32581 + Interview Questions in Mathematics Page 202 InterviewSolution

10051.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes (in hours) 0 − 20 20 − 40 40 − 60 60 − 80 80 − 100 100 − 120 Frequency 10 35 52 61 38 29 Determine the modal lifetimes of the components.

Answer»

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)	0 − 20	20 − 40	40 − 60	60 − 80	80 − 100	100 − 120
Frequency	10	35	52	61	38	29

Determine the modal lifetimes of the components.

Discussion

10052.	Question 5 If AOBC is a rectangle whose three vertices are A(0,3), 0(0,0) and B(5,0), then the length of its diagonal is: (A) 5 (B) 3 (C) √34 (D) 4
Answer» Question 5 If AOBC is a rectangle whose three vertices are A(0,3), 0(0,0) and B(5,0), then the length of its diagonal is: (A) 5 (B) 3 (C) $\sqrt{34}$ (D) 4

Discussion

10053.	B (-5, 6) and D (1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.
Answer» B (-5, 6) and D (1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

Discussion

10054.	Question 4The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Answer» Question 4 The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

Discussion

10055.	On dividing x³+3x²+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.Find g(x).
Answer» On dividing x³+3x²+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.Find g(x).

Discussion

10056.	In the given figure, if D is the mid- point of BC and DE is the bisector of ADE and EF \|\| BC, then which of the following is correct.
Answer» In the given figure, if D is the mid- point of BC and DE is the bisector of ADE and EF \|\| BC, then which of the following is correct.

Discussion

10057.	The probability of getting 53 Fridays in a leap year is .
Answer» The probability of getting 53 Fridays in a leap year is .

Discussion

10058.	The second number of and arithmetic sequence is 5. Find the sum of its first and third numbers.
Answer» The second number of and arithmetic sequence is 5. Find the sum of its first and third numbers.

Discussion

10059.	Question 1 (iv)For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.iv) =−32√5,−12
Answer» Question 1 (iv) For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization. iv) $= \frac{- 3}{2 \sqrt{5}}, - \frac{1}{2}$

Discussion

10060.	If 4 P(A) =6 P(B) = 10 PA∩B = 1, then P(B/A) = ______________.
Answer» If 4 P(A) =6 P(B) = 10 P $(A \cap B)$ = 1, then P(B/A) = ______________.

Discussion

10061.	The diameters of two cones are equal. If their slant heights are in the ratio 5:3, then find the ratio of their curved surface areas.
Answer» The diameters of two cones are equal. If their slant heights are in the ratio $5 : 3$ , then find the ratio of their curved surface areas.

Discussion

10062.	In a ∆ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE \|\| BC :(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 and AE = 1.8 cm.(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm
Answer» In a ∆ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE \|\| BC : (i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm. (ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 and AE = 1.8 cm. (iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm. (iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm

Discussion

10063.	find the volume of a sphere of radius 11.2 cm ?
Answer» find the volume of a sphere of radius 11.2 cm ?

Discussion

10064.	Let p(x) because cubic polynomial such that coefficient of x ki power 3 is 1 p(1)=1,p(2)=2 and (3)=3 ,then value of p(4)is
Answer» Let p(x) because cubic polynomial such that coefficient of x ki power 3 is 1 p(1)=1,p(2)=2 and (3)=3 ,then value of p(4)is

Discussion

10065.	In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?
Answer» In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?

Discussion

10066.	{ Solve the equation }24x^3-14x^2-63x+λ=0 , one root being double of another. Hence tind the }}{ value(s) of }λ . }}{ Solve the equation }18x^3+81x^2+2x+60=0 , one root being half the sum of the other two. }}{ Hence find the value of }λ .
Answer» { Solve the equation }24x^3-14x^2-63x+λ=0 , one root being double of another. Hence tind the }}{ value(s) of }λ . }}{ Solve the equation }18x^3+81x^2+2x+60=0 , one root being half the sum of the other two. }}{ Hence find the value of }λ .

Discussion

10067.	Solve x and y using substitution method: √7x +√13y=0 ; √5x +√17y=0
Answer» Solve x and y using substitution method: √7x +√13y=0 ; √5x +√17y=0

Discussion

10068.	Venus Ltd. had 9,000, 9% Debentures of ₹ 100 each due for redemption . These debentures are to be redeemed in 3 equal installments (starting from 31st March,2015) at a premium of 10%. The company had a balance of ₹ 25,000 in the Debentures Redemption Reserve .Pass necessary entries for redemption of debentures assuming that company transfer the balance of DRR to General Reserve after redeeming all the debentures.
Answer» Venus Ltd. had 9,000, 9% Debentures of ₹ 100 each due for redemption . These debentures are to be redeemed in 3 equal installments (starting from 31st March,2015) at a premium of 10%. The company had a balance of ₹ 25,000 in the Debentures Redemption Reserve . Pass necessary entries for redemption of debentures assuming that company transfer the balance of DRR to General Reserve after redeeming all the debentures.

Discussion

10069.	The sides of a triangle are in the ratio 12 : 14 : 25 and its perimeter is 25.5 cm. The largest side of the triangle is(a) 7 cm(b) 14 cm(c) 12.5 cm(d) 18 cm
Answer» The sides of a triangle are in the ratio 12 : 14 : 25 and its perimeter is 25.5 cm. The largest side of the triangle is (a) 7 cm (b) 14 cm (c) 12.5 cm (d) 18 cm

Discussion

10070.	is a solution of the equation 3x+2y=6.
Answer» is a solution of the equation $3 x + 2 y = 6$ .

Discussion

10071.	Length, breadth and height of a cuboidal tank are in the ratio of 6:2:1.The lateral surface area of the tank is 400 sq.m. Find i) Volume of the tank. ii)If water flows into the tank at a rate of 10 cubic meters per minute, calculate no. of hours for the tank to get completely filled.
Answer» Length, breadth and height of a cuboidal tank are in the ratio of 6:2:1.The lateral surface area of the tank is 400 sq.m. Find i) Volume of the tank. ii)If water flows into the tank at a rate of 10 cubic meters per minute, calculate no. of hours for the tank to get completely filled.

10071.

Length, breadth and height of a cuboidal tank are in the ratio of 6:2:1.The lateral surface area of the tank is 400 sq.m. Find i) Volume of the tank. ii)If water flows into the tank at a rate of 10 cubic meters per minute, calculate no. of hours for the tank to get completely filled.

Answer»

Length, breadth and height of a cuboidal tank are in the ratio of 6:2:1.The lateral surface area of the tank is 400 sq.m.

Find i) Volume of the tank.

ii)If water flows into the tank at a rate of 10 cubic meters per minute, calculate no. of hours for the tank to get completely filled.

Discussion

10072.	In an isosceles triangle ABC, AB = BC, ∠B = 20◦. M, N are on AB and BC respectively such that ∠MCA = 60◦, ∠NAC = 50◦. Find ∠NMC in degrees.
Answer» In an isosceles triangle ABC, AB = BC, ∠B = 20◦. M, N are on AB and BC respectively such that ∠MCA = 60◦, ∠NAC = 50◦. Find ∠NMC in degrees.

Discussion

10073.	Solve. (i) (6a -5b - 8c) + (15b + 2a - 5c) (ii) (3x+2y)(7x - 8y) (iii) (7m - 5n) - ( - 4n - 11m) (iv) (11m - 12n+3p) - (9m+7n-8p)
Answer» Solve. (i) (6a $-$ 5b $-$ 8c) + (15b + 2a $-$ 5c) (ii) (3x+2y)(7x $-$ 8y) (iii) (7m $-$ 5n) $-$ ( $-$ 4n $-$ 11m) (iv) (11m $-$ 12n+3p) $-$ (9m+7n $-$ 8p)

Discussion

10074.

From the following Trial Balance and other information prepare Trading and Profit and Loss Account for the year ended 31st March 2016 and Balance Sheet as at that date. Heads of Accounts Debit (₹) Credit (₹) Sundry Debtors 32,000 Stock (1st April 2015) 22,000 Cash in hand 35 Cash at bank 1,545 Plant and Machinery 17,500 Sundry Creditors 10,650 Trade Expenses 1,075 Sales 1,34,500 Salaries 2,225 Carriage Outwards 400 Rent 900 Bills Payable 7,500 Purchases 1,18,870 Discounts 1,100 Premises 34,500 Capital (1st April 2015) 79,500 Total 2,32,150 2,32,150 Additional Information:Stock on 31st March 2016 was ₹ 12,450. Rent was unpaid to the extent of ₹ 85 and ₹ 150 were outstanding for Trade Expenses. ₹ 400 are to be written off as bad debts out of the above debtors, and 5% is to be provided for doubtful debts. Depreciate plant and machinery 10% and premises by 2%. Manager is entitled a commission of 5% on net profit after charging his commission.

Answer» From the following Trial Balance and other information prepare Trading and Profit and Loss Account for the year ended 31st March 2016 and Balance Sheet as at that date.

Heads of Accounts	Debit (₹)	Credit (₹)
Sundry Debtors	32,000
Stock (1st April 2015)	22,000
Cash in hand	35
Cash at bank	1,545
Plant and Machinery	17,500
Sundry Creditors		10,650
Trade Expenses	1,075
Sales		1,34,500
Salaries	2,225
Carriage Outwards	400
Rent	900
Bills Payable		7,500
Purchases	1,18,870
Discounts	1,100
Premises	34,500
Capital (1st April 2015)		79,500
Total	2,32,150	2,32,150
Total

Additional Information:

Stock on 31st March 2016 was ₹ 12,450. Rent was unpaid to the extent of ₹ 85 and ₹ 150 were outstanding for Trade Expenses. ₹ 400 are to be written off as bad debts out of the above debtors, and 5% is to be provided for doubtful debts. Depreciate plant and machinery 10% and premises by 2%. Manager is entitled a commission of 5% on net profit after charging his commission.

Discussion

10075.	Prove that Sec41°sin49° + cos29°cosec61° - 2/√3(tan20°tan60°tan30°)/3(sin^31° + sin^59°)=0
Answer» Prove that Sec41°sin49° + cos29°cosec61° - 2/√3(tan20°tan60°tan30°)/3(sin^31° + sin^59°)=0

Discussion

10076.	In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained him in the two subjects separately. [CBSE 2008]
Answer» In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained him in the two subjects separately. [CBSE 2008]

Discussion

10077.	Construct a triangle ABC, in which ∠B = 60∘ , ∠ C = 45∘ and AB + BC+ CA = 22 cm.
Answer» Construct a triangle ABC, in which $∠$ B = $60^{\circ}$ , $∠$ C = $45^{\circ}$ and AB + BC+ CA = 22 cm.

Discussion

10078.	Question 1A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.
Answer» Question 1 A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^{\circ}$ .

Discussion

10079.	Construct a ΔPQR with QR = 8 cm, PQ = 7 cm, PR = 5 cm. Construct the incircle of the triangle and find the radius of the incircle.
Answer» Construct a $Δ$ PQR with QR = 8 cm, PQ = 7 cm, PR = 5 cm. Construct the incircle of the triangle and find the radius of the incircle.

Discussion

10080.	The area of ∆AOB having vertices A(0, 6), O(0, 0) and B(6, 0) is(a) 12 sq units(b) 36 sq units(c) 18 sq units(d) 24 sq units
Answer» The area of ∆AOB having vertices A(0, 6), O(0, 0) and B(6, 0) is (a) 12 sq units (b) 36 sq units (c) 18 sq units (d) 24 sq units

Discussion

10081.	The area of a circular path of uniform width h surrounding a circular region of radius r is(a) π(2r+h)r(b) π(2r+h)h(c) π(h+r)r(d) π(h+r)h
Answer» The area of a circular path of uniform width h surrounding a circular region of radius r is (a) $π (2 r + h) r$ (b) $π (2 r + h) h$ (c) $π (h + r) r$ (d) $π (h + r) h$

Discussion

10082.	Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.
Answer» Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

Discussion

10083.	One third of total numbers of students in a class are in chemistry laboratory, one fourth is in physics laboratory, one sixth is in biology laboratory and 12 are in mathematics lab. How many students are there in the class?
Answer» One third of total numbers of students in a class are in chemistry laboratory, one fourth is in physics laboratory, one sixth is in biology laboratory and 12 are in mathematics lab. How many students are there in the class?

Discussion

10084.	If 8 times the 8th term of an AP is equal to 15 times the 15th term of that AP, then 23rd term of the same AP is
Answer» If 8 times the 8th term of an AP is equal to 15 times the 15th term of that AP, then 23rd term of the same AP is

Discussion

10085.	A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number, 1, 2, 3, ..., 12 as shown in following figure. What is the probability that it will point to:(i) 10?(ii) an odd number?(iii) a number which is multiple of 3?(iv) an even number?
Answer» A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number, 1, 2, 3, ..., 12 as shown in following figure. What is the probability that it will point to: (i) 10? (ii) an odd number? (iii) a number which is multiple of 3? (iv) an even number?

Discussion

10086.	A card is drawn from a pack of cards. What is the probability of drawing a Queen of Heart?
Answer» A card is drawn from a pack of cards. What is the probability of drawing a Queen of Heart?

Discussion

10087.	In the given figure if C is the centre of the circle and ∠PQC=250 and ∠PRC=150, then ∠QCR is equal to
Answer» In the given figure if C is the centre of the circle and $∠ P Q C = 25^{0}$ and $∠ P R C = 15^{0}$ , then $∠ Q C R$ is equal to

Discussion

10088.	The solution set of the inequation x+1x-1<0 is ___________.
Answer» The solution set of the inequation $\frac{\|x\| + 1}{\|x\| - 1} < 0$ is ___________.

Discussion

10089.	Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh (2r + h).
Answer» Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh (2r + h).

Discussion

10090.	Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes.But,if he travels 260 km by train and 240 km by taxi,he takes 6 minutes longer.Find the speed of the train and that of the taxi.
Answer» Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes.But,if he travels 260 km by train and 240 km by taxi,he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Discussion

10091.	Rewrite the quadratic equation 1x+4−1x−7=1130,x≠−4,7in the standard form of a quadratic equation. Also,identify a,b and c in the given equation.
Answer» Rewrite the quadratic equation $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$ in the standard form of a quadratic equation. Also,identify a,b and c in the given equation.

Discussion

10092.	In division algorithm when should one stop the division process? 1. When the remainder is zero. 2. When the degree of the remainder is less than the degree of the divisor. 3. When the degree of the quotient is less than the degree of the divisor.
Answer» In division algorithm when should one stop the division process? 1. When the remainder is zero. 2. When the degree of the remainder is less than the degree of the divisor. 3. When the degree of the quotient is less than the degree of the divisor.

Discussion

10093.	The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.
Answer» The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.

Discussion

10094.	A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.
Answer» A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

Discussion

10095.	In △ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the value of sin P, cos P and tan P.
Answer» In $△$ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the value of sin P, cos P and tan P.

Discussion

10096.

Modern Club's Balance Sheet as at 1st April , 2017 was as under: Liabilities ₹ Assets ₹ Capital Fund 2,00,000 Sports Equipments 50,000 Tournament Fund 60,000 Grounds 1,20,000 Subscriptions in Advance 6,000 Billiards Table 60,000 Salaries Unpaid 11,000 Subscriptions Outstanding 8,000 Cash and Bank Balances 39,000 2,77,000 2,77,000 The Receipts and Payments Account for the year ended 31st March, 2018 was: RECEIPTS AND PAYMENTS ACCOUNT Dr. Cr. Receipts ₹ Payments ₹ To Opening Balance 39,000 By Wages and Salaries 60,000 To Subscriptions 1,81,000 By Upkeep of Grounds 10,000 To Sale of old Materials 1,500 By Stationery 15,000 To Sale of Sports Equipment 6,000 By Audit Fee 2,000 ( Costing ₹ 10,000) By Expenses on Teams 65,000 To Entrance Fees 2,000 By Sports Equipments 20,000 To Life Membership Fees 50,000 By 5% Investments 40,000 To Donations for Tournament 20,000 ( On 1st October, 2017) By Cash and Bank Balances 87,500 2,99,500 2,99,500 Subscriptions still to be received are ₹ 5,500 but subscriptions already received include ₹ 4,000 for next year. Salaries still unpaid are ₹ 6,000 . Sports Equipments are now valued at ₹ 45,000. Prepare Income and Expenditure Account and the Balance Sheet , after charging 10% depreciation on Billiards Tables.

Answer» Modern Club's Balance Sheet as at 1st April , 2017 was as under:


Liabilities	₹	Assets	₹
Capital Fund	2,00,000	Sports Equipments	50,000
Tournament Fund	60,000	Grounds	1,20,000
Subscriptions in Advance	6,000	Billiards Table	60,000
Salaries Unpaid	11,000	Subscriptions Outstanding	8,000
		Cash and Bank Balances	39,000



	2,77,000		2,77,000

The Receipts and Payments Account for the year ended 31st March, 2018 was:

RECEIPTS AND PAYMENTS ACCOUNT
Dr.				Cr.
Receipts	₹	Payments	₹
To Opening Balance	39,000	By Wages and Salaries	60,000
To Subscriptions	1,81,000	By Upkeep of Grounds	10,000
To Sale of old Materials	1,500	By Stationery	15,000
To Sale of Sports Equipment	6,000	By Audit Fee	2,000
( Costing ₹ 10,000)		By Expenses on Teams	65,000
To Entrance Fees	2,000	By Sports Equipments	20,000
To Life Membership Fees	50,000	By 5% Investments	40,000
To Donations for Tournament	20,000	( On 1st October, 2017)
		By Cash and Bank Balances	87,500


	2,99,500		2,99,500

Subscriptions still to be received are ₹ 5,500 but subscriptions already received include ₹ 4,000 for next year. Salaries still unpaid are ₹ 6,000 . Sports Equipments are now valued at ₹ 45,000. Prepare Income and Expenditure Account and the Balance Sheet , after charging 10% depreciation on Billiards Tables.

Discussion

10097.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of ∠BAC. [3 MARKS]

Answer»

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of $∠ B A C$ . [3 MARKS]

Discussion

10098.	Q. A tank is filled by two pipes P & Q. If P takes 2 hours more than Q to fill the tank alone & P and Q together fill the tank in 15/8 hours, then find the time taken by P and Q alone to fill the tank.
Answer» Q. A tank is filled by two pipes P & Q. If P takes 2 hours more than Q to fill the tank alone & P and Q together fill the tank in 15/8 hours, then find the time taken by P and Q alone to fill the tank.

Discussion

10099.	30. If x and y are two distinct positive integers , then the mean of x and y is always greater than A) 4xy/(x+y) B) 3xy/(x+y) C) 2xy/(x+y) D) 5xy/(x+y)
Answer» 30. If x and y are two distinct positive integers , then the mean of x and y is always greater than A) 4xy/(x+y) B) 3xy/(x+y) C) 2xy/(x+y) D) 5xy/(x+y)

Discussion

10100.

Question 105The following items are purchased from showroom T-Shirt worth Rs. 1200Jeans worth Rs. 10002 skirts worth Rs. 1350 each.What will these items cost to Shikha if the sales tax is 7 % ?

Answer»

Question 105

The following items are purchased from showroom

T-Shirt worth Rs. 1200

Jeans worth Rs. 1000

2 skirts worth Rs. 1350 each.

What will these items cost to Shikha if the sales tax is 7 % ?

Discussion

Explore topic-wise InterviewSolutions in .

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes (in hours) 0 − 20 20 − 40 40 − 60 60 − 80 80 − 100 100 − 120 Frequency 10 35 52 61 38 29 Determine the modal lifetimes of the components.

Question 5 If AOBC is a rectangle whose three vertices are A(0,3), 0(0,0) and B(5,0), then the length of its diagonal is: (A) 5 (B) 3 (C) √34 (D) 4

B (-5, 6) and D (1, 4) are the vertices of rhombus ABCD. Find the equations of diagonals BD and AC.

Question 4The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

On dividing x³+3x²+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.Find g(x).

In the given figure, if D is the mid- point of BC and DE is the bisector of ADE and EF || BC, then which of the following is correct.

The probability of getting 53 Fridays in a leap year is .

The second number of and arithmetic sequence is 5. Find the sum of its first and third numbers.

Question 1 (iv)For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.iv) =−32√5,−12

If 4 P(A) =6 P(B) = 10 PA∩B = 1, then P(B/A) = ______________.

The diameters of two cones are equal. If their slant heights are in the ratio 5:3, then find the ratio of their curved surface areas.

find the volume of a sphere of radius 11.2 cm ?

Let p(x) because cubic polynomial such that coefficient of x ki power 3 is 1 p(1)=1,p(2)=2 and (3)=3 ,then value of p(4)is

In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test ?

{ Solve the equation }24x^3-14x^2-63x+λ=0 , one root being double of another. Hence tind the }}{ value(s) of }λ . }}{ Solve the equation }18x^3+81x^2+2x+60=0 , one root being half the sum of the other two. }}{ Hence find the value of }λ .

Solve x and y using substitution method: √7x +√13y=0 ; √5x +√17y=0

The sides of a triangle are in the ratio 12 : 14 : 25 and its perimeter is 25.5 cm. The largest side of the triangle is(a) 7 cm(b) 14 cm(c) 12.5 cm(d) 18 cm

is a solution of the equation 3x+2y=6.

Length, breadth and height of a cuboidal tank are in the ratio of 6:2:1.The lateral surface area of the tank is 400 sq.m. Find i) Volume of the tank. ii)If water flows into the tank at a rate of 10 cubic meters per minute, calculate no. of hours for the tank to get completely filled.

In an isosceles triangle ABC, AB = BC, ∠B = 20◦. M, N are on AB and BC respectively such that ∠MCA = 60◦, ∠NAC = 50◦. Find ∠NMC in degrees.

Solve. (i) (6a -5b - 8c) + (15b + 2a - 5c) (ii) (3x+2y)(7x - 8y) (iii) (7m - 5n) - ( - 4n - 11m) (iv) (11m - 12n+3p) - (9m+7n-8p)

Prove that Sec41°sin49° + cos29°cosec61° - 2/√3(tan20°tan60°tan30°)/3(sin^31° + sin^59°)=0

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained him in the two subjects separately. [CBSE 2008]

Construct a triangle ABC, in which ∠B = 60∘ , ∠ C = 45∘ and AB + BC+ CA = 22 cm.

Question 1A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30∘.

Construct a ΔPQR with QR = 8 cm, PQ = 7 cm, PR = 5 cm. Construct the incircle of the triangle and find the radius of the incircle.

The area of ∆AOB having vertices A(0, 6), O(0, 0) and B(6, 0) is(a) 12 sq units(b) 36 sq units(c) 18 sq units(d) 24 sq units

The area of a circular path of uniform width h surrounding a circular region of radius r is(a) π(2r+h)r(b) π(2r+h)h(c) π(h+r)r(d) π(h+r)h

Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

One third of total numbers of students in a class are in chemistry laboratory, one fourth is in physics laboratory, one sixth is in biology laboratory and 12 are in mathematics lab. How many students are there in the class?

If 8 times the 8th term of an AP is equal to 15 times the 15th term of that AP, then 23rd term of the same AP is

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number, 1, 2, 3, ..., 12 as shown in following figure. What is the probability that it will point to:(i) 10?(ii) an odd number?(iii) a number which is multiple of 3?(iv) an even number?

A card is drawn from a pack of cards. What is the probability of drawing a Queen of Heart?

In the given figure if C is the centre of the circle and ∠PQC=250 and ∠PRC=150, then ∠QCR is equal to

The solution set of the inequation x+1x-1&lt;0 is ___________.

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh (2r + h).

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes.But,if he travels 260 km by train and 240 km by taxi,he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Rewrite the quadratic equation 1x+4−1x−7=1130,x≠−4,7in the standard form of a quadratic equation. Also,identify a,b and c in the given equation.

In division algorithm when should one stop the division process? 1. When the remainder is zero. 2. When the degree of the remainder is less than the degree of the divisor. 3. When the degree of the quotient is less than the degree of the divisor.

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.

A number is chosen at random among the first 100 natural numbers. Find the probability that the number chosen is prime.

In △ PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Find the value of sin P, cos P and tan P.

In the adjoining figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisector of ∠BAC. [3 MARKS]

Q. A tank is filled by two pipes P & Q. If P takes 2 hours more than Q to fill the tank alone & P and Q together fill the tank in 15/8 hours, then find the time taken by P and Q alone to fill the tank.

30. If x and y are two distinct positive integers , then the mean of x and y is always greater than A) 4xy/(x+y) B) 3xy/(x+y) C) 2xy/(x+y) D) 5xy/(x+y)

Question 105The following items are purchased from showroom T-Shirt worth Rs. 1200Jeans worth Rs. 10002 skirts worth Rs. 1350 each.What will these items cost to Shikha if the sales tax is 7 % ?

The solution set of the inequation x+1x-1<0 is ___________.