32581 + Interview Questions in Mathematics

1.	The first term of an arithmetic sequence is 5 and the common difference is 2. Find the sum of its first 25 terms.
Answer» The first term of an arithmetic sequence is 5 and the common difference is 2. Find the sum of its first 25 terms.

Discussion

2.	A tent is in the form of a cylinder of diameter 15 m and height 2.4 m, surmounted by a cone of equal base and height 4 m. Find the capacity of the tent and the cost of the canvas at Rs. 50 per square meter.
Answer» A tent is in the form of a cylinder of diameter 15 m and height 2.4 m, surmounted by a cone of equal base and height 4 m. Find the capacity of the tent and the cost of the canvas at Rs. 50 per square meter.

Discussion

3.	A fraction becomes 911, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction. [3 MARKS]
Answer» A fraction becomes $\frac{9}{11}$ , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$ . Find the fraction. [3 MARKS]

Discussion

4.	In what ratio does y-axis divide the line segment joining the points (−4, 7) and (3, −7)? [CBSE 2012]
Answer» In what ratio does y-axis divide the line segment joining the points (−4, 7) and (3, −7)? [CBSE 2012]

Discussion

5.	A chord divides a circle into ___.
Answer» A chord divides a circle into ___.

Discussion

6.	Cos a + cos b - cos ( a+ b) = 1.5 then which of the following is true ? 1] , a+ b = 0 2], a= 2b 3], a= b 4], 2a= b
Answer» Cos a + cos b - cos ( a+ b) = 1.5 then which of the following is true ? 1] , a+ b = 0 2], a= 2b 3], a= b 4], 2a= b

Discussion

7.	If A=[3−24−2] and I=[1001], find k so that A2=kA−2I
Answer» If $A = [\begin{matrix} 3 & - 2 4 & - 2 \end{matrix}]$ and $I = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}],$ find $k$ so that $A^{2} = k A - 2 I$

Discussion

8.	Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC=60o. Then construct a triangle whose sides are 34 of the corresponding sides of the ΔABC.
Answer» Draw a triangle ABC with BC = 6 cm, AB = 5 cm and $∠ A B C = 60^{o}$ . Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the $Δ A B C$ .

Discussion

9.	If x (0,/2) prove that sin(cosx) < cos (sinx)
Answer» If x (0,/2) prove that sin(cosx) < cos (sinx)

Discussion

10.

Following Trial Balance has been extracted from the books of M/s. Ram Prasad & Sons on 31st March, 2018: Particulars Dr. ₹ Particulars Cr. ₹ Machinery 4,00,000 Capital 9,00,000 Cash at Bank 1,00,000 Sales 16,00,000 Cash in Hand 50,000 Sundry Creditors 4,50,000 Wages 1,00,000 Interest Received 30,000 Purchases 8,00,000 Stock on 1st April, 2017 6,00,000 Sundry Debtors 4,40,000 Bills Receivable 2,90,000 Rent 45,000 Commission 25,000 General Expenses 80,000 Salaries 50,000 29,80,000 29,80,000 Additional Information:(i) Outstanding salaries were ₹ 45,000.(ii) Depreciate Machinery at 10%.(iii) Wages outstanding were ₹ 5,000.(iv) Rent prepaid ₹ 10,000.(v) Provide for interest on capital 5% per annum.(vi) Stock on 31st March, 2018 ₹ 8,00,000.Prepare Trading and Profit and Loss Account for the year ended 31st March, 2018 and Balance Sheet as at that date.

Answer» Following Trial Balance has been extracted from the books of M/s. Ram Prasad & Sons on 31st March, 2018:

Particulars	Dr. ₹	Particulars	Cr. ₹
Machinery	4,00,000	Capital	9,00,000
Cash at Bank	1,00,000	Sales	16,00,000
Cash in Hand	50,000	Sundry Creditors	4,50,000
Wages	1,00,000	Interest Received	30,000
Purchases	8,00,000
Stock on 1st April, 2017	6,00,000
Sundry Debtors	4,40,000
Bills Receivable	2,90,000
Rent	45,000
Commission	25,000
General Expenses	80,000
Salaries	50,000
	29,80,000		29,80,000

Additional Information:

(i) Outstanding salaries were ₹ 45,000.

(ii) Depreciate Machinery at 10%.

(iii) Wages outstanding were ₹ 5,000.

(iv) Rent prepaid ₹ 10,000.

(v) Provide for interest on capital 5% per annum.

(vi) Stock on 31^st March, 2018 ₹ 8,00,000.

Prepare Trading and Profit and Loss Account for the year ended 31^st March, 2018 and Balance Sheet as at that date.

Discussion

11.	Convert the given class intervals in exclusive form.
Answer» Convert the given class intervals in exclusive form.

Discussion

12.	Find the least number of square tiles of equal dimensions required to pave the floor of a room 4.03 m long and 2.17 m broad.
Answer» Find the least number of square tiles of equal dimensions required to pave the floor of a room 4.03 m long and 2.17 m broad.

Discussion

13.	If (3,7) is a solution of 7x=ky+14, find the value of k.
Answer» If (3,7) is a solution of 7x=ky+14, find the value of k.

Discussion

14.	The area enclosed by the ellipse x2a2+y2b2=1 is equal to (a) π2ab (b) π ab (c) π a2b (d) π ab2
Answer» The area enclosed by the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is equal to $(a) π^{2} ab (b) π ab (c) π a^{2} b (d) π {ab}^{2}$

Discussion

15.	If α, β and are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 +γ^3 isOptions: – 3b+ 3b– 2b+ 2b
Answer» If α, β and are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 +γ^3 is Options: – 3b + 3b – 2b + 2b

Discussion

16.	In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD⊥AC. If DP⊥AB and DQ⊥BC thenprove that(a) DQ2 = DP.QC(b) DP2 = DQ.AP
Answer» In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD⊥AC. If DP⊥AB and DQ⊥BC then prove that (a) DQ² = DP.QC (b) DP² = DQ.AP

Discussion

17.	16. Which of the following is not a quadratic equation? (1) 3x ^ 2 + 4x = 0 (2) - 2x + 5x ^ 2 + 2 = 0 (3) sqrt x + 7 sqrt x =4 sqrt x (x ne0) 1+ 3x=4(x ne0) (4) 3х 3x
Answer» 16. Which of the following is not a quadratic equation? (1) 3x ^ 2 + 4x = 0 (2) - 2x + 5x ^ 2 + 2 = 0 (3) sqrt x + 7 sqrt x =4 sqrt x (x ne0) 1+ 3x=4(x ne0) (4) 3х 3x

Discussion

18.	How many circles can be drawn circumscribing a given triangle?
Answer» How many circles can be drawn circumscribing a given triangle?

Discussion

19.	A lending library has a fixed charge for the first three days and an additional charge for each day thereafter.Mona paid ₹27 for a book kept for 7 days, while Tanvy paid ₹21 for the book she kept for 5 days.Find the fixed charge and the charge for each extra day.
Answer» A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Mona paid ₹27 for a book kept for 7 days, while Tanvy paid ₹21 for the book she kept for 5 days. Find the fixed charge and the charge for each extra day.

Discussion

20.	If tan A=34, then find the value of Sin A + Cos ASin A − Cos A.-7
Answer» If $t a n A = \frac{3}{4}$ , then find the value of $\frac{S i n A + C o s A}{S i n A - C o s A}$ . -7

Discussion

21.	The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is
Answer» The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is

Discussion

22.	The function f(x)=0 has eight distinct real solution and f also satisfy f(4+x)=f(4-x). The sum of all the eight solution of f(x)=0 is?
Answer» The function f(x)=0 has eight distinct real solution and f also satisfy f(4+x)=f(4-x). The sum of all the eight solution of f(x)=0 is?

Discussion

23.	If secβ–cosec9β=0, then the value of sin10β is ?
Answer» If secβ–cosec9β=0, then the value of sin10β is ?

Discussion

24.	Find the roots of the following quadratic equations (if they exist) by the method of completing the square.x2-2+1x+2=0
Answer» Find the roots of the following quadratic equations (if they exist) by the method of completing the square. $x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

Discussion

25.	If m=cosθ-sinθ and n=cosθ+sinθ, then show that mn+nm=21-tan2θ.
Answer» If $m = (\cos θ - \sin θ) and n = (\cos θ + \sin θ)$ , then show that $\sqrt{\frac{m}{n}} + \sqrt{\frac{n}{m}} = \frac{2}{\sqrt{1 - \tan^{2} θ}}$ .

Discussion

26.	One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour(ii) a face card(iii) a red face card(iv) the jack of hearts(v) a spade(vi) the queen of diamonds
Answer» One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting $\begin{matrix} (i) a king of red colour & (ii) a face card (iii) a red face card & (iv) the jack of hearts (v) a spade & (vi) the queen of diamonds \end{matrix}$

Discussion

27.	2 If sinA +sinC +sinB =3 Then find value of cosA +cos C +cosB
Answer» 2 If sinA +sinC +sinB =3 Then find value of cosA +cos C +cosB

Discussion

28.	Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.
Answer» Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.

Discussion

29.	Two tangents making an angle of 120° with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to(a) 3 cm(b) 6 3 cm(c) 2 cm(d) 2 3 cm
Answer» Two tangents making an angle of 120° with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to (a) $\sqrt{3} c m$ (b) 6 $\sqrt{3} c m$ (c) $\sqrt{2} c m$ (d) 2 $\sqrt{3} c m$

Discussion

30.	What is the degree of the polynomial 7x + 1?
Answer» What is the degree of the polynomial 7x + 1?

Discussion

31.	Find the coordinates of those points in the line passing through the point (-1,-2,3) and parallel to line with DRs (2,3,6) which is at a distance of 3 units from the point (1,-2,3)
Answer» Find the coordinates of those points in the line passing through the point (-1,-2,3) and parallel to line with DRs (2,3,6) which is at a distance of 3 units from the point (1,-2,3)

Discussion

32.	In fig., ∠E > ∠A and ∠C > ∠D. Prove that AD > EC.
Answer» In fig., $∠$ E $>$ $∠$ A and $∠$ C $>$ $∠$ D. Prove that AD $>$ EC.

32.

In fig., ∠E > ∠A and ∠C > ∠D. Prove that AD > EC.

Answer»

In fig., $∠$ E $>$ $∠$ A and $∠$ C $>$ $∠$ D. Prove that AD $>$ EC.

Discussion

33.	From the top of a light house 100 m high the angles of depression of 2 ships on same side of it are 48o & 36o respectively. Find the distance between the 2 ships to the nearest metre.
Answer» From the top of a light house 100 m high the angles of depression of 2 ships on same side of it are 48^o & 36^o respectively. Find the distance between the 2 ships to the nearest metre.

Discussion

34.	In Fig., OABD is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Use π=227)
Answer» In Fig., OABD is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Use $π = \frac{22}{7}$ )

Discussion

35.	SecA . √1-sin^2 A
Answer» SecA . √1-sin^2 A

Discussion

36.	ntLet A = {1,2,3}, B={a,b,c}, C={a1,b1,c1,d1,e1} and consider the following statementsn ntS1: the no. of one one function from A to C is 60n ntS2: the no. of onto function from C to A is 150n ntS3: the no. of one one function from B to C is 0n ntS4: the no. of bijective function from A to B is 6n ntWhich of the following combinations is true ?n
Answer» ntLet A = {1,2,3}, B={a,b,c}, C={a1,b1,c1,d1,e1} and consider the following statementsn ntS1: the no. of one one function from A to C is 60n ntS2: the no. of onto function from C to A is 150n ntS3: the no. of one one function from B to C is 0n ntS4: the no. of bijective function from A to B is 6n ntWhich of the following combinations is true ?n

Discussion

37.	A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 'l' of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Answer» A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 'l' of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Discussion

38.	If the sum of n terms of an A.P. be 3n2−n and its common difference is 6, then its first term is
Answer» If the sum of n terms of an A.P. be $3 n^{2} - n$ and its common difference is 6, then its first term is

Discussion

39.	A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm,find(a) The perimeter of the figure,(b) The area of the figure. [4 MARKS]
Answer» A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm, find (a) The perimeter of the figure, (b) The area of the figure. [4 MARKS]

39.

A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm,find(a) The perimeter of the figure,(b) The area of the figure. [4 MARKS]

Answer»

A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm,

find

(a) The perimeter of the figure,

(b) The area of the figure. [4 MARKS]

Discussion

40.	In which Schedule is the Anti-Defection law added?
Answer» In which Schedule is the Anti-Defection law added?

Discussion

41.	Do the equations 5x+7y=8 and 10x+14y=4 represent a pair of concident lines ? Justify your answer.
Answer» Do the equations 5x+7y=8 and 10x+14y=4 represent a pair of concident lines ? Justify your answer.

Discussion

42.	What is an algorithm?
Answer» What is an algorithm?

Discussion

43.	If x=3+22, check whether x+1x is rational or irrational.
Answer» If $x = 3 + 2 \sqrt{2}$ , check whether $x + \frac{1}{x}$ is rational or irrational.

Discussion

44.	The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?
Answer» The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

Discussion

45.	each side of an of an equilateral triangle measure 10 cm. then find area of triangle and the height
Answer» each side of an of an equilateral triangle measure 10 cm. then find area of triangle and the height

Discussion

46.	The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.
Answer» The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

Discussion

47.	A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water (in L) will fall into the sea in a minute?
Answer» A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water (in L) will fall into the sea in a minute?

Discussion

48.	The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is [CBSE 2012](a) 20 (b) 12 (c) 6 (d) 16
Answer» The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is [CBSE 2012] (a) 20 (b) 12 (c) 6 (d) 16

Discussion

49.	The areas of the major and the minor sector of a circle are equal when the central angle is .
Answer» The areas of the major and the minor sector of a circle are equal when the central angle is .

Discussion

50.	Mrs. Goswami deposits Rs 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value.
Answer» Mrs. Goswami deposits Rs 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The first term of an arithmetic sequence is 5 and the common difference is 2. Find the sum of its first 25 terms.

A tent is in the form of a cylinder of diameter 15 m and height 2.4 m, surmounted by a cone of equal base and height 4 m. Find the capacity of the tent and the cost of the canvas at Rs. 50 per square meter.

A fraction becomes 911, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction. [3 MARKS]

In what ratio does y-axis divide the line segment joining the points (−4, 7) and (3, −7)? [CBSE 2012]

A chord divides a circle into ___.

Cos a + cos b - cos ( a+ b) = 1.5 then which of the following is true ? 1] , a+ b = 0 2], a= 2b 3], a= b 4], 2a= b

If A=[3−24−2] and I=[1001], find k so that A2=kA−2I

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC=60o. Then construct a triangle whose sides are 34 of the corresponding sides of the ΔABC.

If x (0,/2) prove that sin(cosx) < cos (sinx)

Convert the given class intervals in exclusive form.

Find the least number of square tiles of equal dimensions required to pave the floor of a room 4.03 m long and 2.17 m broad.

If (3,7) is a solution of 7x=ky+14, find the value of k.

The area enclosed by the ellipse x2a2+y2b2=1 is equal to (a) π2ab (b) π ab (c) π a2b (d) π ab2

If α, β and are zeroes of the polynomial x^3 + ax + b, then the value of α^3 + β^3 +γ^3 isOptions: – 3b+ 3b– 2b+ 2b

In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD⊥AC. If DP⊥AB and DQ⊥BC thenprove that(a) DQ2 = DP.QC(b) DP2 = DQ.AP

16. Which of the following is not a quadratic equation? (1) 3x ^ 2 + 4x = 0 (2) - 2x + 5x ^ 2 + 2 = 0 (3) sqrt x + 7 sqrt x =4 sqrt x (x ne0) 1+ 3x=4(x ne0) (4) 3х 3x

How many circles can be drawn circumscribing a given triangle?

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter.Mona paid ₹27 for a book kept for 7 days, while Tanvy paid ₹21 for the book she kept for 5 days.Find the fixed charge and the charge for each extra day.

If tan A=34, then find the value of Sin A + Cos ASin A − Cos A.-7

The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is

The function f(x)=0 has eight distinct real solution and f also satisfy f(4+x)=f(4-x). The sum of all the eight solution of f(x)=0 is?

If secβ–cosec9β=0, then the value of sin10β is ?

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.x2-2+1x+2=0

If m=cosθ-sinθ and n=cosθ+sinθ, then show that mn+nm=21-tan2θ.

One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour(ii) a face card(iii) a red face card(iv) the jack of hearts(v) a spade(vi) the queen of diamonds

2 If sinA +sinC +sinB =3 Then find value of cosA +cos C +cosB

Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.

Two tangents making an angle of 120° with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to(a) 3 cm(b) 6 3 cm(c) 2 cm(d) 2 3 cm

What is the degree of the polynomial 7x + 1?

Find the coordinates of those points in the line passing through the point (-1,-2,3) and parallel to line with DRs (2,3,6) which is at a distance of 3 units from the point (1,-2,3)

In fig., ∠E &gt; ∠A and ∠C &gt; ∠D. Prove that AD &gt; EC.

From the top of a light house 100 m high the angles of depression of 2 ships on same side of it are 48o &amp; 36o respectively. Find the distance between the 2 ships to the nearest metre.

In Fig., OABD is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Use π=227)

SecA . √1-sin^2 A

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 'l' of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

If the sum of n terms of an A.P. be 3n2−n and its common difference is 6, then its first term is

A semicircle CDE is mounted on a parallelogram ABCE as shown, If AB = 24 cm, AE = 13 cm and EF = 12 cm,find(a) The perimeter of the figure,(b) The area of the figure. [4 MARKS]

In which Schedule is the Anti-Defection law added?

Do the equations 5x+7y=8 and 10x+14y=4 represent a pair of concident lines ? Justify your answer.

What is an algorithm?

If x=3+22, check whether x+1x is rational or irrational.

The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

each side of an of an equilateral triangle measure 10 cm. then find area of triangle and the height

The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water (in L) will fall into the sea in a minute?

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is [CBSE 2012](a) 20 (b) 12 (c) 6 (d) 16

The areas of the major and the minor sector of a circle are equal when the central angle is .

Mrs. Goswami deposits Rs 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value.

In fig., ∠E > ∠A and ∠C > ∠D. Prove that AD > EC.

From the top of a light house 100 m high the angles of depression of 2 ships on same side of it are 48o & 36o respectively. Find the distance between the 2 ships to the nearest metre.