24740 + Interview Questions in Mathematics Page 86 InterviewSolution

4251.

On 31st March, 2017, the Balance Sheet of Abhir and Divya, who were sharing profits in the ratio of 3 : 1 was as follows: BALANCE SHEET OF ABHIR AND DIVYA as on 31st March, 2017 Liabilities Amount (₹) Assets Amount (₹) Creditors 2,20,000 Cash at Bank 1,40,000 Employees' Provident Fund 1,00,000 Debtors 6,50,000 Investment Fluctuation Fund 1,00,000 Less: Provision for Bad Debts 50,000 6.00,000 General Reserve 1,20,000 Stock 3,00,000 Capitals: Investments (Market value ₹ 4,40,000) 5,00,000 Abhir 6,00,000 Divya 4,00,000 10,00,000 15,40,000 15,40,000 They decided to admit Vibhor on 1st April, 2017 for 1/5th share.(a) Vibhor shall bring ₹ 80,000 as his share of goodwill premium.(b) Stock was overvalued by ₹ 20,000.(c) A debtor whose dues of ₹ 5,000 were written off as bad debts, paid ₹ 4,000 in full settlement.(d) Two months' salary ₹ 6,000 per month was outstanding.(e) Vibhor was to bring in Capital to the extent of 1/5th of the total capital of the new firm.Prepare Revaluation Account, Partners' Capital Accounts and the Balance Sheet of the reconstituted firm.

Answer»

On 31st March, 2017, the Balance Sheet of Abhir and Divya, who were sharing profits in the ratio of 3 : 1 was as follows:

BALANCE SHEET OF ABHIR AND DIVYA as on 31st March, 2017
Liabilities		Amount (₹)	Assets		Amount (₹)
Creditors		2,20,000	Cash at Bank		1,40,000
Employees' Provident Fund		1,00,000	Debtors	6,50,000
Investment Fluctuation Fund		1,00,000	Less: Provision for Bad Debts	50,000	6.00,000
General Reserve		1,20,000	Stock		3,00,000
Capitals:			Investments (Market value ₹ 4,40,000)		5,00,000
Abhir	6,00,000
Divya	4,00,000	10,00,000
		15,40,000			15,40,000

They decided to admit Vibhor on 1st April, 2017 for 1/5th share.

(a) Vibhor shall bring ₹ 80,000 as his share of goodwill premium.

(b) Stock was overvalued by ₹ 20,000.

(c) A debtor whose dues of ₹ 5,000 were written off as bad debts, paid ₹ 4,000 in full settlement.

(d) Two months' salary ₹ 6,000 per month was outstanding.

(e) Vibhor was to bring in Capital to the extent of 1/5th of the total capital of the new firm.

Prepare Revaluation Account, Partners' Capital Accounts and the Balance Sheet of the reconstituted firm.

4252.	Question 5(c) Find the product, using suitable properties: 15×(−25)×(−4)×(−10)
Answer» Question 5(c) Find the product, using suitable properties: $15 \times (- 25) \times (- 4) \times (- 10)$

4253.	principle of independent assortment
Answer» principle of independent assortment

4254.	The number of children in 10 families of a locality are:2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.
Answer» The number of children in 10 families of a locality are: 2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

4255.	Can integers be natural and rational number or only rational numbers?
Answer» Can integers be natural and rational number or only rational numbers?

4256.	18. Prove that angle bisector of any angle of a triangle and the perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.
Answer» 18. Prove that angle bisector of any angle of a triangle and the perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

4257.	Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Answer» Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

4258.	In the given figure, ABCD is a square. The value of 'x' is equal to:
Answer» In the given figure, ABCD is a square. The value of 'x' is equal to:

4259.	Factorise the expressions and divide them as directed. 12xy(9x2−16y2)+4xy(3x+4y)
Answer» Factorise the expressions and divide them as directed. $12 x y (9 x^{2} - 16 y^{2}) + 4 x y (3 x + 4 y)$

4260.	111.Find the value of Cot70 degree+4cos70degree
Answer» 111.Find the value of Cot70 degree+4cos70degree

4261.	Factorise:x2 – 21x + 90
Answer» Factorise: x² – 21x + 90

4262.	A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?
Answer» A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

4263.	Factorize 8x^3 - (28y^3)/27 - 2xy^2
Answer» Factorize 8x^3 - (28y^3)/27 - 2xy^2

4264.	Why √2/1 is not a rational number? Where p = √2 and q=1 which is satisfying the need for a rational number.
Answer» Why √2/1 is not a rational number? Where p = √2 and q=1 which is satisfying the need for a rational number.

4265.	(x^2+4x)^2-5(x^2+4x)-y(x^2+4x)+5y Factorize it
Answer» (x^2+4x)^2-5(x^2+4x)-y(x^2+4x)+5y Factorize it

4266.	If you have 'x' number of chocolates and receive the same number of chocolates from your friend, then the total number of chocolates you have is .
Answer» If you have ' $x$ ' number of chocolates and receive the same number of chocolates from your friend, then the total number of chocolates you have is .

4267.	ABCD is a rhombus with diagonals AC and BD.The value of p+q+r+s+t is .
Answer» ABCD is a rhombus with diagonals AC and BD. $The value of p + q + r + s + t is$ .

4268.	The median of the distribution 2,3,4,7,5,1,6 is:
Answer» The median of the distribution $2, 3, 4, 7, 5, 1, 6$ is:

4269.	The decimal expansion of pi is:
Answer» The decimal expansion of pi is:

4270.	If the factors of a2 + b2 + 2 (ab + bx + xa) are (a + b + m) and (a + b + nx), then the value of (m – 2n) is
Answer» If the factors of a2 + b2 + 2 (ab + bx + xa) are (a + b + m) and (a + b + nx), then the value of (m – 2n) is

4271.	Question 8 Parveen wanted to make a temporary shelter for her car, by making a box-like structure with a tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how many tarpaulins would be required to make the shelter of height 2.5m, with base dimensions 4m×3m?
Answer» Question 8 Parveen wanted to make a temporary shelter for her car, by making a box-like structure with a tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how many tarpaulins would be required to make the shelter of height 2.5m, with base dimensions $4 m \times 3 m$ ?

4272.	In case of division algorithm of polynomialz, we compare the degrees. Why?
Answer» In case of division algorithm of polynomialz, we compare the degrees. Why?

4273.	24. if p,q,r denote the vectors bc , ca and ab respectively , show that a is parallel to qr , b to rp , c to pq respectively
Answer» 24. if p,q,r denote the vectors bc , ca and ab respectively , show that a is parallel to qr , b to rp , c to pq respectively

4274.	In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB \|\| side SR and A-T-B)
Answer» In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS²+ TQ²= TP²+ TR²(As shown in the figure, draw seg AB \|\| side SR and A-T-B)

4275.	Question 1(iii)The following graph shows the temperature of a patient in a hospital, recorded every hourThe patient’s temperature was the same two times during the period given.What were these two times?
Answer» Question 1(iii) The following graph shows the temperature of a patient in a hospital, recorded every hour The patient’s temperature was the same two times during the period given. What were these two times?

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Question 5(c) Find the product, using suitable properties: 15×(−25)×(−4)×(−10)

principle of independent assortment

The number of children in 10 families of a locality are:2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

Can integers be natural and rational number or only rational numbers?

18. Prove that angle bisector of any angle of a triangle and the perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

In the given figure, ABCD is a square. The value of 'x' is equal to:

Factorise the expressions and divide them as directed.​ 12xy(9x2−16y2)+4xy(3x+4y)

111.Find the value of Cot70 degree+4cos70degree

Factorise:x2 – 21x + 90

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be red?

Factorize 8x^3 - (28y^3)/27 - 2xy^2

Why √2/1 is not a rational number? Where p = √2 and q=1 which is satisfying the need for a rational number.

(x^2+4x)^2-5(x^2+4x)-y(x^2+4x)+5y Factorize it

If you have 'x' number of chocolates and receive the same number of chocolates from your friend, then the total number of chocolates you have is .

ABCD is a rhombus with diagonals AC and BD.The value of p+q+r+s+t is .

The median of the distribution 2,3,4,7,5,1,6 is:

The decimal expansion of pi is:

If the factors of a2 + b2 + 2 (ab + bx + xa) are (a + b + m) and (a + b + nx), then the value of (m – 2n) is

In case of division algorithm of polynomialz, we compare the degrees. Why?

24. if p,q,r denote the vectors b*c , c*a and a*b respectively , show that a is parallel to q*r , b to r*p , c to p*q respectively

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)

Question 1(iii)The following graph shows the temperature of a patient in a hospital, recorded every hourThe patient’s temperature was the same two times during the period given.What were these two times?

Q: If √2^n = 1024, then the value of 2/3.(n/4-4) is??

The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?14

In each of the figures below, find the area of the shaded part

The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?

The number 0.318564318564318564….. is:

Question 5D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find the ratio of the area of ΔDEF and ΔABC.

Rita has 15 coins in denomination of 25 paise and 50 .if the amount with her is ₹5 find the number of coins of each denomination with her

Question 9 In the following question out of the four options only one is correct, write the correct answer. Which of the following is a linear expression? (a) x2+1 (b) y+y2 (c) 4 (d) 1 + z

In the given figure, areas have been drawn of radius 21 cm each with vertices A,B,C, and D of quadrilateral ABCD as centres. Find the area in cm2of the shaded region. [1 MARK]

Question 87 State whether the statement is True or False. (−3)×3=(−12)−(−3)

If each side of a square is of length (x+5) units, then find its area?

3χ^2+4χ+5=0 solve it

The perimeter of a triangle with sides 3^i+4^j+5^k,4^i−3^j−5^k,7^i+^j is p√2. Then the value of p is

22.Let ø1, ø2, ø3, ø4 be the eccentric angles of the end points of two chords of the ellipse x²/a² + y²/b² = 1 which intersect the major axis at two points equidistant from the centre. Then find the relation between the angles.

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.

Question 11The point P(-2,4) lies on a circle of radius 6 and centre (3,5).

Let A and B be two events. If P(A/B) = P(A), then A is ______________ of B.

The y co-ordinate of the point is called its _______ .

Convert 35.5 into its simplest fractional form.

The given graph shows a frequency curve. What is the frequency of the class 160-180?

55 How to construct Quadrilateral PRAS if PR=10cm R = 120^° RA= 4cm A=60^° and AS= 6cm

What is the meaning of irrational number? With eg.

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

If ¯x is the mean of x1,x2,...,xn and ¯y is the mean of y1,y2,...,yn . If ¯z is the mean of x1,x2,...,xn , y1,y2,...,yn then ¯z is equal to :

Factorise the expressions and divide them as directed. 12xy(9x2−16y2)+4xy(3x+4y)

24. if p,q,r denote the vectors bc , ca and ab respectively , show that a is parallel to qr , b to rp , c to pq respectively

4276.	Q: If √2^n = 1024, then the value of 2/3.(n/4-4) is??
Answer» Q: If √2^n = 1024, then the value of 2/3.(n/4-4) is??

4279.	The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?
Answer» The shaded region consists of a chord and the arcs of the circle. Which of the following option is correct?

4280.	The number 0.318564318564318564….. is:
Answer» The number 0.318564318564318564….. is:

4281.	Question 5D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find the ratio of the area of ΔDEF and ΔABC.
Answer» Question 5 D, E and F are respectively the mid-points of sides AB, BC and CA of $Δ A B C$ . Find the ratio of the area of $Δ D E F$ and $Δ A B C$ .

4282.	Rita has 15 coins in denomination of 25 paise and 50 .if the amount with her is ₹5 find the number of coins of each denomination with her
Answer» Rita has 15 coins in denomination of 25 paise and 50 .if the amount with her is ₹5 find the number of coins of each denomination with her

4286.	If each side of a square is of length (x+5) units, then find its area?
Answer» $If each side of a square is of length$ $(x + 5) units, then find its area?$

4288.	The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. In the given figure, the side AC of ΔABC is produced of E such that CE=12AC. If D is the mid - points of BC and ED produced meets AB at F and CP, DQ are drawn parallel to BA, then FD =
Answer» The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. In the given figure, the side AC of $Δ A B C$ is produced of E such that $C E = \frac{1}{2} A C$ . If D is the mid - points of BC and ED produced meets AB at F and CP, DQ are drawn parallel to BA, then FD =

4289.	The perimeter of a triangle with sides 3^i+4^j+5^k,4^i−3^j−5^k,7^i+^j is p√2. Then the value of p is
Answer» The perimeter of a triangle with sides $3^i + 4^j + 5^k, 4^i - 3^j - 5^k, 7^i +^j$ is $p \sqrt{2}$ . Then the value of $p$ is

4290.	22.Let ø1, ø2, ø3, ø4 be the eccentric angles of the end points of two chords of the ellipse x²/a² + y²/b² = 1 which intersect the major axis at two points equidistant from the centre. Then find the relation between the angles.
Answer» 22.Let ø1, ø2, ø3, ø4 be the eccentric angles of the end points of two chords of the ellipse x²/a² + y²/b² = 1 which intersect the major axis at two points equidistant from the centre. Then find the relation between the angles.

4291.	A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.
Answer» A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.