32581 + Interview Questions in Mathematics Page 86 InterviewSolution

4251.

Gopal keeps incomplete records. On 1st April, 2016, his position was as follows: STATEMENT OF AFFAIRS Liabilities (₹) Assets (₹) Bank Overdraft 7,500 Cash 6,400 Sundry Creditors 15,000 Stock 52,000 Capital 1,64,500 Sundry Debtors 28,000 Fixed Assets 1,00,000 Prepaid Expenses 600 1,87,000 1,87,000 His position on 31st March, 2017 was as follows:Cash in hand ₹ 3,000; Cash at Bank ₹ 5,000; Stock ₹ 44,000; Debtors ₹ 21,000; Fixed Assets ₹ 80,000; Creditors ₹ 22,000.You are informed that Gopal has taken stocks worth ₹ 4,500 for his private use and that he has been regularly transferring ₹ 2,000 per month from his business banking account by way of drawings. Out of his drawings he spent ₹ 15,000 for purchasing a Scooter for the business on 1st October, 2016.You are requested to find out his profit or loss and to prepare the Statement of Affairs after considering the following :1. Depreciate Fixed Assets and Scooter by 10% p.a.2. Write off Bad-Debts ₹ 1,000 and provide 5% for doubtful debts on Sundry Debtors.3. Commission earned but not received by him was ₹ 2,500.

Answer» Gopal keeps incomplete records. On 1st April, 2016, his position was as follows:

STATEMENT OF AFFAIRS
Liabilities	(₹)	Assets	(₹)
Bank Overdraft	7,500	Cash	6,400
Sundry Creditors	15,000	Stock	52,000
Capital	1,64,500	Sundry Debtors	28,000
		Fixed Assets	1,00,000
		Prepaid Expenses	600

	1,87,000		1,87,000

His position on 31st March, 2017 was as follows:

Cash in hand ₹ 3,000; Cash at Bank ₹ 5,000; Stock ₹ 44,000; Debtors ₹ 21,000; Fixed Assets ₹ 80,000; Creditors ₹ 22,000.

You are informed that Gopal has taken stocks worth ₹ 4,500 for his private use and that he has been regularly transferring ₹ 2,000 per month from his business banking account by way of drawings. Out of his drawings he spent ₹ 15,000 for purchasing a Scooter for the business on 1st October, 2016.

You are requested to find out his profit or loss and to prepare the Statement of Affairs after considering the following :

1. Depreciate Fixed Assets and Scooter by 10% p.a.

2. Write off Bad-Debts ₹ 1,000 and provide 5% for doubtful debts on Sundry Debtors.

3. Commission earned but not received by him was ₹ 2,500.

4252.	A train covered a certain distance at a uniform speed. If the train had been 5kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.
Answer» A train covered a certain distance at a uniform speed. If the train had been 5kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.

4253.	Joey buys an article at a rebate of 30% on the printed price. He spends ₹ 40 on transportation of the article. After charging sales tax at the rate of 7% on the printed price, he sells the article for ₹ 1284. Find his profit percentage.
Answer» Joey buys an article at a rebate of 30% on the printed price. He spends ₹ 40 on transportation of the article. After charging sales tax at the rate of 7% on the printed price, he sells the article for ₹ 1284. Find his profit percentage.

4254.	(x+a)(x+b)=x2 + (a+b)x +ab. Evaluate 99×106 without multiplying directly.
Answer» (x+a)(x+b)=x² + (a+b)x +ab. Evaluate 99×106 without multiplying directly.

4255.	If discriminant of a quadratic equation < 0, how many distinct real roots does it have?
Answer» If discriminant of a quadratic equation < 0, how many distinct real roots does it have?

4256.	how to find †an 30^°
Answer» how to find †an 30^°

4257.	The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.
Answer» The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.

4258.	The height of a tree is 10√3 m, if a boy looks at the top of the tree with an angle of elevation of 30∘, find the distance between the boy and the tree.
Answer» The height of a tree is 10 $\sqrt{3}$ m, if a boy looks at the top of the tree with an angle of elevation of $30^{\circ}$ , find the distance between the boy and the tree.

4259.	13. A person standing at the foot of at a tower walks a distance 3a away from the tower and observes that the angle of elevation of the top of the tower is alpha. He then walks a distance 4a perpendicular to the previous direction and observes the angle to be beta, then find the height of the tower in terms of beta.
Answer» 13. A person standing at the foot of at a tower walks a distance 3a away from the tower and observes that the angle of elevation of the top of the tower is alpha. He then walks a distance 4a perpendicular to the previous direction and observes the angle to be beta, then find the height of the tower in terms of beta.

4260.	6. Two circles with centre O&P intersect Each other in points C&D.Chord AB of the circle with centre O touches the circle with centre P in point E . Prove that ANGLE ADE+ANGLE BCE=180 degree.
Answer» 6. Two circles with centre O&P intersect Each other in points C&D.Chord AB of the circle with centre O touches the circle with centre P in point E . Prove that ANGLE ADE+ANGLE BCE=180 degree.

4262.	how many tiles whoes length and breadth are 13cm and 7 cm respectively are needed to cover a rec†an gular region whose lenghth and breadth
Answer» how many tiles whoes length and breadth are 13cm and 7 cm respectively are needed to cover a rec†an gular region whose lenghth and breadth

4263.	prove that (root3 + 1)(3 - cot30degrees) = tancube60degrees - 2sin60dgrees
Answer» prove that (root3 + 1)(3 - cot30degrees) = tancube60degrees - 2sin60dgrees

4264.	The sum of r terms of an AP is 2r2+3r. The nth term is ___.
Answer» The sum of $r$ terms of an AP is $2 r^{2} + 3 r .$ The $n^{th}$ term is ___.

4265.	In ΔABC, AD is the median. Which of these conditions should be satisfied to make ΔADB and ΔADC similar triangles?
Answer» In $Δ A B C$ , AD is the median. Which of these conditions should be satisfied to make $Δ A D B$ and $Δ A D C$ similar triangles?

4266.	if zeroes of the polynomial f(x)=x^3-3px^2+qx-r are in A.P. , then prove that 2p^3= pq-
Answer» if zeroes of the polynomial f(x)=x^3-3px^2+qx-r are in A.P. , then prove that 2p^3= pq-

4267.	If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 − 4x + 9 is 3, then its third zero is(a) 32(b) -32(c) 92(d) -92
Answer» If the product of two zeros of the polynomial f(x) = 2x³ + 6x² − 4x + 9 is 3, then its third zero is (a) $\frac{3}{2}$ (b) $- \frac{3}{2}$ (c) $\frac{9}{2}$ (d) $- \frac{9}{2}$

4268.	In fig.4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π=3.14)
Answer» In fig.4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take $π = 3.14$ )

4269.	In a circus, a motorcyclist performs his stunts in a hollow sphere.The thickness of the sphere negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform stunts.(Take π=227)
Answer» In a circus, a motorcyclist performs his stunts in a hollow sphere.The thickness of the sphere negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform stunts.(Take $π = \frac{22}{7}$ )

4270.	If the area of base of a cone is 49π m2 and its CSA is 175π m2, then its height is __ m.24
Answer» If the area of base of a cone is 49 $π m^{2}$ and its CSA is 175 $π m^{2}$ , then its height is __ m. 24

4271.	Find the mode of the given data:5,6,9,13,6,5,6,7,6,6,2
Answer» Find the mode of the given data: $5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 2$

4272.	12. From a point P, two tangents PA and PB are drawn to a circle C(O,r). If OP=2r, then what is the type of Δ APB.why? 2) PQ=SR 3) PQRS IS A PARALLELOGRAM.
Answer» 12. From a point P, two tangents PA and PB are drawn to a circle C(O,r). If OP=2r, then what is the type of Δ APB.why? 2) PQ=SR 3) PQRS IS A PARALLELOGRAM.

4273.	To find the sum of the 1st 24 terms of the list of numbers whose nth term is given by an=3+2n, what is the best approach to solve this question?
Answer» To find the sum of the $1^{s t}$ 24 terms of the list of numbers whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$ , what is the best approach to solve this question?

4274.	Find the length of the medians of a ΔABC having vertices at A(0, −1), B(2, 1) and C(0, 3).
Answer» Find the length of the medians of a ΔABC having vertices at A(0, −1), B(2, 1) and C(0, 3).

4275.	Find the signs of a, b and c in given graph of polynomial,f(x)=ax2+bx+c,where a≠0.
Answer» Find the signs of a, b and c in given graph of polynomial, $f (x) = a x^{2} + b x + c, w h e r e a \neq 0.$

4276.	Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.
Answer» Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.

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A train covered a certain distance at a uniform speed. If the train had been 5kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.

Joey buys an article at a rebate of 30% on the printed price. He spends ₹ 40 on transportation of the article. After charging sales tax at the rate of 7% on the printed price, he sells the article for ₹ 1284. Find his profit percentage.

(x+a)(x+b)=x​​​​​​2 + (a+b)x +ab. Evaluate 99×106 without multiplying directly.

If discriminant of a quadratic equation &lt; 0, how many distinct real roots does it have?

how to find †an 30^°

The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.

The height of a tree is 10√3 m, if a boy looks at the top of the tree with an angle of elevation of 30∘, find the distance between the boy and the tree.

6. Two circles with centre O&P intersect Each other in points C&D.Chord AB of the circle with centre O touches the circle with centre P in point E . Prove that ANGLE ADE+ANGLE BCE=180 degree.

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides areof the corresponding sides of the triangle ABC.Give the justification of the construction.

how many tiles whoes length and breadth are 13cm and 7 cm respectively are needed to cover a rec†an gular region whose lenghth and breadth

prove that (root3 + 1)(3 - cot30degrees) = tancube60degrees - 2sin60dgrees

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

In ΔABC, AD is the median. Which of these conditions should be satisfied to make ΔADB and ΔADC similar triangles?

if zeroes of the polynomial f(x)=x^3-3px^2+qx-r are in A.P. , then prove that 2p^3= pq-

If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 − 4x + 9 is 3, then its third zero is(a) 32(b) -32(c) 92(d) -92

In fig.4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π=3.14)

In a circus, a motorcyclist performs his stunts in a hollow sphere.The thickness of the sphere negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform stunts.(Take π=227)

If the area of base of a cone is 49π m2 and its CSA is 175π m2, then its height is __ m.24

Find the mode of the given data:5,6,9,13,6,5,6,7,6,6,2

12. From a point P, two tangents PA and PB are drawn to a circle C(O,r). If OP=2r, then what is the type of Δ APB.why? 2) PQ=SR 3) PQRS IS A PARALLELOGRAM.

To find the sum of the 1st 24 terms of the list of numbers whose nth term is given by an=3+2n, what is the best approach to solve this question?

Find the length of the medians of a ΔABC having vertices at A(0, −1), B(2, 1) and C(0, 3).

Find the signs of a, b and c in given graph of polynomial,f(x)=ax2+bx+c,where a≠0.

Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.

If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks.A∆ABCA∆PQR=AB2 =2232=

The locus of mid-points of all parallel chords in a circle is

25. Two trains start from P and Q respectively and travel toward each other at a speed of 50 km/ hr and 40km/hr respectively . By the time ghey meet , the first train has travelled 100 km more than the second .the distance between P and Q is

Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.

If an denotes the nth term of the A.P. 3, 8, 13, 18, ..., then the value of a30 – a20 is __________.

ABCD is a quadrilateral the p(3,7) and q(7,3) are coordinates of midpoints of diagonals AC and BD respectively then find the corrdinates of midpoint of pq.

1.A circle touches all four sides of a quad ABCD whose sides are AB=6cm BC=9cm CD=8cm. Find the length of side AD.

The sum of the first six terms of an A.P is zero and the fourth term is 2. Find the sum of its 30 terms.

Question 2 (v) Express as rupees using decimals: 235 paise

Q)Maximum radius of sphere that can be fitted in octahedral hole of cubical closed packing of sphere of radius r is?

5 years ago, the sum of ages of father and his son was 30 years. 3 years hence the sum of their ages would be ......... years

Find the ratio in which the point P(34,512) divides the line segment joining the point A(12,32) and B(2,-5)

Draw a circle of radius 5 cm. Take a point P on it. Without using the centre of the circle construct a tangent at the point P.

The zeroes of the polynomial P(x)=ax2+bx+c are 1 and 2. Find the value of a, b and c.

If D and E are respectively the midpoints of the sides AB and BC of ∆ABC in which AB = 7.2 cm, BC = 9.8 cm and AC = 3.6 cm then determine the length of DE.

Question 2The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

If E is a point on side CA of an equilateral triangle ABC such that BE ⊥ CA, then AB2 + BC2 + CA2 =(a) 2 BE2(b) 3 BE2(c) 4 BE2(d) 6 BE2

The cost of a headphone was ₹ 1500. The sales tax charged was 7%. Find the bill amount.

Find n if: (a) nP2 = 30 (b) nP3 = 210

If a pair of linear equations is consistent, then the lines representing them are either _______ or ________.

20.How many 5-digit multiples of 11 are there; If the five digits are 3,4,5,6,7 in some order?

The centripetalacceleration of the conical coloum is

(x+a)(x+b)=x2 + (a+b)x +ab. Evaluate 99×106 without multiplying directly.

If discriminant of a quadratic equation < 0, how many distinct real roots does it have?

The sum of r terms of an AP is 2r2+3r. The nth term is ___.

If a pair of linear equations is consistent, then the lines representing them are either _ or __.

4277.	If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks.A∆ABCA∆PQR=AB2 =2232=
Answer» If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks. $\frac{A (∆ ABC)}{A (∆ PQR)} = \frac{{AB}^{2}}{} = \frac{2^{2}}{3^{2}} = \frac{}{}$

4278.	The locus of mid-points of all parallel chords in a circle is
Answer» The locus of mid-points of all parallel chords in a circle is

4279.	25. Two trains start from P and Q respectively and travel toward each other at a speed of 50 km/ hr and 40km/hr respectively . By the time ghey meet , the first train has travelled 100 km more than the second .the distance between P and Q is
Answer» 25. Two trains start from P and Q respectively and travel toward each other at a speed of 50 km/ hr and 40km/hr respectively . By the time ghey meet , the first train has travelled 100 km more than the second .the distance between P and Q is

4280.	Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
Answer» Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.

4281.	A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always the retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.
Answer» A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always the retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

4282.	If an denotes the nth term of the A.P. 3, 8, 13, 18, ..., then the value of a30 – a20 is __________.
Answer» If a_n denotes the n^th term of the A.P. 3, 8, 13, 18, ..., then the value of a₃₀ – a₂₀ is __________.

4283.	ABCD is a quadrilateral the p(3,7) and q(7,3) are coordinates of midpoints of diagonals AC and BD respectively then find the corrdinates of midpoint of pq.
Answer» ABCD is a quadrilateral the p(3,7) and q(7,3) are coordinates of midpoints of diagonals AC and BD respectively then find the corrdinates of midpoint of pq.

4284.	1.A circle touches all four sides of a quad ABCD whose sides are AB=6cm BC=9cm CD=8cm. Find the length of side AD.
Answer» 1.A circle touches all four sides of a quad ABCD whose sides are AB=6cm BC=9cm CD=8cm. Find the length of side AD.

4285.	The sum of the first six terms of an A.P is zero and the fourth term is 2. Find the sum of its 30 terms.
Answer» The sum of the first six terms of an A.P is zero and the fourth term is $2$ . Find the sum of its $30$ terms.

4287.	Q)Maximum radius of sphere that can be fitted in octahedral hole of cubical closed packing of sphere of radius r is?
Answer» Q)Maximum radius of sphere that can be fitted in octahedral hole of cubical closed packing of sphere of radius r is?