8677 + Interview Questions in Maths in Class 14 Page 85 InterviewSolution

4201.	Find the remainder when 10^(1) + 10^2 + 10^3 + 10^4 + 10^5 + …….. + 10^(99) is divided by 6.
Answer» Solution :The REMAINDER when `10^1` is DIVIDED by 6 is 4 The remainder when `10^2` is divided by 6 is 4 The remainder when `10^3` is divided by 6 is 4 The remainder when `10^4` is divided by 6 is 4 The remainder when `10^5` is divided by 6 is 4 THUS the requried remainder is always 4. So, the requried remainder=`4+4+4+...99times/6`=396/6` Thus the remainder is zero.

Discussion

4202.	ABC is an isosceles right angle Delta. IfPerimeter is P find Area
Answer» <P> Answer :`(P^(2))/(4) (3 - 2 SQRT(2))`

Discussion

4203.	Let b be a positive integer and a=b^(2)-b. If bge4 then a^(2)-2a is divisible by?
Answer» 15 20 24 All of the above ANSWER :C

Discussion

4204.	A certain number of men can do a work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men are there?
Answer» 50 40 56 58 Answer :40

Discussion

4205.	Shantanu started cycling along the boundaries of a square field ABCD from corner point A. After 1/2 h,he reached the corner point C,diagonally opposite to pointA.If his speed was16km/h,find the are a of the field.
Answer» 8 SQ km 9 sq km 32 sq km noneof theabove Answer :D

Discussion

4206.	While selling a watch a shopkeeper gives a discount of 5%. If he gives a discount of 7% he earns Rs. 15 less as profit, then the marked price of the watch is
Answer» RS. 697.50 Rs. 712.50 Rs. 787.50 Rs. 750 Answer :D

Discussion

4207.	A can do a piece of work in 10 days and B can do the same work in 12 days. How long will they take to finish the work, if both work together?
Answer» a.12/11 b.27/11 c.60/11 d.47/11 Answer :A

Discussion

4208.	x^(log _(5)x) gt 5 implies:
Answer» `X in (0, INFTY)` `x in (1, infty)` `x in (1,2)` `x in (0,1//5) cup (5, infty)` ANSWER :D

Discussion

4209.	If f(x)=64x^(3)+(1)/(x^(3)) and alpha, beta are the roots of 4x+(1)/(x)=2 then :
Answer» F(`ALPHA`)=-24 f(`alpha`)=-16 f(`BETA`)=-16 both (B) and © Answer :D

Discussion

4210.	A alone can do a work in 12 days. Time taken by A in completing 1//3 of work is equal to the time taken by B in completing 1//2 of the work. In what time A and B together will complete the work?
Answer» 6 days 4 days 12 days `24/5 days` Solution :According to question, TIME taken by A in completing `1//3` of WORK ` = 12 xx 1/3 = 4 ` days 4 day = time taken by B in completing `1//2 ` of work B alone will complete the work the work = 8 days REQUIRED time `RARR (12xx8)/20 = 24/5` days

Discussion

4211.	An express train travelled at an average speed of100km/h ,stopping for 3 min after every 75 km.A localtrain travelled data speed of 50km/h ,stopping for 1 min after every 25km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time in which the express train travel 600 km?
Answer» 400 km 405 km 307.25 km 415.5 km Answer :C

Discussion

4212.	The shopkeeper mixed 40 kg refined oil with vegetable oil worth rs 60 per kg. Thus he gains rs 10 after selling the mixture of the two oils. The price of the first oil is:
Answer» 20 25 45 can't be determined Answer :D

Discussion

4213.	P and Q can do a piece of work in 8 days, Q and R can do the same work in 12 days and P and R complete it in 8 days In how many days can P,Q and R complete the whole work, working together?
Answer» 4 6 12 9 Answer :B

Discussion

4214.	The corners of a square of side '3' are cut away so as to form a regular octagon. What is the side of the octagon ?
Answer» `SQRT2` `SQRT3` `sqrt5` NONE of these Answer :B

Discussion

4215.	Find the value of x that satisfy the inequation x^6-19x^3-216gt0.
Answer» `[-3,-2]UU[2,3]` `(-oo,-2]uu[3,oo)` `(-oo,-2)uu(3,oo)` `(-oo,-8]uu[27,00)` Answer :C

Discussion

4216.	trianglePQR and triangleJWN are similar. If 3PQ = JW and WN = 9 cm, then QR is equal to
Answer» 3 cm 6cm 9 cm 12 cm Answer :A

Discussion

4217.	In a 1500 m race A wins over B by 350 m and in 1500 m race C can give a startup of 250 m to B. By how much distance A give start up to C, so that A beats C by 50 metres?
Answer» ANSWER :70 m

Discussion

4218.	Harsh vardhan started a business by investing ₹ 36000. after 4 months Gyan Vardhan joined him with some investments. At the end of the year, the total profit was divided between them in the ratio of 9:7. How much capital was invested by Gyan Vardhan in the business?
Answer» Solution :`(36000xx12)/(x xx8)=9/7 IMPLIES x=42,0000` therefore GYAN Vardhan invested ₹ 42000 for 8 months only

Discussion

4219.	The probability that a leap year selected atrandom will contain 53 Sundays is
Answer» `5/7` `3/4` `4/7` `2/7` ANSWER :D

Discussion

4220.	If n arithmetic means are inserted between two quantities a and b , then their sum is equal to :
Answer» N(a+B) n/2 (a+b) 2N(a+b) n/2 (a-b) ANSWER :B

Discussion

4221.	Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2028. The sum of the numbers is:
Answer» 68 72 86 91 Answer :D

Discussion

4222.	Solve the following expressions. (243)^(4/5)
Answer» SOLUTION :`(3^5)^4/5 = 3^4 = 81`

Discussion

4223.	Fair-Asia is well known for its queer marketing practices. To lure its customers, out of the blue, it comes up with a very lucrative offer: In that offer it promises to sell and the air tickets, for a one-way trip to Bangkok that originates from Jakrata, in such a manner that the nth customer has to pay exactly Rs.n to buy an air ticket,but each prospective passenger has to bay a separate ticket for oneself. The airline claims that it had sold out all the seats at throm away prices in no time. However, at the last moment one of the customers had returned her ticket and got the full refund from the airline. Consequently, the average income of the airline from this particular flight is exactly rs 100 per passenger. What could be the customer numbe, who returned her ticket to airline?
Answer» 99 100 75 225 Answer :B

Discussion

4224.	Fair-Asia is well known for its queer marketing practices. To lure its customers, out of the blue, it comes up with a very lucrative offer: In that offer it promises to sell and the air tickets, for a one-way trip to Bangkok that originates from Jakrata, in such a manner that the nth customer has to pay exactly Rs.n to buy an air ticket,but each prospective passenger has to bay a separate ticket for oneself. The airline claims that it had sold out all the seats at throm away prices in no time. However, at the last moment one of the customers had returned her ticket and got the full refund from the airline. Consequently, the average income of the airline from this particular flight is exactly rs 100 per passenger. What could be the maximum number of passengers allowed to travel in this airline, if only one passenger occupies each seat and cabin crew or anyone else does not occupy any seat intended for the passengers?
Answer» 320 240 200 none of these Answer :C

Discussion

4225.	Which one of the following is true? (i) The least positive value of n for which n! can be divided by (n + 1) is 5 (ii) The square root of 123454321 is 1111 (iii) The sum of the squares of the first 24 natural numbers is a perfect square
Answer» (i) and (II) (ii) and (III) (i) and (iii) all of these Answer :C

Discussion

4226.	The side of a regular decagon is 2 cm Find the longest possible diagonal of the decagon.
Answer» `SQRT(5+2sqrt5) CM` `2sqrt(5+sqrt5) cm` `sqrt(4+2sqrt5) cm` `sqrt(10+4sqrt5) cm` ANSWER :B

Discussion

4227.	When (x-a) is a factor of (x^3-3x^2a+2a^2x+p) then find the value of p is:
Answer» 0 1 2 3 Answer :A

Discussion

4228.	Devic Mathematics are as follows : +rarr" multiplication" - rarr" division" xx rarr" addition" // rarr" subtraction" ^^ rarr" power (or index) for exponential expression." But Devic (Mathematics must follow the same conventional BODMAS rule of mathematics. Solve the following questions in Devic Mathematics. 50//40-5+4xx54 is euqal to :
Answer» 720 72 144 none of these Answer :B

Discussion

4229.	In a 3 litre mixture of water and milk, 50% is milk. How much water should be added so that the percentage of milk becomes 20%?
Answer» 1.5 litre 4.5 litre 2.5 litre 3 litre Answer :B

Discussion

4230.	Fair-Asia is well known for its queer marketing practices. To lure its customers, out of the blue, it comes up with a very lucrative offer: In that offer it promises to sell and the air tickets, for a one-way trip to Bangkok that originates from Jakrata, in such a manner that the nth customer has to pay exactly Rs.n to buy an air ticket,but each prospective passenger has to bay a separate ticket for oneself. The airline claims that it had sold out all the seats at throm away prices in no time. However, at the last moment one of the customers had returned her ticket and got the full refund from the airline. Consequently, the average income of the airline from this particular flight is exactly rs 100 per passenger. What's the loss incurred by the airline due to the refund of a ticket?
Answer» rs199 rs100 rs 200 Cannot be determined Answer :D

Discussion

4231.	Which of the following pairs is not correctly matched :
Answer» (A) (B) (C) (D) ANSWER :C

Discussion

4232.	If one of the interior angles of a regular polygon is equal to 5//6 times of one of the interior angles of a regular pentagon, then the number of sides of the polygon is:
Answer» 3 4 6 8 Answer :B

Discussion

4233.	What should be added to the expression x (x + a) (x + 2a) (x + 3a) so that the sum may be a perfect square ?
Answer» `a^(2)` `8^(4)` `a^(3)` None of these ANSWER :B

Discussion

4234.	findthe valueof ""^(9) P_3 .
Answer» 504 309 405 600 Answer :A

Discussion

4235.	There are three boats B_1, B_2 and B_3 working together they carry 60 people in each trip. One day an early morning carried 50 people in few trips alone. When it stopped carrying the passengers B_2 and B_3 started carrying the people together. It took a total of 10 trips to carry 300 people by B_1, B_2 and B_3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B_1,B_2 and B_3. How many trips it would take to B_1 to carry 150 passengers alone?
Answer» 15 30 25 10 Answer :A

Discussion

4236.	The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. which can be the A.P.as per the given conditions?
Answer» 2,4,6,8,10,..... 25/2,79/6,83/6, ..... 2,5,8,11,..... both (B) and (C) ANSWER :D

Discussion

4237.	A right circular cylinder is circumscribed about a hemisphere so that they share the same base. The ratio of the volumes of cylinder and hemisphere is
Answer» `3 : SQRT(3) : 2` `3:2:1` `1:2:3` `2:3:1` ANSWER :B

Discussion

4238.	Two pipes A and B can fill a cistern in 30 minutes and 40 minutes respectibely. Both the pipes are opened. Find when the second pipe Bmust be turned off so the cistern may just be full in 10 minutes.
Answer» `26 2/3 min` 25 min `40 2/3 min` `42 2/3 min` Solution :Let a and B together work for x minutes than amount of WATERR filled in the period `= x (1/30 + 1/40) =(7X)/120` Remaining part `= 1- (7x)/120 + ((120-7x)/120)` Work done by A in `(10 - x)` minutes `= (120 -7x)/120 `= 1- (7x)/120 `(7x)/120 + (10-x)/30 =1 or 7 x + 40 - 4 x = 120 ` `3x= 120 - 40 = 80` `x= 26 2/3 min`

Discussion

4239.	The ratio of milk and water in a mixture is 3:5 .We added 10ltwater to the mixture then ratio becomes 3:7 Find the initial quantity of milk .
Answer» 15 lt 12lt 20 lt 17 lt Answer :A

Discussion

4240.	The value of (4^nxx20^(m-1)xx12^(m-n)xx15^(m+n-2))/(16^mxx5^(2m+n)xx9^(m-1)) s-
Answer» `1/200` `1/500` `1/700` `1/900` ANSWER :B

Discussion

4241.	An article of jewellery of 35 gram made up of gold and silver and cost of the article is Rs. 13440. If theweight of gold and silver is interchanged then the cost of the article becomes Rs. 9660. If the cost of gold per gram be Rs. 540, find per gram cost of silver.
Answer» ANSWER :Rs 120 , Gold `to 22 ` gm , SILVER `to 13` gm

Discussion

4242.	If the sum of two numbers added to the sum of their squares is 42 and the product of these numbers is 15, then the numbers are :
Answer» 15, 1 `15/6, 6` `2(1)/2, 6` 5, 3 Answer :D

Discussion

4243.	What was the average profit earned by shopkeeper R in the months of October 2009 and November 2009 together?
Answer» 5405 5040 4850 4950 Answer :A

Discussion

4244.	Five boys and five girls are sitting in a row. Find the probability that All the girls are sitting together.
Answer» `41/42` `39/42` `31/42` `31/35` ANSWER :A

Discussion

4245.	Alfred and Bernard run on the circular track of 600 m. Speeds of Alfred and Bernard are 30 m/s and 20 m/s respectively. Initially they are diametrically opposite to each other. (i) When will they meet for the first time if both move in the same direction? (ii) If both of them move in opposite directions, when will they meet for the second time?
Answer» ANSWER :(i) 30 s (II) 18 s

Discussion

4246.	An integer is divisible by 16 if and only ifits last X digits are divisible by 16.The value of X would be3(b) 4 (c) 5 (d) 6
Answer» three four five six Answer :B

Discussion

4247.	If sinA+cosA=(3)/(5), then find the value of sinA-cosA.
Answer» `(sqrt(41))/(5)` `(9)/(4)` `(5)/(sqrt(41))` `(7)/(sqrt(41))` ANSWER :A

Discussion

4248.	A person gave 20% of his income to his elder son, 30% of the remaining to the younger son and 10% of the balance, he donated to a trust. He is left with Rs. 10080. His income was:
Answer» ANSWER :Rs.20000

Discussion

4249.	Shankuntala asked Aryabhatta to assume any two values of three digits say P and Q then she told him to multiply P by R and Q by S where the values of R and S were given by Shakuntala herself. Aryabhatta exactly told her the values of PR + QS = 888222. Then Shankuntala told him the value of P by Q (i.e. P/Q) is :
Answer» a. 43834 b. 4 C. can't be determined d. NONE of these Answer :C

Discussion

4250.	Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 m/s into a cyl- indrical tank, the radius of whose base is 60 cm, By how much will the level of water rise in 30 min?
Answer» 3M 3.5 m 4 m 4.5 m Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the remainder when 10^(1) + 10^2 + 10^3 + 10^4 + 10^5 + …….. + 10^(99) is divided by 6.

ABC is an isosceles right angle Delta. IfPerimeter is P find Area

Let b be a positive integer and a=b^(2)-b. If bge4 then a^(2)-2a is divisible by?

A certain number of men can do a work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men are there?

Shantanu started cycling along the boundaries of a square field ABCD from corner point A. After 1/2 h,he reached the corner point C,diagonally opposite to pointA.If his speed was16km/h,find the are a of the field.

While selling a watch a shopkeeper gives a discount of 5%. If he gives a discount of 7% he earns Rs. 15 less as profit, then the marked price of the watch is

A can do a piece of work in 10 days and B can do the same work in 12 days. How long will they take to finish the work, if both work together?

x^(log _(5)x) gt 5 implies:

If f(x)=64x^(3)+(1)/(x^(3)) and alpha, beta are the roots of 4x+(1)/(x)=2 then :

A alone can do a work in 12 days. Time taken by A in completing 1//3 of work is equal to the time taken by B in completing 1//2 of the work. In what time A and B together will complete the work?

The shopkeeper mixed 40 kg refined oil with vegetable oil worth rs 60 per kg. Thus he gains rs 10 after selling the mixture of the two oils. The price of the first oil is:

P and Q can do a piece of work in 8 days, Q and R can do the same work in 12 days and P and R complete it in 8 days In how many days can P,Q and R complete the whole work, working together?

The corners of a square of side '3' are cut away so as to form a regular octagon. What is the side of the octagon ?

Find the value of x that satisfy the inequation x^6-19x^3-216gt0.

trianglePQR and triangleJWN are similar. If 3PQ = JW and WN = 9 cm, then QR is equal to

In a 1500 m race A wins over B by 350 m and in 1500 m race C can give a startup of 250 m to B. By how much distance A give start up to C, so that A beats C by 50 metres?

Harsh vardhan started a business by investing ₹ 36000. after 4 months Gyan Vardhan joined him with some investments. At the end of the year, the total profit was divided between them in the ratio of 9:7. How much capital was invested by Gyan Vardhan in the business?

The probability that a leap year selected atrandom will contain 53 Sundays is

If n arithmetic means are inserted between two quantities a and b , then their sum is equal to :

Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2028. The sum of the numbers is:

Solve the following expressions. (243)^(4/5)

Which one of the following is true? (i) The least positive value of n for which n! can be divided by (n + 1) is 5 (ii) The square root of 123454321 is 1111 (iii) The sum of the squares of the first 24 natural numbers is a perfect square

The side of a regular decagon is 2 cm Find the longest possible diagonal of the decagon.

When (x-a) is a factor of (x^3-3x^2a+2a^2x+p) then find the value of p is:

In a 3 litre mixture of water and milk, 50% is milk. How much water should be added so that the percentage of milk becomes 20%?

Which of the following pairs is not correctly matched :

If one of the interior angles of a regular polygon is equal to 5//6 times of one of the interior angles of a regular pentagon, then the number of sides of the polygon is:

What should be added to the expression x (x + a) (x + 2a) (x + 3a) so that the sum may be a perfect square ?

findthe valueof ""^(9) P_3 .

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. which can be the A.P.as per the given conditions?

A right circular cylinder is circumscribed about a hemisphere so that they share the same base. The ratio of the volumes of cylinder and hemisphere is

Two pipes A and B can fill a cistern in 30 minutes and 40 minutes respectibely. Both the pipes are opened. Find when the second pipe Bmust be turned off so the cistern may just be full in 10 minutes.

The ratio of milk and water in a mixture is 3:5 .We added 10ltwater to the mixture then ratio becomes 3:7 Find the initial quantity of milk .

The value of (4^nxx20^(m-1)xx12^(m-n)xx15^(m+n-2))/(16^mxx5^(2m+n)xx9^(m-1)) s-

An article of jewellery of 35 gram made up of gold and silver and cost of the article is Rs. 13440. If theweight of gold and silver is interchanged then the cost of the article becomes Rs. 9660. If the cost of gold per gram be Rs. 540, find per gram cost of silver.

If the sum of two numbers added to the sum of their squares is 42 and the product of these numbers is 15, then the numbers are :

What was the average profit earned by shopkeeper R in the months of October 2009 and November 2009 together?

Five boys and five girls are sitting in a row. Find the probability that All the girls are sitting together.

An integer is divisible by 16 if and only ifits last X digits are divisible by 16.The value of X would be3(b) 4 (c) 5 (d) 6

If sinA+cosA=(3)/(5), then find the value of sinA-cosA.

A person gave 20% of his income to his elder son, 30% of the remaining to the younger son and 10% of the balance, he donated to a trust. He is left with Rs. 10080. His income was:

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 m/s into a cyl- indrical tank, the radius of whose base is 60 cm, By how much will the level of water rise in 30 min?