8677 + Interview Questions in Maths in Class 14 Page 162 InterviewSolution

8051.	How many spheres of radius 1.5 cm can be cut out of a wooden cube of edge 9 cm ?
Answer» 216 81 27 can't be determined Answer :C

Discussion

8052.	Find the unit digit of 123 + 345 + 780 + 65 + 44.
Answer» Solution :We can find the unit digit just by ADDING the unit DIGITS 3,5,0,5,4 as 3+5+0+5+4=17 So the unit digit (or the lest digit) of the resultant value of the expression 123+ 345+ 780+65+ 44 will be 7. (you can verify it by doing the whole sum)

Discussion

8053.	(sqrt3)/(sqrt3 + sqrt2) - (3sqrt3)/(sqrt5 +sqrt2) + (2sqrt2)/(sqrt5 + sqrt3)is equal to
Answer» 0 `2sqrt15` `2sqrt10` `2sqrt6` ANSWER :A

Discussion

8054.	If p and q are two distinct inegers such that p^2 - pq = 0 then we can deduce that
Answer» p = q q is only NEGATIVE integer p = 0 EITHER (a) OR (C) Answer :C

Discussion

8055.	The ratio of the roots of the equation ax^(2)+bx+c=0 is same as the ratio of the roots of equation px^(2)+qx+r=0. If D_(1) and D_(2) are the discriminants of ax^(2)+bx+c=0 and px^(2)+qx+r=0 respectively then D_(1):D_(2)=
Answer» `a^2/q^2` `a^2/p^2` `b^2/q^2` NONE of these Answer :C

Discussion

8056.	If a+b+c=13 What is the maximum value of (a-3)(b-2)(c+1)?
Answer» 26 27 30 19 Answer :B

Discussion

8057.	If the equation ax^(2)+2bx+c=0 has real roots, a,b,c being real numbers and if m and n are real numbers such that m^(2)gtngt0 then prove that the equation ax^(2)+2mbx+nc=0 has real roots.
Answer» REAL and DISTINCT roots complex both real and complex cannot be determined Answer :A

Discussion

8058.	Find the value of sintheta in terms of sectheta.
Answer» `(1)/(SQRT(SEC^(2)-1))` `(sec^(2)theta)/(sqrt(sec^(2)-1))` `sqrt(sec^(2)theta-1)/(SECTHETA)` `sqrt(sec^(2)theta-1)` ANSWER :C

Discussion

8059.	16 days after the 20% typist left the job it was decided to complete the work on time by increasing the work-force again. By how much percentage increase in work-force is requried?
Answer» `100%` `50%` `200%` NONE of these Answer :D

Discussion

8060.	A and B are said to spend their income at 6(1)/(4)%per annum, If they do so for 8 years and 10 years then they left with equal amount after starting. Find the ratio of their incomes.
Answer» ANSWER :`(A)/(B)=(225)/(256)`

Discussion

8061.	Find the remainder when 38 + 71+ 85 is divided by 16.
Answer» Solution :When we divided 38,71 and 85 we obtain the respective REMAINDERS as 6,7 and 5. Now we can obtain the requried remainder by dividing the sum of remainders (i.e.,6+7+5=18) by 16, which is 2 instead of DIVING the sum of actual given NUMBERS (i.e., 38+71+85=194) by 16, which also gives US the same reminder 2.

Discussion

8062.	Between 6 am and 7 am when the two hands of a clock coincide.
Answer» ANSWER :`6:32:43`

Discussion

8063.	A house and a shop were sold for Rs. 1 lakh each, In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in :
Answer» ANSWER :`(1)/(12)` LAKH

Discussion

8064.	Some times ago the height of my son 90 cm at the end of 1996. When I have observed that his height is increasing equally every year. After seven years in the last month of 2003. I have found that his height was 1/9 th more than that at the end of 2002. Can you find the height of my son at the end of 2008 ?
Answer» 360 cm 450 cm 250 cm 270 cm Answer :B

Discussion

8065.	A boy on being asked what 6/7 of a certain fraction was, made the mistake of dividing the fraction by 6/7 and so got an answer which exceeded the correct answer by 13/70 Find the fraction :
Answer» `(2)/(3)` `(3)/(5)` `(4)/(5)` `(7)/(9)` Answer :B

Discussion

8066.	If secx=P, cosecx=Q, then:
Answer» `P^2+Q^2=PQ` `P^2+Q^2=P^2Q^2` `P^2-Q^2=P^2Q^2` `P^2+Q^2=-P^2Q^2` ANSWER :B

Discussion

8067.	A man sells two horses for Rs. 38. The cost price of the first of equal to the selling price of the second . If the first is sold at 10% loss and the second at 25%gain, what is his total gain or loss (in rupees)?
Answer» 0.2 20 2 1 Answer :C

Discussion

8068.	A man sells a scooter to his friend at 10% loss. If the friend sells it for Rs. 54000 and gains 20%. Find the original cost price of the scooter.
Answer» ANSWER :50000 RS

Discussion

8069.	Find the number of integral values of p if the roots of the equation2x^2+p^2-(5x+6p)+8=0 are of opposite sign.
Answer» 1 2 3 6 Answer :A

Discussion

8070.	The sum of (2^2+4^2+6^2+…+100^2)-(1^2+3^2+5^2+…+99^2) is :
Answer» 5555 5050 888 222 Answer :B

Discussion

8071.	If x, y ,z are in G.P. and a^x = b^y = c^z , then :
Answer» `log_b a=log_c B` `log_b a=log_a C ` `log_c b=log_a c ` none Answer :A

Discussion

8072.	The value of a diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into three pieces with weights in the ratio of 3 : 4 : 5 thus a loss of ₹ 9.4 lakh is incurred. What is the actual value of diamond :
Answer» 28.8 lakh 13.5 lakh 14.4 lakh 18.8 lakh Answer :C

Discussion

8073.	Aman Verma and Mini Mathur jointly host a TV programme in which one day n guests attended the show. There each guest shakes hands with every other guest and each guest has to shake hand with each of the hosts. If there happens to be total 65 shake hands, find the number of guests attended the show.
Answer» 13 14 10 9 Answer :C

Discussion

8074.	750.0003 /19.999 = ?
Answer» a. 49 b. 18 c. 22 d. 38 Answer :D

Discussion

8075.	The radian measure of 63^(@)14'51" is
Answer» `((2811pi)/(8000))^("C")` `((3811pi)/(8000))^("c")` `((4811pi)/(8000))^("c")` `((5811pi)/(8000))^("c")` ANSWER :A

Discussion

8076.	Let A be a pyramid on a square base and B be a cube. let a,b and c denote the number of edges, number of faces and number of comers, respectively. Then, the result a = b + c is true for
Answer» a.only A b.only B c.both A and B d.neither A nor B Answer :D

Discussion

8077.	If (sin^(4)alpha)/a +(cos^(4)alpha)/b = 1/(a+b), show that sin^(8)alpha/a^(3) +cos^(8)alpha/b^(3) =1/(a+b)^(3)
Answer» `(1)/((a+B)^(3))` `(a^(2)b^(2))/((a+b)^(2))` `(a^(3)b^(3))/((a+b)^(3))` `(ab)/(a+b)` Answer :A::B::C

Discussion

8078.	Hari Lal and Hari Prasad have equal amounts. Hari Lal invested all his amount at 10% compounded annually for 2 years and Hari Prasad invested 1//4 at 10% compound interest (annually) and rest at r% per annum at simple interest for the same 2 years period. The amount received by both at the end of 2 year is same. What is the value of r?
Answer» `14%` `12.5%` `10.5%` `11%` ANSWER :C

Discussion

8079.	The ratio of milk and water in a mixture is3 : 8. We added x lt of milk to the mixture then ratio becomes 5 : 4and we added 18 lt water to the mixture, then ratio becomes4 : 5. Find the value of x.
Answer» a. 26 lt b. 25 lt c. 28 lt d. 21 lt Answer :B

Discussion

8080.	A train crosses a man coming from the opposite direction in 7.5 sec.if the speed of man be 10m/s and speed of train is 20 m/s find the length of the train.
Answer» ANSWER :225 m

Discussion

8081.	If 653xy is divisible by 80 then the value of x + y is :
Answer» 2 3 4 6 Answer :D

Discussion

8082.	If tanA=(1)/(2),tanB=(1)/(3), then cos2A=?
Answer» SIN B sin 2B sin 3B cos 3B Answer :B

Discussion

8083.	A student finds the average of ten 2-digit numbers. While copying numbers, by mistake, he writes one number with its digits interchanged. As a result his answer is 1.8 less than the correct answer. The difference of the digits of the number, in which he made mistake, is :
Answer» 2 3 4 6 Answer :B

Discussion

8084.	A mixture of water and milk contains 80% milk. In 50 litre of such a mixture, how many litres of water is required to increase the percentage of water to, 50%?
Answer» 20 15 30 none of the above Answer :C

Discussion

8085.	If log2,log(2^x-1)a n dlog2log(2^x+3)are in A.P., write the value of xdot
Answer» 2 3 `log_2 3` `log_2 5` ANSWER :B

Discussion

8086.	On selling 25 articles a person incurred loss equal to cost price of 5 articles. Find profit/loss.
Answer» ANSWER :20% LOSS

Discussion

8087.	7x + 6y + 4z = 122 4x + 5y + 3z = 88
Answer» `x GT y` ` x lt y` ` x ge y` ` x le y` SOLUTION :` 7x+6y + 4z = 122 …………..(1)` ` 4x+5y+3z = 88 …………….(2)` ` 9x + 2y + x = 78 ……………….(3)` From (1) and (2) `rArr5x -2y = 4-(a)` From (2) and (3) ` rArr23x+y = 146 -(b)` From (a) and (b) ` rArr x = 6, y = 8`.Put VALUES in eqn (3) ` rArrz = 8`

Discussion

8088.	A dishonest retailer cheats his wholesaler.and customer both . He purchases 19% more from the wholesaler and sells 15% less while selling to its customer. What is, profit percentage by selling the goods at cost price?
Answer» `36.78%` `34%` `40%` `36.85%` ANSWER :C

Discussion

8089.	ABCD is a trapeziumin which AD\|\|BC, AB = 9 cm BC = 12 cmCD= 15 cm DA = 30 cm find the sum of diagonals'ssquare
Answer» ANSWER :786

Discussion

8090.	123xx123+77xx77+2xx123xx77=?
Answer» SOLUTION :`123xx123+77xx77+2xx123xx77` `=(123)^2+(77)^2+2xx123xx77` `=(123+77)^2 [(a+b)^2=a^2+b^2+2ab]` `=(200)^2=40000`

Discussion

8091.	Which is not a prime number?
Answer» 97 1001 127 101 Answer :B

Discussion

8092.	10 students are to be seated in two rows equally for the MOCK CAT in a room. There are two sets of papers, code A and code B. Each of the two rows can have only one set of paper but different that from the other row. In how many ways these students can be arranged?
Answer» 2775600 1200560 125600 7259600 Answer :D

Discussion

8093.	Adjoiningfigure shows a square ABCD in which O is the point of intersections of diagonals AC and BD . Four squares of maximum possible area are formedinside each four triangles AOB , BOC , COD and AOD .What is the total area of these 4 squares ?
Answer» `400 CM^(2) ` `100 cm^(2) ` `80 cm^(2) ` none of these ANSWER :D

Discussion

8094.	How many kilograms of tea worth Rs 25 per kg must be blended with 30kg of tea worth Rs 30 per kg, so that by selling the blended variety at Rs 30 per kg, there should bea gain of 10%?
Answer» 36 KG 40 kg, 15 kg 32 kg 42 kg Answer :A

Discussion

8095.	Find all the values of p for which both roots of the equation x^2+x+p=0 exceed the quantity p.
Answer» `plt-1/2` `plt1/4` `PGT0` `plt-2` ANSWER :D

Discussion

8096.	A team of 11 cricketers containing 1 wicket keeper, 2 bowlers, 3 all rounders and 5 batsmen, is to be formed from a group of 25 cricketers containing 2 wicket keepers, 8 bowlers, 5 allrounders and 10 batsmen ?
Answer» 141120 111240 101240 none of (a), (B),( C) ANSWER :A

Discussion

8097.	a"@"b=(a+b)(ab+b) a#b=(a-b)(ab-b) aDeltab=(a"@"b)-(a#b) Find the value of (1"@"1)Delta(2#2)
Answer» 5 22 17 none of these Answer :D

Discussion

8098.	As man is known to speak truth 3 out of 4 times. He throws a die andreports that it is a six. Find the probability that it is actually a six.
Answer» `3/8` `5/8` `7/8` `1/12` ANSWER :A

Discussion

8099.	If sectheta+tantheta=p, then sectheta=?
Answer» <P>`(1)/(2)(p+(1)/(p))` `p-(1)/(p)` `2(p+(1)/(p))` `-p+(1)/(p)` ANSWER :A

Discussion

8100.	A man sells a scooter to his friend at 10% loss. If the friend sells it for Rs. 54000 andgains 20%. Find the original cost price of the scooter.
Answer» ANSWER :RS. 50000

Discussion

Explore topic-wise InterviewSolutions in .

How many spheres of radius 1.5 cm can be cut out of a wooden cube of edge 9 cm ?

Find the unit digit of 123 + 345 + 780 + 65 + 44.

(sqrt3)/(sqrt3 + sqrt2) - (3sqrt3)/(sqrt5 +sqrt2) + (2sqrt2)/(sqrt5 + sqrt3)is equal to

If p and q are two distinct inegers such that p^2 - pq = 0 then we can deduce that

The ratio of the roots of the equation ax^(2)+bx+c=0 is same as the ratio of the roots of equation px^(2)+qx+r=0. If D_(1) and D_(2) are the discriminants of ax^(2)+bx+c=0 and px^(2)+qx+r=0 respectively then D_(1):D_(2)=

If a+b+c=13 What is the maximum value of (a-3)(b-2)(c+1)?

If the equation ax^(2)+2bx+c=0 has real roots, a,b,c being real numbers and if m and n are real numbers such that m^(2)gtngt0 then prove that the equation ax^(2)+2mbx+nc=0 has real roots.

Find the value of sintheta in terms of sectheta.

16 days after the 20% typist left the job it was decided to complete the work on time by increasing the work-force again. By how much percentage increase in work-force is requried?

A and B are said to spend their income at 6(1)/(4)%per annum, If they do so for 8 years and 10 years then they left with equal amount after starting. Find the ratio of their incomes.

Find the remainder when 38 + 71+ 85 is divided by 16.

Between 6 am and 7 am when the two hands of a clock coincide.

A house and a shop were sold for Rs. 1 lakh each, In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in :

A boy on being asked what 6/7 of a certain fraction was, made the mistake of dividing the fraction by 6/7 and so got an answer which exceeded the correct answer by 13/70 Find the fraction :

If secx=P, cosecx=Q, then:

A man sells two horses for Rs. 38. The cost price of the first of equal to the selling price of the second . If the first is sold at 10% loss and the second at 25%gain, what is his total gain or loss (in rupees)?

A man sells a scooter to his friend at 10% loss. If the friend sells it for Rs. 54000 and gains 20%. Find the original cost price of the scooter.

Find the number of integral values of p if the roots of the equation2x^2+p^2-(5x+6p)+8=0 are of opposite sign.

The sum of (2^2+4^2+6^2+…+100^2)-(1^2+3^2+5^2+…+99^2) is :

If x, y ,z are in G.P. and a^x = b^y = c^z , then :

The value of a diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into three pieces with weights in the ratio of 3 : 4 : 5 thus a loss of ₹ 9.4 lakh is incurred. What is the actual value of diamond :

Aman Verma and Mini Mathur jointly host a TV programme in which one day n guests attended the show. There each guest shakes hands with every other guest and each guest has to shake hand with each of the hosts. If there happens to be total 65 shake hands, find the number of guests attended the show.

750.0003 /19.999 = ?

The radian measure of 63^(@)14'51" is

Let A be a pyramid on a square base and B be a cube. let a,b and c denote the number of edges, number of faces and number of comers, respectively. Then, the result a = b + c is true for

If (sin^(4)alpha)/a +(cos^(4)alpha)/b = 1/(a+b), show that sin^(8)alpha/a^(3) +cos^(8)alpha/b^(3) =1/(a+b)^(3)

The ratio of milk and water in a mixture is3 : 8. We added x lt of milk to the mixture then ratio becomes 5 : 4and we added 18 lt water to the mixture, then ratio becomes4 : 5. Find the value of x.

A train crosses a man coming from the opposite direction in 7.5 sec.if the speed of man be 10m/s and speed of train is 20 m/s find the length of the train.

If 653xy is divisible by 80 then the value of x + y is :

If tanA=(1)/(2),tanB=(1)/(3), then cos2A=?

A student finds the average of ten 2-digit numbers. While copying numbers, by mistake, he writes one number with its digits interchanged. As a result his answer is 1.8 less than the correct answer. The difference of the digits of the number, in which he made mistake, is :

A mixture of water and milk contains 80% milk. In 50 litre of such a mixture, how many litres of water is required to increase the percentage of water to, 50%?

If log2,log(2^x-1)a n dlog2log(2^x+3)are in A.P., write the value of xdot

On selling 25 articles a person incurred loss equal to cost price of 5 articles. Find profit/loss.

7x + 6y + 4z = 122 4x + 5y + 3z = 88

A dishonest retailer cheats his wholesaler.and customer both . He purchases 19% more from the wholesaler and sells 15% less while selling to its customer. What is, profit percentage by selling the goods at cost price?

ABCD is a trapeziumin which AD||BC, AB = 9 cm BC = 12 cmCD= 15 cm DA = 30 cm find the sum of diagonals'ssquare

123xx123+77xx77+2xx123xx77=?

Which is not a prime number?

10 students are to be seated in two rows equally for the MOCK CAT in a room. There are two sets of papers, code A and code B. Each of the two rows can have only one set of paper but different that from the other row. In how many ways these students can be arranged?

Adjoiningfigure shows a square ABCD in which O is the point of intersections of diagonals AC and BD . Four squares of maximum possible area are formedinside each four triangles AOB , BOC , COD and AOD .What is the total area of these 4 squares ?

How many kilograms of tea worth Rs 25 per kg must be blended with 30kg of tea worth Rs 30 per kg, so that by selling the blended variety at Rs 30 per kg, there should bea gain of 10%?

Find all the values of p for which both roots of the equation x^2+x+p=0 exceed the quantity p.

A team of 11 cricketers containing 1 wicket keeper, 2 bowlers, 3 all rounders and 5 batsmen, is to be formed from a group of 25 cricketers containing 2 wicket keepers, 8 bowlers, 5 allrounders and 10 batsmen ?

a"@"b=(a+b)(ab+b) a#b=(a-b)(ab-b) aDeltab=(a"@"b)-(a#b) Find the value of (1"@"1)Delta(2#2)

As man is known to speak truth 3 out of 4 times. He throws a die andreports that it is a six. Find the probability that it is actually a six.

If sectheta+tantheta=p, then sectheta=?

A man sells a scooter to his friend at 10% loss. If the friend sells it for Rs. 54000 andgains 20%. Find the original cost price of the scooter.