32581 + Interview Questions in Mathematics

1.	If the sum and the product of zeros of a quadratic polynomial kx2−(k+1)x+(t−1) are 5 and 6 respectively, find the value of k × t.
Answer» If the sum and the product of zeros of a quadratic polynomial $k x^{2} - (k + 1) x + (t - 1)$ are 5 and 6 respectively, find the value of k $\times$ t.

Discussion

2.	A chord in a circle of radius 15 cm subtends an angle of 60∘ at the centre. Find the areas in cm2 of the corresponding minor and major segments of the circle.(Use π = 3.14 and √3 = 1.73)
Answer» A chord in a circle of radius 15 cm subtends an angle of 60 $^{\circ}$ at the centre. Find the areas in $c m^{2}$ of the corresponding minor and major segments of the circle.(Use $π$ = 3.14 and $\sqrt{3}$ = 1.73)

Discussion

3.	The ladder resting against a vertical wall is inclined at an angle of 30∘ to the ground. The foot of the ladder is 9 m away from the wall. Find the length of the ladder.
Answer» The ladder resting against a vertical wall is inclined at an angle of 30 $^{\circ}$ to the ground. The foot of the ladder is 9 m away from the wall. Find the length of the ladder.

Discussion

4.	Which of the following satisfies the equation a2b2x2−b2x−a2x+1=0?
Answer» Which of the following satisfies the equation $a^{2} b^{2} x^{2} - b^{2} x - a^{2} x + 1 = 0 ?$

Discussion

5.	From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that ΔAPB is equilateral.
Answer» From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that $Δ A P B$ is equilateral.

Discussion

6.	On certain article if rate of CGST is 9% then what is the rate of SGST? and what is the rate of GST?
Answer» On certain article if rate of CGST is 9% then what is the rate of SGST? and what is the rate of GST?

Discussion

7.	Two numbers are in the ratio 3:5. If 9 is subtracted from each number, the ratio becomes 12:23. The smaller number is:
Answer» Two numbers are in the ratio 3:5. If 9 is subtracted from each number, the ratio becomes 12:23. The smaller number is:

Discussion

8.	A plot of land is in the form of a quadrilateral, where one of its diagonal is 230 m long. The two vertices on either side of this diagonal are at a perpendicular distance of 60 m and 70 m from it. The area of the plot of land is
Answer» A plot of land is in the form of a quadrilateral, where one of its diagonal is 230 m long. The two vertices on either side of this diagonal are at a perpendicular distance of 60 m and 70 m from it. The area of the plot of land is

Discussion

9.	Construct a tangent to a circle of radius 3 cm at any point ‘P’ on it.
Answer» Construct a tangent to a circle of radius 3 cm at any point ‘P’ on it.

Discussion

10.	Solve the following systems of equations graphically: 3x + y + 1 = 0 2x - 3y + 8 = 0
Answer» Solve the following systems of equations graphically: 3x + y + 1 = 0 2x - 3y + 8 = 0

10.

Solve the following systems of equations graphically: 3x + y + 1 = 0 2x - 3y + 8 = 0

Answer»

Solve the following systems of equations graphically:

3x + y + 1 = 0

2x - 3y + 8 = 0

Discussion

11.	Question 39(i)A die has its six faces marked 0,1,1,1,6,6. Two such dice are thrown together and the total score is recorded.How many different scores are possible?
Answer» Question 39(i) A die has its six faces marked 0,1,1,1,6,6. Two such dice are thrown together and the total score is recorded. How many different scores are possible?

Discussion

12.	In the given figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.
Answer» In the given figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.

Discussion

13.	If the p.th, q.th and r.th term of an A.P as well as a G.P (same first term) are a, b and c respectively, then prove that a^(b-c) × b^(c-a) × c^(a-b) = 1
Answer» If the p.th, q.th and r.th term of an A.P as well as a G.P (same first term) are a, b and c respectively, then prove that a^(b-c) × b^(c-a) × c^(a-b) = 1

Discussion

14.	A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After that he counts at the rate of Rs 3 less every minute then the preceding minute. Find the time taken by him to count the entire amount
Answer» A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After that he counts at the rate of Rs 3 less every minute then the preceding minute. Find the time taken by him to count the entire amount

Discussion

15.	Question 7 (iv)In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.
Answer» Question 7 (iv) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.

Discussion

16.	Measures of some angles in the figure are given. Prove that APPB=AQQC
Answer» Measures of some angles in the figure are given. Prove that $\frac{AP}{PB} = \frac{AQ}{QC}$

Discussion

17.	Identify the region which represents the probability of event B not happening.
Answer» Identify the region which represents the probability of event B not happening.

Discussion

18.	If \|x\|, \|x-1\|, \|x+1\| are the first three terms of an AP and d is the common difference between them, T(r) is the rth term then, A)T(5)= 9/4B) d=0.5C) d=0.25D) T(10)= 19/4
Answer» If \|x\|, \|x-1\|, \|x+1\| are the first three terms of an AP and d is the common difference between them, T(r) is the rth term then, A)T(5)= 9/4 B) d=0.5 C) d=0.25 D) T(10)= 19/4

Discussion

19.	In the above figure O is the centre of the circle ∠AOB = 80∘ ,then complete the matching. AngleValue1. ACB a. 90∘2. ADBb. 40∘3. ABCc. 80∘4. AOCd. 180∘
Answer» In the above figure O is the centre of the circle $∠$ AOB = $80^{\circ}$ ^,then complete the matching. $\begin{matrix} A n g l e & V a l u e 1. A C B & a . 90^{\circ} 2. A D B & b . 40^{\circ} 3. A B C & c . 80^{\circ} 4. A O C & d . 180^{\circ} \end{matrix}$

19.

In the above figure O is the centre of the circle ∠AOB = 80∘ ,then complete the matching. AngleValue1. ACB a. 90∘2. ADBb. 40∘3. ABCc. 80∘4. AOCd. 180∘

Answer»

In the above figure O is the centre of the circle $∠$ AOB = $80^{\circ}$ ^,then complete the matching.
$\begin{matrix} A n g l e & V a l u e 1. A C B & a . 90^{\circ} 2. A D B & b . 40^{\circ} 3. A B C & c . 80^{\circ} 4. A O C & d . 180^{\circ} \end{matrix}$

Discussion

20.	41. If the nth term of an AP is (2n + 1) ,then what is the sum of the first three terms ?
Answer» 41. If the nth term of an AP is (2n + 1) ,then what is the sum of the first three terms ?

Discussion

21.	There is a retangular metal plate. I make a dent on the middle of the plate with a hammer to produce a conical depression. The top side of the metal is polished. What is the area of the metal polished?
Answer» There is a retangular metal plate. I make a dent on the middle of the plate with a hammer to produce a conical depression. The top side of the metal is polished. What is the area of the metal polished?

Discussion

22.	Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y = −5
Answer» Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y = −5

Discussion

23.	20. Why cos (-theta)is equal to cos( theta)
Answer» 20. Why cos (-theta)is equal to cos( theta)

Discussion

24.	In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of ∠BAC.
Answer» In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $∠$ BAC.

24.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of ∠BAC.

Answer»

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $∠$ BAC.

Discussion

25.	3\|x\| +5\|x\|=8 ,7\|x\| - 3\|y\|=48 then find x+y
Answer» 3\|x\| +5\|x\|=8 ,7\|x\| - 3\|y\|=48 then find x+y

Discussion

26.	(cotA-cosecA)(cotA-cosecA) =1-cosA/1+cosA
Answer» (cotA-cosecA)(cotA-cosecA) =1-cosA/1+cosA

Discussion

27.	Question 8 (ii)Justify whether it is true to say that the following are the nth terms of an AP.3n2+5
Answer» Question 8 (ii) Justify whether it is true to say that the following are the nth terms of an AP. $3 n^{2} + 5$

Discussion

28.	For the month of February, a class teacher of Class IX has the following absentee record for 45 students. Find the mean number of days, a student was absent. Number of days of absent0−44−88−1212−1616−2020−24Number of students1836201
Answer» For the month of February, a class teacher of Class IX has the following absentee record for 45 students. Find the mean number of days, a student was absent. $\begin{matrix} Number of days of absent & 0 - 4 & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 & 20 - 24 Number of students & 18 & 3 & 6 & 2 & 0 & 1 \end{matrix}$

Discussion

29.	X^-5x-7=0 is a quadratic equations
Answer» X^-5x-7=0 is a quadratic equations

Discussion

30.	If the sum of first n terms of an A.P. is 12(3n2+7n), then find its nth term. Hence write its 20th term.
Answer» If the sum of first n terms of an A.P. is $\frac{1}{2} (3 n^{2} + 7 n)$ , then find its nth term. Hence write its 20th term.

Discussion

31.	34. What's the difference between lateral surface area and total surface area?
Answer» 34. What's the difference between lateral surface area and total surface area?

Discussion

32.	There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.
Answer» There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.

Discussion

33.	A closed rectangular box 42 cm long, 33 cm wide & 25 cm deep has the same volume as that of a cylindrical tin of radius 17.5 cm. Calculate the height of the cylindrical tin.
Answer» A closed rectangular box 42 cm long, 33 cm wide & 25 cm deep has the same volume as that of a cylindrical tin of radius 17.5 cm. Calculate the height of the cylindrical tin.

Discussion

34.	What is the difference between remainder theorm and factor theorm ??
Answer» What is the difference between remainder theorm and factor theorm ??

Discussion

35.	Loans which have to be paid after certain fixed time periods and whose interest payments are to be made regularly till the loans are finally paid off are called
Answer» Loans which have to be paid after certain fixed time periods and whose interest payments are to be made regularly till the loans are finally paid off are called

Discussion

36.	Very-Short and Short-Answer QuestionsIf 18, a, (b − 3) are in AP, then find the value of (2a − b). [CBSE 2014]
Answer» Very-Short and Short-Answer Questions If 18, a, (b − 3) are in AP, then find the value of (2a − b). [CBSE 2014]

Discussion

37.	The sum of 'r' terms of an AP is 2r2+3r. The nth term of the AP is :
Answer» The sum of 'r' terms of an AP is $2 r^{2} + 3 r$ . The $n^{t h}$ term of the AP is :

Discussion

38.	The area of the bounded by the parabola y2 = 4ax and its latusrectum is ____________.
Answer» The area of the bounded by the parabola y² = 4ax and its latusrectum is ____________.

Discussion

39.	In a right angled triangle, with respect to an acute angle θ, the opposite side is twice the adjacent side. Find the value of cosecθ.
Answer» In a right angled triangle, with respect to an acute angle $θ$ , the opposite side is twice the adjacent side. Find the value of cosec $θ$ .

Discussion

40.	Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [π=3.14] [4 MARKS]
Answer» Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [ $π = 3.14$ ] [4 MARKS]

40.

Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [π=3.14] [4 MARKS]

Answer»

Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [ $π = 3.14$ ] [4 MARKS]

Discussion

41.	A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?
Answer» A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

Discussion

42.	Given that p,p 1 and 2p+1 are prime numbers, find the sum of all possible values of p.
Answer» Given that p,p 1 and 2p+1 are prime numbers, find the sum of all possible values of p.

Discussion

43.	What will be the antilog of 3.8420+0.1656
Answer» What will be the antilog of 3.8420+0.1656

Discussion

44.

Following balances are taken from the books of Mr. Niranjan. You are required to prepare Trading and Profit and Loss Account and Balance Sheet for the year ended 31st March, 2018: Particulars ₹ Particulars ₹ Capital 1,20,000 Drawings 21,000 Opening Stock 45,000 Plant and Machinery 24,000 Furniture 1,500 Purchases 2,95,000 Sales 4,35,000 Insurances 1,500 Purchases Return 4,000 Sales Return 7,000 Rent 5,000 Trade Expenses 2,000 Salaries 24,000 Wages 40,000 Bad Debts 1,000 6% Investments 50,000 Sundry Debtors 40,000 Sundry Creditors 19,000 Bills Payable 800 Cash 12,200 Advertisement Expenses 6,000 Miscellaneous Receipts 1,200 Patents 4,800 Adjustments:(i) Closing Stock ₹ 75,000.(ii) Depreciate Machinery by 10% and Furniture by 20%.(iii) Wages ₹ 5,000 and salaries ₹ 2,000 are outstanding.(iv) Write off ₹ 5,000 as further Bad Debts and create 5% Provision for Doubtful Debts.(v) Investments were made on 1st July, 2017 and no interest has been received so far.

Answer» Following balances are taken from the books of Mr. Niranjan. You are required to prepare Trading and Profit and Loss Account and Balance Sheet for the year ended 31st March, 2018:

Particulars	₹	Particulars	₹
Capital	1,20,000	Drawings	21,000
Opening Stock	45,000	Plant and Machinery	24,000
Furniture	1,500	Purchases	2,95,000
Sales	4,35,000	Insurances	1,500
Purchases Return	4,000	Sales Return	7,000
Rent	5,000	Trade Expenses	2,000
Salaries	24,000	Wages	40,000
Bad Debts	1,000	6% Investments	50,000
Sundry Debtors	40,000	Sundry Creditors	19,000
Bills Payable	800	Cash	12,200
Advertisement Expenses	6,000	Miscellaneous Receipts	1,200
Patents	4,800

Adjustments:

(i) Closing Stock ₹ 75,000.

(ii) Depreciate Machinery by 10% and Furniture by 20%.

(iii) Wages ₹ 5,000 and salaries ₹ 2,000 are outstanding.

(iv) Write off ₹ 5,000 as further Bad Debts and create 5% Provision for Doubtful Debts.

(v) Investments were made on 1st July, 2017 and no interest has been received so far.

Discussion

45.	In fig., DE ∥ AC and DC ∥ AP. Prove that BEBC = BCCP.
Answer» In fig., DE $∥$ AC and DC $∥$ AP. Prove that $\frac{B E}{B C}$ = $\frac{B C}{C P}$ .

45.

In fig., DE ∥ AC and DC ∥ AP. Prove that BEBC = BCCP.

Answer»

In fig., DE $∥$ AC and DC $∥$ AP. Prove that $\frac{B E}{B C}$ = $\frac{B C}{C P}$ .

Discussion

46.	The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Answer» The sum of first n terms of an A.P. is 3n² + 4n. Find the 25th term of this A.P.

Discussion

47.	A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears(1) an odd number(2) a complete square number.
Answer» A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears (1) an odd number (2) a complete square number.

Discussion

48.	The distance between the origin and point (6,0) is ___ units.
Answer» The distance between the origin and point (6,0) is ___ units.

Discussion

49.	O is the centre of the circle. If ∠BOA=90∘ and ∠COA=110∘, find ∠BAC.
Answer» O is the centre of the circle. If $∠ B O A = 90^{\circ}$ and $∠ C O A = 110^{\circ}$ , find $∠ B A C$ .

Discussion

50.	Determine the A.P. whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
Answer» Determine the A.P. whose $3^{r d}$ term is 16 and $7^{t h}$ term exceeds the $5^{t h}$ term by 12.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the sum and the product of zeros of a quadratic polynomial kx2−(k+1)x+(t−1) are 5 and 6 respectively, find the value of k × t.

A chord in a circle of radius 15 cm subtends an angle of 60∘ at the centre. Find the areas in cm2 of the corresponding minor and major segments of the circle.(Use π = 3.14 and √3 = 1.73)

The ladder resting against a vertical wall is inclined at an angle of 30∘ to the ground. The foot of the ladder is 9 m away from the wall. Find the length of the ladder.

Which of the following satisfies the equation a2b2x2−b2x−a2x+1=0?

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that ΔAPB is equilateral.

On certain article if rate of CGST is 9% then what is the rate of SGST? and what is the rate of GST?

Two numbers are in the ratio 3:5. If 9 is subtracted from each number, the ratio becomes 12:23. The smaller number is:

A plot of land is in the form of a quadrilateral, where one of its diagonal is 230 m long. The two vertices on either side of this diagonal are at a perpendicular distance of 60 m and 70 m from it. The area of the plot of land is

Construct a tangent to a circle of radius 3 cm at any point ‘P’ on it.

Solve the following systems of equations graphically: 3x + y + 1 = 0 2x - 3y + 8 = 0

Question 39(i)A die has its six faces marked 0,1,1,1,6,6. Two such dice are thrown together and the total score is recorded.How many different scores are possible?

In the given figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.

If the p.th, q.th and r.th term of an A.P as well as a G.P (same first term) are a, b and c respectively, then prove that a^(b-c) × b^(c-a) × c^(a-b) = 1

A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After that he counts at the rate of Rs 3 less every minute then the preceding minute. Find the time taken by him to count the entire amount

Question 7 (iv)In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The number of bacteria in a certain food item after each second, when they double in every second.

Measures of some angles in the figure are given. Prove that APPB=AQQC

Identify the region which represents the probability of event B not happening.

If |x|, |x-1|, |x+1| are the first three terms of an AP and d is the common difference between them, T(r) is the rth term then, A)T(5)= 9/4B) d=0.5C) d=0.25D) T(10)= 19/4

In the above figure O is the centre of the circle ∠AOB = 80∘ ,then complete the matching. AngleValue1. ACB a. 90∘2. ADBb. 40∘3. ABCc. 80∘4. AOCd. 180∘

41. If the nth term of an AP is (2n + 1) ,then what is the sum of the first three terms ?

There is a retangular metal plate. I make a dent on the middle of the plate with a hammer to produce a conical depression. The top side of the metal is polished. What is the area of the metal polished?

Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y = −5

20. Why cos (-theta)is equal to cos( theta)

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of ∠BAC.

3|x| +5|x|=8 ,7|x| - 3|y|=48 then find x+y

(cotA-cosecA)(cotA-cosecA) =1-cosA/1+cosA

Question 8 (ii)Justify whether it is true to say that the following are the nth terms of an AP.3n2+5

For the month of February, a class teacher of Class IX has the following absentee record for 45 students. Find the mean number of days, a student was absent. Number of days of absent0−44−88−1212−1616−2020−24Number of students1836201

X^-5x-7=0 is a quadratic equations

If the sum of first n terms of an A.P. is 12(3n2+7n), then find its nth term. Hence write its 20th term.

34. What's the difference between lateral surface area and total surface area?

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square, (ii) is a prime number greater than 80.

A closed rectangular box 42 cm long, 33 cm wide &amp; 25 cm deep has the same volume as that of a cylindrical tin of radius 17.5 cm. Calculate the height of the cylindrical tin.

What is the difference between remainder theorm and factor theorm ??

Loans which have to be paid after certain fixed time periods and whose interest payments are to be made regularly till the loans are finally paid off are called

Very-Short and Short-Answer QuestionsIf 18, a, (b − 3) are in AP, then find the value of (2a − b). [CBSE 2014]

The sum of 'r' terms of an AP is 2r2+3r. The nth​ term of the AP is :

​The area of the bounded by the parabola y2 = 4ax and its latusrectum is ____________.

In a right angled triangle, with respect to an acute angle θ, the opposite side is twice the adjacent side. Find the value of cosecθ.

Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [π=3.14] [4 MARKS]

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

Given that p,p 1 and 2p+1 are prime numbers, find the sum of all possible values of p.

What will be the antilog of 3.8420+0.1656

In fig., DE ∥ AC and DC ∥ AP. Prove that BEBC = BCCP.

The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.

A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears(1) an odd number(2) a complete square number.

The distance between the origin and point (6,0) is ___ units.

O is the centre of the circle. If ∠BOA=90∘ and ∠COA=110∘, find ∠BAC.

Determine the A.P. whose 3rd term is 16 and 7th term exceeds the 5th term by 12.

A closed rectangular box 42 cm long, 33 cm wide & 25 cm deep has the same volume as that of a cylindrical tin of radius 17.5 cm. Calculate the height of the cylindrical tin.

The sum of 'r' terms of an AP is 2r2+3r. The nth term of the AP is :

The area of the bounded by the parabola y2 = 4ax and its latusrectum is ____________.