32581 + Interview Questions in Mathematics

1.	A line passing through origin can be represented by an equation
Answer» A line passing through origin can be represented by an equation

Discussion

2.	Two ships are on either side of a 100 m lighthouse. The angles of elevation from the two ships to the top of the lighthouse are 30° and 45°. Find the distance between the ships.
Answer» Two ships are on either side of a 100 m lighthouse. The angles of elevation from the two ships to the top of the lighthouse are 30° and 45°. Find the distance between the ships.

Discussion

3.	A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre. [Use π = 22/7] [CBSE 2014]
Answer» A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre. [Use π = 22/7] [CBSE 2014]

Discussion

4.	A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of Rs.10 per 100 sq.cm. [4 MARKS]
Answer» A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of Rs.10 per 100 sq.cm. [4 MARKS]

Discussion

5.	Solve each of the following quadratic equations:x2+22x-6=0
Answer» Solve each of the following quadratic equations: $x^{2} + 2 \sqrt{2} x - 6 = 0$

Discussion

6.	Very-Short-Answer QuestionsIf the roots of the quadratic equation pxx-2+6=0 are equal, find the value of p. [CBSE 2013]
Answer» Very-Short-Answer Questions If the roots of the quadratic equation $p x (x - 2) + 6 = 0$ are equal, find the value of p. [CBSE 2013]

Discussion

7.	In a △ ABC, AB = AC and AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Then about which of the following is the triangle symmetrical?
Answer» In a $△$ ABC, AB = AC and AD $⊥$ BC, BE $⊥$ AC and CF $⊥$ AB. Then about which of the following is the triangle symmetrical?

Discussion

8.	Number of solutions for the line 4x-Ay = 0 where HCF(A,4) = 1 and 0
Answer» Number of solutions for the line 4x-Ay = 0 where HCF(A,4) = 1 and 0

Discussion

9.	If a and b are real and a ≠ b then show that the roots of the equation a-bx2+5a+bx-2a-b=0 are real and unequal.
Answer» If a and b are real and a ≠ b then show that the roots of the equation $(a - b) x^{2} + 5 (a + b) x - 2 (a - b) = 0$ are real and unequal.

Discussion

10.	A path of 4 m width runs round a semi-circular grassy plot whose circumference is 163 37 m Find:(i) the area of the path(ii) the cost of gravelling the path at the rate of Rs 1.50 per square metre(iii) the cost of turfing the plot at the rate of 45 paise per m2.
Answer» A path of 4 m width runs round a semi-circular grassy plot whose circumference is 163 $\frac{3}{7}$ m Find: (i) the area of the path (ii) the cost of gravelling the path at the rate of Rs 1.50 per square metre (iii) the cost of turfing the plot at the rate of 45 paise per m².

Discussion

11.	14. Explain about Vanderwaal Radius.
Answer» 14. Explain about Vanderwaal Radius.

Discussion

12.	Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that
Answer» Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that

Discussion

13.	The product of two consecutive positive integer is 306. Find the interger
Answer» The product of two consecutive positive integer is 306. Find the interger

Discussion

14.	The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?
Answer» The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?

Discussion

15.	Solve each of the following quadratic equations:2x2+x-6=0
Answer» Solve each of the following quadratic equations: $2 x^{2} + x - 6 = 0$

Discussion

16.	If m. times the. mth. term of an AP is equal to nth term and m is not equal to. n , show that it's. ( m+n)th term is zero.
Answer» If m. times the. mth. term of an AP is equal to nth term and m is not equal to. n , show that it's. ( m+n)th term is zero.

Discussion

17.	If the product of two numbers is 1080 and their HCF is 30, find their LCM.
Answer» If the product of two numbers is 1080 and their HCF is 30, find their LCM.

Discussion

18.	In the following figure (i) and (ii), DE \|\| BC. Find EC in (i) and AD in (ii).
Answer» In the following figure (i) and (ii), DE \|\| BC. Find EC in (i) and AD in (ii).

Discussion

19.	Paul Rogers, an employee of the Prince Xavier Corporation, has received his salary slip. Use the information in the slip to calculate the new salary credited to his bank account.
Answer» Paul Rogers, an employee of the Prince Xavier Corporation, has received his salary slip. Use the information in the slip to calculate the new salary credited to his bank account.

Discussion

20.	With reference to the following figure, the dimension of the side GI is inches.
Answer» With reference to the following figure, the dimension of the side $G I$ is inches.

Discussion

21.	In Euclid's division Lemma and algorithm. Why finding HCF of 3 numbers if the HCF with the third number comes different then what should be done.
Answer» In Euclid's division Lemma and algorithm. Why finding HCF of 3 numbers if the HCF with the third number comes different then what should be done.

Discussion

22.	The sum of four consecutive terms which are in an arithmetic progression is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15 . Find the number .
Answer» The sum of four consecutive terms which are in an arithmetic progression is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15 . Find the number .

Discussion

23.	For a triangle ABC, which of the following is true ?
Answer» For a triangle ABC, which of the following is true ?

Discussion

24.	The H.C.F and L.C.M. of the two expression are (m − 3) and (m3 + m2 − 17m + 15) respectively. Find the expressions.
Answer» The H.C.F and L.C.M. of the two expression are (m − 3) and (m³ + m² − 17m + 15) respectively. Find the expressions.

Discussion

25.	A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. If AB = 60 m and BC = 28 m, find the area of the plot.
Answer» A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. If AB = 60 m and BC = 28 m, find the area of the plot.

25.

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. If AB = 60 m and BC = 28 m, find the area of the plot.

Answer»

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. If AB = 60 m and BC = 28 m, find the area of the plot.

Discussion

26.	a invested Rs.76000 in a business. After few months, B joined him with Rs.57000 At the end of the year the total profit was divided between them in the ratio 2 : 1. After how many months did B join (1) 4 month (2) 6 month (3) 8 month (4) 3 month
Answer» a invested Rs.76000 in a business. After few months, B joined him with Rs.57000 At the end of the year the total profit was divided between them in the ratio 2 : 1. After how many months did B join (1) 4 month (2) 6 month (3) 8 month (4) 3 month

26.

a invested Rs.76000 in a business. After few months, B joined him with Rs.57000 At the end of the year the total profit was divided between them in the ratio 2 : 1. After how many months did B join (1) 4 month (2) 6 month (3) 8 month (4) 3 month

Answer»

a invested Rs.76000 in a business. After few months, B joined him with Rs.57000 At the end of the year the total profit was divided between them in the ratio 2 : 1. After how many months did B join

(1) 4 month

(2) 6 month

(3) 8 month

(4) 3 month

Discussion

27.	For what integer value/s of s, the quadratic equation (s+2)x2+1=(s+3)x has co-incident roots.
Answer» For what integer value/s of s, the quadratic equation $(s + 2) x^{2} + 1 = (s + 3) x$ has co-incident roots.

Discussion

28.	A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height. HEIGHT (IN CM)NUMBER OF GIRLSBELOW 1404140−1457145−15018150−15511155−1606160−1655
Answer» A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height. $\begin{matrix} H E I G H T (I N C M) & N U M B E R O F G I R L S B E L O W 140 & 4 140 - 145 & 7 145 - 150 & 18 150 - 155 & 11 155 - 160 & 6 160 - 165 & 5 \end{matrix}$

28.

A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height. HEIGHT (IN CM)NUMBER OF GIRLSBELOW 1404140−1457145−15018150−15511155−1606160−1655

Answer»

A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height.

$\begin{matrix} H E I G H T (I N C M) & N U M B E R O F G I R L S B E L O W 140 & 4 140 - 145 & 7 145 - 150 & 18 150 - 155 & 11 155 - 160 & 6 160 - 165 & 5 \end{matrix}$

Discussion

29.	The value of 2+12+12+... is
Answer» The value of $2 + \frac{1}{2 + \frac{1}{2 + . . .}}$ is

Discussion

30.	In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 14 cm, BC = 8 cm and AC = 12 cm. Find the lengths of AD, BE and CF [CBSE 2013]
Answer» In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 14 cm, BC = 8 cm and AC = 12 cm. Find the lengths of AD, BE and CF [CBSE 2013]

Discussion

31.	The product of two irrational numbers is a/an
Answer» The product of two irrational numbers is a/an

Discussion

32.	Question 2 (ii)Write whether the given statement is true or false. Justify your answer.Every quadratic equation has at least one real roots.
Answer» Question 2 (ii) Write whether the given statement is true or false. Justify your answer. Every quadratic equation has at least one real roots.

Discussion

33.	Select the statements that are true.
Answer» Select the statements that are true.

Discussion

34.	Solve each of the following equations by using the method of completing the square:2x2+5x-3=0
Answer» Solve each of the following equations by using the method of completing the square: $2 x^{2} + 5 x - 3 = 0$

Discussion

35.	An event with only 1 outcome is called __.
Answer» An event with only 1 outcome is called __.

Discussion

36.	Question 9If √3tan θ=1, find the value of sin2 θ−cos2 θ.
Answer» Question 9 If $\sqrt{3} t a n θ = 1$ , find the value of $s i n^{2} θ - c o s^{2} θ$ .

Discussion

37.	Water is pouring into a reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 cubic metres, find the number of hours it will take to fill the reservoir.
Answer» Water is pouring into a reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 cubic metres, find the number of hours it will take to fill the reservoir.

Discussion

38.

From the following Trial Balance you are required to prepare trading and profit and loss account for the year ending March 31, 2017 and Balance Sheet on that date. Particulars Amount (₹) Particulars Amount (₹) Opening stock 25,000 Sales 7,00,000 Furniture 16,000 Creditors 72,500 Purchases 5,55,300 Bank Overdraft 50,000 Carriage Inwards 4,700 Provision for bad and doubtful debts 2,100 Bad debts 1,800 Discount 500 Wages 52,000 Capital 2,00,000 Debtors 80,000 Purchases Return 20,000 Sales Return 15,000 Rent 24,000 Miscellaneous Expenses 3,400 Salaries 68,000 Cash 8,900 Drawings 14,000 Buildings 1,60,000 Advertising 10,000 Interest on Bank Overdraft 7,000 10,45,100 10,45,100 Adjustments1. Closing stock valued at ₹ 36,000.2. Private purchases amounting to ₹ 5,000 debited to purchases account.3. Provision for doubtful debts 5% on debtors.4. Sign board costing ₹ 4,000 includes in advertising.5. Depreciate furniture by 10%.

Answer» From the following Trial Balance you are required to prepare trading and profit and loss account for the year ending March 31, 2017 and Balance Sheet on that date.

Particulars	Amount (₹)	Particulars	Amount (₹)
Opening stock	25,000	Sales	7,00,000
Furniture	16,000	Creditors	72,500
Purchases	5,55,300	Bank Overdraft	50,000
Carriage Inwards	4,700	Provision for bad and doubtful debts	2,100
Bad debts	1,800	Discount	500
Wages	52,000	Capital	2,00,000
Debtors	80,000	Purchases Return	20,000
Sales Return	15,000
Rent	24,000
Miscellaneous Expenses	3,400
Salaries	68,000
Cash	8,900
Drawings	14,000
Buildings	1,60,000
Advertising	10,000
Interest on Bank Overdraft	7,000

	10,45,100		10,45,100

Adjustments

1. Closing stock valued at ₹ 36,000.

2. Private purchases amounting to ₹ 5,000 debited to purchases account.

3. Provision for doubtful debts 5% on debtors.

4. Sign board costing ₹ 4,000 includes in advertising.

5. Depreciate furniture by 10%.

Discussion

39.	24. AB and CD are common tangents of circles with unequal radii. Prove that AB=CD.
Answer» 24. AB and CD are common tangents of circles with unequal radii. Prove that AB=CD.

Discussion

40.	Question 3 (iii)In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that(iii)AD2=BD×CD
Answer» Question 3 (iii) In the given figure, ABD is a triangle right angled at A and $A C ⊥ B D$ . Show that $(i i i) A D^{2} = B D \times C D$

Discussion

41.	How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
Answer» How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?

Discussion

42.	The slope of the tangent at a point (x,y) on a curve passing through the point (1,π4) is given by yx−cos2(yx), then the value of y(e) is
Answer» The slope of the tangent at a point $(x, y)$ on a curve passing through the point $(1, \frac{π}{4})$ is given by $\frac{y}{x} - {cos}^{2} (\frac{y}{x}),$ then the value of $y (e)$ is

Discussion

43.	If A and B invest some amount for the same time and after one year share their profit in the ratio of 3: 4 respectively. If the total investment is Rs. 7000, what is the investment of A?
Answer» If A and B invest some amount for the same time and after one year share their profit in the ratio of 3: 4 respectively. If the total investment is Rs. 7000, what is the investment of A?

Discussion

44.	secA -cosecA +secA cosecA/secA+cosecA -secAcosecA =secA +tanA. prove it
Answer» secA -cosecA +secA cosecA/secA+cosecA -secAcosecA =secA +tanA. prove it

Discussion

45.	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

46.	Find the sum of first 100 even natural numbers which are divisible by 5.
Answer» Find the sum of first 100 even natural numbers which are divisible by 5.

Discussion

47.	Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………
Answer» Which of the following sequences are APs? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

47.

Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Answer»

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

Discussion

48.	Find the roots of each of the following equations, if they exist, by applying the quadratic formula:3x2-2x+2=0
Answer» Find the roots of each of the following equations, if they exist, by applying the quadratic formula: $3 x^{2} - 2 x + 2 = 0$

Discussion

49.	Simran and Reema are partners sharing profits in the ratio of 3 : 2. Their capitals as on 31st March, 2018 were ₹ 2,00,000 each whereas Current Accounts had balances of ₹ 50,000 and ₹ 25,000 respectively interest is to be allowed 5% p.a. on balances in Capital Accounts. The firm earned net profit of ₹ 3,00,000 for the year ended 31st March 2019.Pass the Journal entries for interest on capital and distribution of profit. Also prepare Profit and Loss Appropriation Account for the year.
Answer» Simran and Reema are partners sharing profits in the ratio of 3 : 2. Their capitals as on 31st March, 2018 were ₹ 2,00,000 each whereas Current Accounts had balances of ₹ 50,000 and ₹ 25,000 respectively interest is to be allowed 5% p.a. on balances in Capital Accounts. The firm earned net profit of ₹ 3,00,000 for the year ended 31st March 2019. Pass the Journal entries for interest on capital and distribution of profit. Also prepare Profit and Loss Appropriation Account for the year.

Discussion

50.

The area of a sector of angle θ∘ of a circle with radius R is (a) 2πRθ180 (b) πR2θ180 (c) 2πRθ360 (d) πR2θ360

Answer»

The area of a sector of angle $θ^{\circ}$ of a circle with radius $R$ is

(a) $\frac{2 π R θ}{180}$

(b) $\frac{π R^{2} θ}{180}$

(c) $\frac{2 π R θ}{360}$

(d) $\frac{π R^{2} θ}{360}$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A line passing through origin can be represented by an equation

Two ships are on either side of a 100 m lighthouse. The angles of elevation from the two ships to the top of the lighthouse are 30° and 45°. Find the distance between the ships.

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre. [Use π = 22/7] [CBSE 2014]

A hemispherical bowl made of brass has inner radius of 3.5 cm. Find the cost of tin-plating the inner part of the bowl as well as tin plating a plate that exactly fits as a lid on bowl. Tin plating is done at the rate of Rs.10 per 100 sq.cm. [4 MARKS]

Solve each of the following quadratic equations:x2+22x-6=0

Very-Short-Answer QuestionsIf the roots of the quadratic equation pxx-2+6=0 are equal, find the value of p. [CBSE 2013]

In a △ ABC, AB = AC and AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Then about which of the following is the triangle symmetrical?

Number of solutions for the line 4x-Ay = 0 where HCF(A,4) = 1 and 0

If a and b are real and a ≠ b then show that the roots of the equation a-bx2+5a+bx-2a-b=0 are real and unequal.

A path of 4 m width runs round a semi-circular grassy plot whose circumference is 163 37 m Find:(i) the area of the path(ii) the cost of gravelling the path at the rate of Rs 1.50 per square metre(iii) the cost of turfing the plot at the rate of 45 paise per m2.

14. Explain about Vanderwaal Radius.

Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that

The product of two consecutive positive integer is 306. Find the interger

The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?

Solve each of the following quadratic equations:2x2+x-6=0

If m. times the. mth. term of an AP is equal to nth term and m is not equal to. n , show that it's. ( m+n)th term is zero.

If the product of two numbers is 1080 and their HCF is 30, find their LCM.

In the following figure (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

Paul Rogers, an employee of the Prince Xavier Corporation, has received his salary slip. Use the information in the slip to calculate the new salary credited to his bank account.

With reference to the following figure, the dimension of the side GI is inches.

In Euclid's division Lemma and algorithm. Why finding HCF of 3 numbers if the HCF with the third number comes different then what should be done.

The sum of four consecutive terms which are in an arithmetic progression is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15 . Find the number .

For a triangle ABC, which of the following is true ?

The H.C.F and L.C.M. of the two expression are (m − 3) and (m3 + m2 − 17m + 15) respectively. Find the expressions.

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig. If AB = 60 m and BC = 28 m, find the area of the plot.

a invested Rs.76000 in a business. After few months, B joined him with Rs.57000 At the end of the year the total profit was divided between them in the ratio 2 : 1. After how many months did B join (1) 4 month (2) 6 month (3) 8 month (4) 3 month

For what integer value/s of s, the quadratic equation (s+2)x2+1=(s+3)x has co-incident roots.

A survey of heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height. HEIGHT (IN CM)NUMBER OF GIRLSBELOW 1404140−1457145−15018150−15511155−1606160−1655

The value of 2+12+12+... is

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 14 cm, BC = 8 cm and AC = 12 cm. Find the lengths of AD, BE and CF [CBSE 2013]

The product of two irrational numbers is a/an

Question 2 (ii)Write whether the given statement is true or false. Justify your answer.Every quadratic equation has at least one real roots.

Select the statements that are true.

Solve each of the following equations by using the method of completing the square:2x2+5x-3=0

An event with only 1 outcome is called __.

Question 9If √3tan θ=1, find the value of sin2 θ−cos2 θ.

Water is pouring into a reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 cubic metres, find the number of hours it will take to fill the reservoir.

24. AB and CD are common tangents of circles with unequal radii. Prove that AB=CD.

Question 3 (iii)In the given figure, ABD is a triangle right angled at A and AC⊥BD. Show that(iii)AD2=BD×CD

How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?

The slope of the tangent at a point (x,y) on a curve passing through the point (1,π4) is given by yx−cos2(yx), then the value of y(e) is

If A and B invest some amount for the same time and after one year share their profit in the ratio of 3: 4 respectively. If the total investment is Rs. 7000, what is the investment of A?

secA -cosecA +secA cosecA/secA+cosecA -secAcosecA =secA +tanA. prove it

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

Find the sum of first 100 even natural numbers which are divisible by 5.

Which of the following sequences are APs?(i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11…….. (iii) -1, -1.25, -1.5, -1.75……. (iv) 1, -1, -3, -5, -7…………

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:3x2-2x+2=0

The area of a sector of angle θ∘ of a circle with radius R is (a) 2πRθ180 (b) πR2θ180 (c) 2πRθ360 (d) πR2θ360