32581 + Interview Questions in Mathematics Page 28 InterviewSolution

1351.	If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is(a) 13(b) 9(c) 21(d) 17
Answer» If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is (a) 13 (b) 9 (c) 21 (d) 17

Discussion

1352.	explain parts per millio
Answer» explain parts per millio

Discussion

1353.	If 17≡4(mod 13) then 51≡x(mod 13), then find the value of x.12
Answer» $If 17 \equiv 4 (m o d 13) then 51 \equiv x (m o d 13)$ , then find the value of $x$ . 12

Discussion

1354.	A vertical stick 24 cm long casts a shadow 16 cm long on the ground. At the same time a tower casts a shadow 80 m long on the ground. Determine the height of the tower.
Answer» A vertical stick 24 cm long casts a shadow 16 cm long on the ground. At the same time a tower casts a shadow 80 m long on the ground. Determine the height of the tower.

Discussion

1355.	A company has an opening credit balance in Surplus, i.e., Balance in Statement of Profit and Loss of ₹ 1,00,000. During the year, it earned a profit of ₹ 75,000. It decided to transfer ₹ 15,000 to Debentures Redemption Reserve (DRR) and also proposed to pay dividend of ₹ 25,000.How will be the appropriations shown in the financial statements?
Answer» A company has an opening credit balance in Surplus, i.e., Balance in Statement of Profit and Loss of ₹ 1,00,000. During the year, it earned a profit of ₹ 75,000. It decided to transfer ₹ 15,000 to Debentures Redemption Reserve (DRR) and also proposed to pay dividend of ₹ 25,000. How will be the appropriations shown in the financial statements?

Discussion

1356.	35. If m sin theeta =n sin(theeta+2 alpha),then tan (theeta + alpha)cot alpha=?
Answer» 35. If m sin theeta =n sin(theeta+2 alpha),then tan (theeta + alpha)cot alpha=?

Discussion

1357.	18.Find the value of P , such that the linear equation 6x-Py=0 has equal values x and y . Where x is not equal to zero
Answer» 18.Find the value of P , such that the linear equation 6x-Py=0 has equal values x and y . Where x is not equal to zero

Discussion

1358.	The medians of a triangle ABC intersect at G.To show: Area (ΔAGB)=13 Area (ΔABC)
Answer» The medians of a triangle ABC intersect at G. To show: $A r e a (Δ A G B) = \frac{1}{3} A r e a (Δ A B C)$

Discussion

1359.	IF the polynomial ×^4 -6×^3+16×^2-25×+10 is divided by another polynomial ×^2-2×+κ the remainder comes out to be ×+a ,find κ and a
Answer» IF the polynomial ×^4 -6×^3+16×^2-25×+10 is divided by another polynomial ×^2-2×+κ the remainder comes out to be ×+a ,find κ and a

Discussion

1360.	22. P is the cicumcircle of an acute angled triangle ABC with circumradius R .Midpoint of BC is D.show that the perimeter of triangle ABC is 2R (sinA+sinB+ sinC).
Answer» 22. P is the cicumcircle of an acute angled triangle ABC with circumradius R .Midpoint of BC is D.show that the perimeter of triangle ABC is 2R (sinA+sinB+ sinC).

Discussion

1361.	Find the volume of a sphere of radius 5.6 cm.
Answer» Find the volume of a sphere of radius 5.6 cm.

Discussion

1362.	The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, What is the mean of b and d?(a) 31(b) 32(c) 33(d) 34
Answer» The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, What is the mean of b and d? (a) 31 (b) 32 (c) 33 (d) 34

Discussion

1363.	Find the missing terms of the AP: ___ , 3, ___ , -5.
Answer» Find the missing terms of the AP: ___ , 3, ___ , -5.

Discussion

1364.	Solve each of the following quadratic equations:x2-3+1x+3=0 [CBSE 2015]
Answer» Solve each of the following quadratic equations: $x^{2} - (\sqrt{3} + 1) x + \sqrt{3} = 0$ [CBSE 2015]

Discussion

1365.	If ∆ XYZ ~ ∆ LMN, write the corresponding angles of the two triangles and also write the ratios of corresponding sides.
Answer» If $∆$ XYZ ~ $∆$ LMN, write the corresponding angles of the two triangles and also write the ratios of corresponding sides.

Discussion

1366.	Question 9 (ii)In triangle ABC, right-angled at B, if tan A = 1√3, find the value of:(ii) cos Acos C - sinAsin C
Answer» Question 9 (ii) In triangle ABC, right-angled at B, if tan A = $\frac{1}{\sqrt{3}}$ , find the value of: (ii) cos Acos C - sinAsin C

Discussion

1367.	A vertically straight tree, 15 m high, is broken by the wind in such a way that it top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?
Answer» A vertically straight tree, 15 m high, is broken by the wind in such a way that it top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

Discussion

1368.	On the basis of the graph shown below which shows the graphical representation of a pair of linear equations, the pair of linear equations has _______________solution(s).
Answer» On the basis of the graph shown below which shows the graphical representation of a pair of linear equations, the pair of linear equations has _______________solution(s).

1368.

On the basis of the graph shown below which shows the graphical representation of a pair of linear equations, the pair of linear equations has _______________solution(s).

Answer»

On the basis of the graph shown below which shows the graphical representation of a pair of linear equations, the pair of linear equations has _______________solution(s).

Discussion

1369.	A polynomial of degree 1 is called __ polynomial.
Answer» A polynomial of degree 1 is called __ polynomial.

Discussion

1370.	Find the centre of the circle passing through the points A(6, - 6), B(3, - 7) and X(3, 3). The centre of the circle is assumed to be X(x,y)
Answer» Find the centre of the circle passing through the points A(6, - 6), B(3, - 7) and X(3, 3). The centre of the circle is assumed to be X(x,y)

Discussion

1371.	The value of the remainder, r, when a positive integer 'a' is divided by 3, are ________.
Answer» The value of the remainder, r, when a positive integer 'a' is divided by 3, are ________.

Discussion

1372.	The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.
Answer» The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

Discussion

1373.	What is meant by the locus of points?
Answer» What is meant by the locus of points?

Discussion

1374.	if 3sin theta + 5cos theta = 5 then 3cos theta - 5sin theta is equal to
Answer» if 3sin theta + 5cos theta = 5 then 3cos theta - 5sin theta is equal to

Discussion

1375.	From the letters of the word ''MOBILE", a letter is selected. The probability that the letter is a vowel, is(a) 13(b) 37(c) 16(d) 12
Answer» From the letters of the word ''MOBILE", a letter is selected. The probability that the letter is a vowel, is (a) $\frac{1}{3}$ (b) $\frac{3}{7}$ (c) $\frac{1}{6}$ (d) $\frac{1}{2}$

Discussion

1376.	A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is V find the total area around the fountain that gets wet.
Answer» A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is V find the total area around the fountain that gets wet.

Discussion

1377.	A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.
Answer» A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.

Discussion

1378.	Disha and Divya are partners in a firm sharing profits in the ratio of 3 : 2 respectively. The fixed capital of Disha is ₹ 4,80,000 and of Divya is ₹ 3,00,000. On 1st April, 2019 they admitted Hina as a new partner for 1/5th share in future profits. Hina brought ₹ 3,00,000 as her capital. Calculate value of goodwill of the firm and record necessary Journal entries on Hina's admission.
Answer» Disha and Divya are partners in a firm sharing profits in the ratio of 3 : 2 respectively. The fixed capital of Disha is ₹ 4,80,000 and of Divya is ₹ 3,00,000. On 1st April, 2019 they admitted Hina as a new partner for 1/5th share in future profits. Hina brought ₹ 3,00,000 as her capital. Calculate value of goodwill of the firm and record necessary Journal entries on Hina's admission.

Discussion

1379.	Solve for x and y:0.3x+0.5y=0.50.5x+0.7y=0.74
Answer» Solve for x and y: $0.3 x + 0.5 y = 0.5 0.5 x + 0.7 y = 0.74$

Discussion

1380.	Question 2 (i) Do the following equations represent a pair of coincident lines? Justify your answer. 3x+17y=3 and 7x+3y=7
Answer» Question 2 (i) Do the following equations represent a pair of coincident lines? Justify your answer. $3 x + \frac{1}{7} y = 3 a n d 7 x + 3 y = 7$

Discussion

1381.	A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per square metre (Use π = 3.14) [CBSE 2014]
Answer» A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per square metre (Use π = 3.14) [CBSE 2014]

Discussion

1382.	6. Convert 2 cubic metres into decimetre scale of volume
Answer» 6. Convert 2 cubic metres into decimetre scale of volume

Discussion

1383.	the projection of the line x+y=0,z=0 on the plane x-y+z=1
Answer» the projection of the line x+y=0,z=0 on the plane x-y+z=1

Discussion

1384.	Consider a Frustum of a cone with radius 2r and r and height h.Liquid of density rho is filled in it.find the force exerted by the walls of the container on the liquid.
Answer» Consider a Frustum of a cone with radius 2r and r and height h.Liquid of density rho is filled in it.find the force exerted by the walls of the container on the liquid.

Discussion

1385.	The value of (1+cotθ−cosecθ)(1+tanθ+secθ) is _____ .2
Answer» The value of $(1 + c o t θ - c o s e c θ) (1 + t a n θ + s e c θ)$ is _____ . 2

Discussion

1386.	The mean of the variates x1,x2,...,xn is ¯x If x2, is replaced by λ, then the new mean is
Answer» The mean of the variates $x_{1}, x_{2}, . . ., x_{n} i s ¯ x$ If $x_{2},$ is replaced by $λ,$ then the new mean is

Discussion

1387.	24. If θ be the angle between two tangents which are drawn to the circle from the origin, then the value of cotθ is ?
Answer» 24. If θ be the angle between two tangents which are drawn to the circle from the origin, then the value of cotθ is ?

Discussion

1388.	Explain why 3 × 5 × 7 + 7 is a composite number.
Answer» Explain why $3 \times 5 \times 7 + 7$ is a composite number.

Discussion

1389.	The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?
Answer» The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

Discussion

1390.	If x = 7 is on the equation 3x-8y = -19, then find the solution.
Answer» If x = 7 is on the equation 3x-8y = -19, then find the solution.

Discussion

1391.	The 9th term of an AP is 449 and 449th term is 9. The term which is equal to zero is
Answer» The 9^th term of an AP is 449 and 449^th term is 9. The term which is equal to zero is

1391.

The 9th term of an AP is 449 and 449th term is 9. The term which is equal to zero is

Answer»

The 9^th term of an AP is 449 and 449^th term is 9. The term

which is equal to zero is

Discussion

1392.	Asuitcase with measures 80 cm × 48 cm × 24 cm is to becovered with a tarpaulin cloth. How many metres of tarpaulin of width96 cm is required to cover 100 such suitcases?
Answer» A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

Discussion

1393.	From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?
Answer» From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?

Discussion

1394.	If a and b are relatively prime, what is their LCM ?
Answer» If a and b are relatively prime, what is their LCM ?

Discussion

1395.	Solve the following systems of equations:3x+y+2x-y=29x+y-4x-y=1
Answer» Solve the following systems of equations: $\frac{3}{x + y} + \frac{2}{x - y} = 2 \frac{9}{x + y} - \frac{4}{x - y} = 1$

Discussion

1396.	Solvethe linear equation
Answer» Solve the linear equation

Discussion

1397.	Objective Questions (MCQ)If α and β are the roots of the equation 3x2+8x+2=0 then 1α+1β = ?(a) -38 (b) 23 (c) −4 (d) 4
Answer» Objective Questions (MCQ) If α and β are the roots of the equation $3 x^{2} + 8 x + 2 = 0$ then $(\frac{1}{α} + \frac{1}{β})$ = ? (a) $\frac{- 3}{8}$ (b) $\frac{2}{3}$ (c) −4 (d) 4

Discussion

1398.	ABC is a triangle . D is a point on AB such that AD=1/4 AB and E is a point on AC such that AE=1/4 AC. Then DE = (in terms of BC )
Answer» ABC is a triangle . D is a point on AB such that AD=1/4 AB and E is a point on AC such that AE=1/4 AC. Then DE = (in terms of BC )

Discussion

1399.	Fond four numbers in AP whose sum is 20 and the sum of whose squares is 120
Answer» Fond four numbers in AP whose sum is 20 and the sum of whose squares is 120

Discussion

1400.	A tower stands at the centre of a circular park. If A and B are 2 points on the boundary of the park, such that AB = a meters subtends an angle of 60° at the foot of tower and angle of elevation of the top of the tower from A or B is 30 degrees, Find the height of the tower
Answer» A tower stands at the centre of a circular park. If A and B are 2 points on the boundary of the park, such that AB = a meters subtends an angle of 60° at the foot of tower and angle of elevation of the top of the tower from A or B is 30 degrees, Find the height of the tower

Discussion

Explore topic-wise InterviewSolutions in .

If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is(a) 13(b) 9(c) 21(d) 17

explain parts per millio

If 17≡4(mod 13) then 51≡x(mod 13), then find the value of x.12

A vertical stick 24 cm long casts a shadow 16 cm long on the ground. At the same time a tower casts a shadow 80 m long on the ground. Determine the height of the tower.

35. If m sin theeta =n sin(theeta+2 alpha),then tan (theeta + alpha)cot alpha=?

18.Find the value of P , such that the linear equation 6x-Py=0 has equal values x and y . Where x is not equal to zero

The medians of a triangle ABC intersect at G.To show: Area (ΔAGB)=13 Area (ΔABC)

IF the polynomial ×^4 -6×^3+16×^2-25×+10 is divided by another polynomial ×^2-2×+κ the remainder comes out to be ×+a ,find κ and a

22. P is the cicumcircle of an acute angled triangle ABC with circumradius R .Midpoint of BC is D.show that the perimeter of triangle ABC is 2R (sinA+sinB+ sinC).

Find the volume of a sphere of radius 5.6 cm.

The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, What is the mean of b and d?(a) 31(b) 32(c) 33(d) 34

Find the missing terms of the AP: ___ , 3, ___ , -5.

Solve each of the following quadratic equations:x2-3+1x+3=0 [CBSE 2015]

If ∆ XYZ ~ ∆ LMN, write the corresponding angles of the two triangles and also write the ratios of corresponding sides.

Question 9 (ii)In triangle ABC, right-angled at B, if tan A = 1√3, find the value of:(ii) cos Acos C - sinAsin C

A vertically straight tree, 15 m high, is broken by the wind in such a way that it top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

On the basis of the graph shown below which shows the graphical representation of a pair of linear equations, the pair of linear equations has _______________solution(s).

A polynomial of degree 1 is called __ polynomial.

Find the centre of the circle passing through the points A(6, - 6), B(3, - 7) and X(3, 3). The centre of the circle is assumed to be X(x,y)

The value of the remainder, r, when a positive integer 'a' is divided by 3, are ________.

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

What is meant by the locus of points?

if 3sin theta + 5cos theta = 5 then 3cos theta - 5sin theta is equal to

From the letters of the word ''MOBILE", a letter is selected. The probability that the letter is a vowel, is(a) 13(b) 37(c) 16(d) 12

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is V find the total area around the fountain that gets wet.

A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.

Solve for x and y:0.3x+0.5y=0.50.5x+0.7y=0.74

Question 2 (i) Do the following equations represent a pair of coincident lines? Justify your answer. 3x+17y=3 and 7x+3y=7

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per square metre (Use π = 3.14) [CBSE 2014]

6. Convert 2 cubic metres into decimetre scale of volume

the projection of the line x+y=0,z=0 on the plane x-y+z=1

Consider a Frustum of a cone with radius 2r and r and height h.Liquid of density rho is filled in it.find the force exerted by the walls of the container on the liquid.

The value of (1+cotθ−cosecθ)(1+tanθ+secθ) is _____ .2

The mean of the variates x1,x2,...,xn is ¯x If x2, is replaced by λ, then the new mean is

24. If θ be the angle between two tangents which are drawn to the circle from the origin, then the value of cotθ is ?

Explain why 3 × 5 × 7 + 7 is a composite number.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

If x = 7 is on the equation 3x-8y = -19, then find the solution.

The 9th term of an AP is 449 and 449th term is 9. The term which is equal to zero is

Asuitcase with measures 80 cm × 48 cm × 24 cm is to becovered with a tarpaulin cloth. How many metres of tarpaulin of width96 cm is required to cover 100 such suitcases?

From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?

If a and b are relatively prime, what is their LCM ?

Solve the following systems of equations:3x+y+2x-y=29x+y-4x-y=1

Solvethe linear equation

Objective Questions (MCQ)If α and β are the roots of the equation 3x2+8x+2=0 then 1α+1β = ?(a) -38 (b) 23 (c) −4 (d) 4

ABC is a triangle . D is a point on AB such that AD=1/4 AB and E is a point on AC such that AE=1/4 AC. Then DE = (in terms of BC )

Fond four numbers in AP whose sum is 20 and the sum of whose squares is 120

A tower stands at the centre of a circular park. If A and B are 2 points on the boundary of the park, such that AB = a meters subtends an angle of 60° at the foot of tower and angle of elevation of the top of the tower from A or B is 30 degrees, Find the height of the tower

Find the missing terms of the AP: _ , 3, _ , -5.