10 cm, then its perimeter =__________________cm

The owner of a milk store finds that he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs.17 / litre?

Condition for ax2 + bx + c = 0 to be a quadratic equation is

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8.

The given diagram shows two isosceles triangles which are similar also. In the given diagram, PQ and BC are not parallel and AP = PQ. Given that PC =4 cm, AQ=3 cm, QB =12 cm, BC =15 cm. Calculate the length of AP.

1/3y+ y + 1/3x-y=3/4 1/2(3x+y)-1/2(3x-y)=-1/8 Solve for x and y

A quadratic equation whose roots are 2+1√2 and 2−1√2 is:

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

What are the inferences that you can get from the given figure?

A two digit number is 3 more than 4 times the sum of the digit. If 18 is added to the number the digits are reversed. Find the number.

Find the integral value of x such that 3x+1x+1+x+13x+1=52

If (3x + 5y)/(3x – 5y) = 7/3, find x:y.

Rohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class?

Question 2 In figure, if ∠AOB=125∘. Then ∠ COD is equal to (A) 62.5° (B) 45° (C) 35° (D) 55°

Which of the following option does not belong to the construction of a circumcircle?

Prove the ideintity: sec θ+1+tan θsec θ+1−tan θ=1+sin θcos θ [4 MARKS]

Describe the locus for questions 1 to 13 given below: The locus of the door-handle, as the door opens.

Shyam is on top of a building of 80m height waving at his friend Ram who is 60m away from the building. what is the direct distance between Ram and Shyam?

The slope of a line passing through points (1,2) and (10,20) is ___.

If a, b, c are pth, qth, and mth terms of a G.P., then (cb)p(ba)m(ac)q is equal to

A weather station recorded the temperatures of a place over a period of 7 days as follows: Day Temperature (in ∘C ) Monday 45 Tuesday 38 Wednesday 40 Thursday 42 Friday 41 Saturday 37 Sunday 36 Find the probability of a day having a temperature of more than 40 ∘ C.

For what values of p are the roots of the equations 4x2+px+3=0 real and equal?

The cumulative frequency table is useful in determining the (a) mean (b) median (c) mode (d) all of these

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

The slope of the line 5x+6y+3=0 is

A box contains 20 tickets which are numbered from 1 to 20. If one card is drawn at random from the box, find the probability that the drawn card bears a perfect square number.

If A(-4 , 3) & B(8 , -6) have respective coordinates a) find the length of AB, b) the ratio in which the – axis divides AB.