32581 + Interview Questions in Mathematics Page 140 InterviewSolution

6951.	18 f one vertex of an equilateral triangle is 1 +i and centroid is at origin, then find other two vertices of triangle
Answer» 18 f one vertex of an equilateral triangle is 1 +i and centroid is at origin, then find other two vertices of triangle

Discussion

6952.	Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.
Answer» Solve the equation 5 $x^{2}$ – 6 $x$ – 2 = 0 by the method of completing the square. Find the positive root.

Discussion

6953.	In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of AD [CBSE 2011]
Answer» In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of AD [CBSE 2011]

Discussion

6954.	The line joining points (2,−1,4) and (4,3,2) intersects the plane x+y+z−3=0 at the point
Answer» The line joining points $(2, - 1, 4)$ and $(4, 3, 2)$ intersects the plane $x + y + z - 3 = 0$ at the point

Discussion

6955.	The angles of elevation of the top of a tower { measured from the points A and B on a horizontal line, on the either side of the foot of the tower are {α and β. If AB=d , then find the height of the tower.
Answer» The angles of elevation of the top of a tower { measured from the points A and B on a horizontal line, on the either side of the foot of the tower are {α and β. If AB=d , then find the height of the tower.

Discussion

6956.	Lal and Pal were partners in a firm sharing profits in the ratio of 3 : 7. On 1st April, 2015 their firm was dissolved. After transferring assets (other than cash) and outsider's liabilities to Realisation Account, you are given the following information:(a) A creditor of ₹ 3,60,000 accepted machinery valued at ₹ 5,00,000 and paid to the firm ₹ 1,40,000.(b) A second creditor for ₹ 50,000 accepted stock at ₹ 45,000 in full settlement of his claim.(c) A third creditor amounting to ₹ 90,000 accepted ₹ 45,000 in cash and investments worth ₹ 43,000 in full settlement of his claim.(d) Loss on dissolution was ₹ 15,000.Pass necessary Journal entries for the above transactions in the books of firm assuming that all payments were made by cheque.
Answer» Lal and Pal were partners in a firm sharing profits in the ratio of 3 : 7. On 1st April, 2015 their firm was dissolved. After transferring assets (other than cash) and outsider's liabilities to Realisation Account, you are given the following information: (a) A creditor of ₹ 3,60,000 accepted machinery valued at ₹ 5,00,000 and paid to the firm ₹ 1,40,000. (b) A second creditor for ₹ 50,000 accepted stock at ₹ 45,000 in full settlement of his claim. (c) A third creditor amounting to ₹ 90,000 accepted ₹ 45,000 in cash and investments worth ₹ 43,000 in full settlement of his claim. (d) Loss on dissolution was ₹ 15,000. Pass necessary Journal entries for the above transactions in the books of firm assuming that all payments were made by cheque.

Discussion

6957.	From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship ish tan α +tan β tan α +tan β metres.
Answer» From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is $\frac{h (\tan α + \tan β)}{\tan α + \tan β}$ metres.

Discussion

6958.	The Quick Ratio of a company is 0.8:1. State with reason, whether the following transactions will increase, decrease or not change the Quick Ratio:(i) Purchase of loose tools for ₹2,000; (ii) Insurance premium paid in advance ₹500; (iii) Sale of goods on credit ₹3,000; (iv) Honoured a bills payable of ₹5,000 on maturity.
Answer» The Quick Ratio of a company is 0.8:1. State with reason, whether the following transactions will increase, decrease or not change the Quick Ratio: (i) Purchase of loose tools for ₹2,000; (ii) Insurance premium paid in advance ₹500; (iii) Sale of goods on credit ₹3,000; (iv) Honoured a bills payable of ₹5,000 on maturity.

Discussion

6959.	Write the number of solutions of the following pair of linear equations:x + 3y − 4 = 02x + 6y = 7
Answer» Write the number of solutions of the following pair of linear equations: x + 3y − 4 = 0 2x + 6y = 7

Discussion

6960.	If x2+xy+x=12 and y2+xy+y=18 then find the value of x-y is
Answer» If x2+xy+x=12 and y2+xy+y=18 then find the value of x-y is

Discussion

6961.	AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, then find BP.
Answer» AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, then find BP.

6961.

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, then find BP.

Answer»

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, then find BP.

Discussion

6962.	The following is a compound plane figure consisting of a parallelogram and a sector of a circle undefinedundefinedundefinedundefined
Answer» The following is a compound plane figure consisting of a parallelogram and a sector of a circle undefined undefined undefined undefined

Discussion

6963.	For the given triangle ABC, G is the centroid and BC = 10 units. Determine the length of BD.
Answer» For the given triangle ABC, G is the centroid and BC = 10 units. Determine the length of BD.

Discussion

6964.	(Assumption: Profit is Rs 20 at each stage of the selling chain). The manufacturer A, the sale distributor B, the wholesaler C, and the retailer D live in the same state where the rate of VAT is 8%. The cost price of A's commodity is Rs 200. Find the amount of VAT if A sells to B, B sells to C, and C sells to D. Also, find the selling price of D. [4 MARKS]
Answer» (Assumption: Profit is Rs 20 at each stage of the selling chain). The manufacturer A, the sale distributor B, the wholesaler C, and the retailer D live in the same state where the rate of VAT is 8%. The cost price of A's commodity is Rs 200. Find the amount of VAT if A sells to B, B sells to C, and C sells to D. Also, find the selling price of D. [4 MARKS]

Discussion

6965.	Choose the correct answer in each of the following questions:The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is [CBSE 2015](a) 4 (b) 5 (c) 3 (d) 2
Answer» Choose the correct answer in each of the following questions: The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is [CBSE 2015] (a) 4 (b) 5 (c) 3 (d) 2

Discussion

6966.	Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, the distance between their tops is(a) 12 m(b) 14 m(c) 13 m(d) 11 m
Answer» Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, the distance between their tops is (a) 12 m (b) 14 m (c) 13 m (d) 11 m

Discussion

6967.	The length of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each sides of the rhombus
Answer» The length of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each sides of the rhombus

Discussion

6968.	40. In a morning walk, 3 persons step off together. If their steps measure 80cm, 85cm and 90cm respectively, then the minimum distance each should walk, so that they can cover the distance in complete steps is
Answer» 40. In a morning walk, 3 persons step off together. If their steps measure 80cm, 85cm and 90cm respectively, then the minimum distance each should walk, so that they can cover the distance in complete steps is

Discussion

6969.	Question 1Classify the following polynomials as polynomials in one variable, two variables etc.(i) x2+x+1(ii) y3−5y(iii) xy+yz+zx(iv) x2–xy+y2+1
Answer» Question 1 Classify the following polynomials as polynomials in one variable, two variables etc. (i) $x^{2} + x + 1$ (ii) $y^{3} - 5 y$ (iii) $x y + y z + z x$ (iv) $x^{2} - x y + y^{2} + 1$

Discussion

6970.	D, E, F are the mid-points of the sides BC, CA and AB respectively of a △ ABC. The ratio of the areas of △ ABC and △ DEF. __
Answer» D, E, F are the mid-points of the sides BC, CA and AB respectively of a $△$ ABC. The ratio of the areas of $△$ ABC and $△$ DEF. __

6970.

D, E, F are the mid-points of the sides BC, CA and AB respectively of a △ ABC. The ratio of the areas of △ ABC and △ DEF. __

Answer»

D, E, F are the mid-points of the sides BC, CA and AB respectively of a $△$ ABC. The ratio of the areas of $△$ ABC and $△$ DEF.

__

Discussion

6971.	Obtain zeroes of 4√3x2 +5x - 2√3 and verify relation between its zeroes and coefficients
Answer» Obtain zeroes of 4√3x²+5x - 2√3 and verify relation between its zeroes and coefficients

Discussion

6972.	20.Find the equation of the circle passing through the points (2,3) and (-1,1) & whose centre lies on the line x-3y-11=0
Answer» 20.Find the equation of the circle passing through the points (2,3) and (-1,1) & whose centre lies on the line x-3y-11=0

Discussion

6973.	Find A if 3sin theta +4cos theta =Asin( theta+ pie)
Answer» Find A if 3sin theta +4cos theta =Asin( theta+ pie)

Discussion

6974.	The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is(a) 2.75 cm2(b) 5.5 cm2(c) 11 cm2(d) 10 cm2
Answer» The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is (a) 2.75 cm² (b) 5.5 cm² (c) 11 cm² (d) 10 cm²

Discussion

6975.	The LCM of two numbers is 14 times their HCF . The sum of LCM and HCF is 600. If one number is 280 , find the other .
Answer» The LCM of two numbers is 14 times their HCF . The sum of LCM and HCF is 600. If one number is 280 , find the other .

Discussion

6976.	A body travels first one third distance with uniform speed u and next one third with speed of v and the next one third distance with average speed w. Find the average speed?
Answer» A body travels first one third distance with uniform speed u and next one third with speed of v and the next one third distance with average speed w. Find the average speed?

Discussion

6977.	Which of the following is the reduced form of the equation (x−2)3 = (2x−1)2+x3 ?
Answer» Which of the following is the reduced form of the equation $(x - 2)^{3}$ = $(2 x - 1)^{2} + x^{3}$ ?

Discussion

6978.	The following bar graph shows the favourite colours of 20 students of a class. From the above data, find the least favoured colour.
Answer» The following bar graph shows the favourite colours of 20 students of a class. From the above data, find the least favoured colour.

Discussion

6979.	A vertical tower s†an ds on a horizontal plane and surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of bottom and the top of the flag staffare a and b respectively. Prove that the height of the tower is h†an a/†an b-†an a
Answer» A vertical tower s†an ds on a horizontal plane and surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of bottom and the top of the flag staffare a and b respectively. Prove that the height of the tower is h†an a/†an b-†an a

Discussion

6980.	Point (-3, -2) lies in ___ quadrant.
Answer» Point (-3, -2) lies in ___ quadrant.

Discussion

6981.	Cards numbered 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card selected has an odd number which is not less than 60.
Answer» Cards numbered 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card selected has an odd number which is not less than 60.

Discussion

6982.	If ABC is a right angled triangle such that AB=AC and bisectors of angleC intersects the side AB at D, then prove that AC +AD=BC
Answer» If ABC is a right angled triangle such that AB=AC and bisectors of angleC intersects the side AB at D, then prove that AC +AD=BC

Discussion

6983.	Question 91 (iii) Factorise the following: y2+18y+65
Answer» Question 91 (iii) Factorise the following: $y^{2} + 18 y + 65$

Discussion

6984.	What we can say about the nature of roots of x2–2x–3=0 ?
Answer» What we can say about the nature of roots of $x^{2} - 2 x - 3 = 0$ ?

Discussion

6985.	If the ratio of three sides of a triangle is √3:√4:√5, then find whether it is a right angle triangle or not.
Answer» If the ratio of three sides of a triangle is $\sqrt{3} : \sqrt{4} : \sqrt{5},$ then find whether it is a right angle triangle or not.

Discussion

6986.	Prove that is irrational.
Answer» Prove that is irrational.

Discussion

6987.	Find the value, tan1°.tan2°.tan3°................tan90
Answer» Find the value, tan1°.tan2°.tan3°................tan90

6987.

Find the value, tan1°.tan2°.tan3°................tan90

Answer»

Find the value,

tan1°.tan2°.tan3°................tan90

Discussion

6988.	Question 8 ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.
Answer» Question 8 ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

Discussion

6989.	Solve : X^2 - X - 1 < 0
Answer» Solve : X^2 - X - 1 < 0

Discussion

6990.	Question 4The 11th term of the AP −5,−52,0,52,⋯⋯ isA) -20B) 20C) -30D) 30
Answer» Question 4 The $11^{t h}$ term of the AP $- 5, \frac{- 5}{2}, 0, \frac{5}{2}, \dots \dots$ is A) -20 B) 20 C) -30 D) 30

Discussion

6991.	Solve the following quadratic equations by factorization:4x2+4bx-a2-b2=0
Answer» Solve the following quadratic equations by factorization: $4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0$

Discussion

6992.	If (2x+1) is a factor of 6x3 + 5x2 + ax - 2 , find the value of a . x3 - cube x2 - square
Answer» If (2x+1) is a factor of 6x3 + 5x2 + ax - 2 , find the value of a . x3 - cube x2 - square

Discussion

6993.	In the following , determine the set of values of k for which the given quadratic equation has real roots:(i) (ii) 2x2+x+k=0 (iii) (iv) (v)
Answer» In the following , determine the set of values of k for which the given quadratic equation has real roots: (i) (ii) $2 x^{2} + x + k = 0$ (iii) (iv) (v)

Discussion

6994.	The floor of a rectangular hall is 24 m long and 18 m wide. How many carpets, each of length 2.5 m and breadth 80 cm, will be required to cover the floor of the hall?
Answer» The floor of a rectangular hall is 24 m long and 18 m wide. How many carpets, each of length 2.5 m and breadth 80 cm, will be required to cover the floor of the hall?

Discussion

6995.	If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.
Answer» If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.

Discussion

6996.	The value of cos26° – cos224° is ___________.
Answer» The value of cos²6° – cos²24° is ___________.

Discussion

6997.	(i) The sum of first n terms of an AP is 5n22+3n2. Find the nth term and the 20th term of this AP. [CBSE 2006C](ii) The sum of the first n terms of an AP is 3n22+5n2. Find its nth term and the 25th term. [CBSE 2006C]
Answer» (i) The sum of first n terms of an AP is $(\frac{5 n^{2}}{2} + \frac{3 n}{2})$ . Find the nth term and the 20th term of this AP. [CBSE 2006C] (ii) The sum of the first n terms of an AP is $(\frac{3 n^{2}}{2} + \frac{5 n}{2})$ . Find its nth term and the 25th term. [CBSE 2006C]

Discussion

6998.	Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Answer» Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

6998.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

Answer»

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

Discussion

6999.	On selling a tea set at 5%loss and a lemon set at 15% gain,a shopkeeper gains ₹70. If he sells the tea set at 5%gain and the lemon set at 10% gain , he gains ₹130 . Find the cost price of lemon set and tea set.
Answer» On selling a tea set at 5%loss and a lemon set at 15% gain,a shopkeeper gains ₹70. If he sells the tea set at 5%gain and the lemon set at 10% gain , he gains ₹130 . Find the cost price of lemon set and tea set.

Discussion

7000.	f tan a = √3 and cos β = 12 where 0° ≤ α, β ≤ 90°, then find the value of α−β.
Answer» f tan a = √3 and cos β = 12 where 0° ≤ α, β ≤ 90°, then find the value of α−β.

Discussion

Explore topic-wise InterviewSolutions in .

18 f one vertex of an equilateral triangle is 1 +i and centroid is at origin, then find other two vertices of triangle

Solve the equation 5x2– 6x– 2 = 0 by the method of completing the square. Find the positive root.

In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of AD [CBSE 2011]

The line joining points (2,−1,4) and (4,3,2) intersects the plane x+y+z−3=0 at the point

The angles of elevation of the top of a tower { measured from the points A and B on a horizontal line, on the either side of the foot of the tower are {α and β. If AB=d , then find the height of the tower.

Write the number of solutions of the following pair of linear equations:x + 3y − 4 = 02x + 6y = 7

If x2+xy+x=12 and y2+xy+y=18 then find the value of x-y is

AB is the diameter of the circle with centre O. P is a point on the circle such that PA = 2PB. If AB = d units, then find BP.

The following is a compound plane figure consisting of a parallelogram and a sector of a circle undefinedundefinedundefinedundefined

For the given triangle ABC, G is the centroid and BC = 10 units. Determine the length of BD.

Choose the correct answer in each of the following questions:The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is [CBSE 2015](a) 4 (b) 5 (c) 3 (d) 2

Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, the distance between their tops is(a) 12 m(b) 14 m(c) 13 m(d) 11 m

The length of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each sides of the rhombus

40. In a morning walk, 3 persons step off together. If their steps measure 80cm, 85cm and 90cm respectively, then the minimum distance each should walk, so that they can cover the distance in complete steps is

Question 1Classify the following polynomials as polynomials in one variable, two variables etc.(i) x2+x+1(ii) y3−5y(iii) xy+yz+zx(iv) x2–xy+y2+1

D, E, F are the mid-points of the sides BC, CA and AB respectively of a △ ABC. The ratio of the areas of △ ABC and △ DEF. __

Obtain zeroes of 4√3x2 +5x - 2√3 and verify relation between its zeroes and coefficients

20.Find the equation of the circle passing through the points (2,3) and (-1,1) & whose centre lies on the line x-3y-11=0

Find A if 3sin theta +4cos theta =Asin( theta+ pie)

The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is(a) 2.75 cm2(b) 5.5 cm2(c) 11 cm2(d) 10 cm2

The LCM of two numbers is 14 times their HCF . The sum of LCM and HCF is 600. If one number is 280 , find the other .

A body travels first one third distance with uniform speed u and next one third with speed of v and the next one third distance with average speed w. Find the average speed?

Which of the following is the reduced form of the equation (x−2)3 = (2x−1)2+x3 ?

The following bar graph shows the favourite colours of 20 students of a class. From the above data, find the least favoured colour.

A vertical tower s†an ds on a horizontal plane and surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of bottom and the top of the flag staffare a and b respectively. Prove that the height of the tower is h†an a/†an b-†an a

Point (-3, -2) lies in ___ quadrant.

Cards numbered 2 to 101 are placed in a box. A card is selected at random from the box. Find the probability that the card selected has an odd number which is not less than 60.

If ABC is a right angled triangle such that AB=AC and bisectors of angleC intersects the side AB at D, then prove that AC +AD=BC

Question 91 (iii) Factorise the following: y2+18y+65

What we can say about the nature of roots of x2–2x–3=0 ?

If the ratio of three sides of a triangle is √3:√4:√5, then find whether it is a right angle triangle or not.

Prove that is irrational.

Find the value, tan1°.tan2°.tan3°................tan90

Question 8 ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

Solve : X^2 - X - 1 < 0

Question 4The 11th term of the AP −5,−52,0,52,⋯⋯ isA) -20B) 20C) -30D) 30

Solve the following quadratic equations by factorization:4x2+4bx-a2-b2=0

If (2x+1) is a factor of 6x3 + 5x2 + ax - 2 , find the value of a . ​​x3 - cube x2 - square

In the following , determine the set of values of k for which the given quadratic equation has real roots:(i) (ii) 2x2+x+k=0 (iii) (iv) (v)

The floor of a rectangular hall is 24 m long and 18 m wide. How many carpets, each of length 2.5 m and breadth 80 cm, will be required to cover the floor of the hall?

If the HCF of 408 and 1032 is expressible in the form 1032 m – 408 × 5, find m.

The value of cos26° – cos224° is ___________.

(i) The sum of first n terms of an AP is 5n22+3n2. Find the nth term and the 20th term of this AP. [CBSE 2006C](ii) The sum of the first n terms of an AP is 3n22+5n2. Find its nth term and the 25th term. [CBSE 2006C]

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

On selling a tea set at 5%loss and a lemon set at 15% gain,a shopkeeper gains ₹70. If he sells the tea set at 5%gain and the lemon set at 10% gain , he gains ₹130 . Find the cost price of lemon set and tea set.

f tan a = √3 and cos β = 12 where 0° ≤ α, β ≤ 90°, then find the value of α−β.

If (2x+1) is a factor of 6x3 + 5x2 + ax - 2 , find the value of a . x3 - cube x2 - square