The simplified value of \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right)...\left( 1-\frac{1}{99} \right)\left( 1-\frac{1}{100} \right)\]
8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?
Two pipes can fill a cistern in 14 h and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom. In how many hours the tank will be empty?
Two trains one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km an hour and the other at 67 km an hour. How long will they take to cross each other?
A path of uniform width surrounds a circular park. The difference of internal and external circumferences of this circular path is 132 m. Its width is \[\left( \text{Take}\,\,\pi =\frac{22}{7} \right)\]
The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in \[\text{c}{{\text{m}}^{2}}\]) of the triangle formed by joining the mid-points of this triangle is
A man sells two tables at the same price. On one he makes profit of 10% and on the other he suffers a loss of 10%. His loss per cent on the whole transaction is
In an examination 70% of the candidates passed in English, 80% passed in Mathematics, 10% failed in both the subjects. If 144 candidates passed in both, the total number of candidates was
Three numbers which are co-prime to one another are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is
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 man covered a certain distance at some speed. He had moved 3 km/h faster, he would have taken 40 min less. If he had moved 2 km/h slower, he would have taken 40 min more. The distance (in km) is
Diameter of a wheel is 3 cm. The wheel revolves 28 times in a minute. To cover 5.280 km distance, the wheel will take \[\left( \text{Take}\,\,\pi =\frac{22}{7} \right)\]
A candidate who gets 20% marks in an examination fails by 30 marks but another candidate who gets 32% gets 42 marks more than the pass marks. Then, the percentage of pass marks is
A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the coefficient of x only and obtained the roots \[-\,\,7\]and \[-1.\]Find the correct roots of the equation.
The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100 m from its base is \[45{}^\circ .\]If the angle of elevation of the top of complete pillar at the same point is to be \[60{}^\circ ,\] then the height of the incomplete pillar is to be increased by
If the height and diameter of a right circular cylinder are 32 cm and 6 cm respectively, then the radius of the sphere whose volume is equal to the volume of the cylinder is
A tank is 225 m long, 162 m broad with what velocity per second must water flow into it through an aperture 60 cm by 45 cm that the level may be raised by 20 cm in 5 h?
A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s. The time it take to fill the tank (in min) is
Jyoti bought a computer system for Rs. 40000. She sold it to Brajesh at a loss of 4%. If Brajesh sells it for Rs. 40320 to Yash, then the profit per cent earned by Brajesh is
If bought two old scooters for Rs. 9000. By selling one at a profit of 25% and the other at a loss of 20%, to neither gain nor loses. The cost of each scooter is
A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?
In a triangle ABC if \[A\equiv (1,2)\] and internal angle bisectors through B and C are \[y=x\] and \[y=-2x,\] then the in radius r of \[\Delta ABC\] is
List price of a video cassette is Rs. 100. A dealer sells three video cassettes for Rs. 274.50 after allowing discount at certain rate. The rate of discount allowed is
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
A student walks from his house at 2 - km/h and reaches his school late by 6 min. Next day, be increases his speed by 1 km/h and reaches 6 min before school time. How far is the school from his house?
A train overtakes two persons walking in the same direction in which the train is going. These person are walking at the rate of 2 km/h and 4 km/h and the train passes them completely in 9 s and 10 s, respectively. The length of the train is
Two pipes A and B can fill a tank in 15 min and 20 min, respectively. Both the pipes are opened together. But, after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Two trains A and B start running together from the same point in the same direction at 60 km/h 72 km/h, respectively. If the length of each train is 240 m, how long will it take for the train B to cross train A?
Directions: Study the following table carefully and answer the questions given below Number of Five Types of Computers Produced and Rejected (for defects) by a Company Over the Years (in thousand)
Computer Year
P
Q
R
S
T
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
1995
20
2
50
3
15
0.5
80
5
60
4
1996
35
3
45
2
20
0.55
75
4
58
4
1997
15
0.5
40
2.5
17
0.75
58
2
62
3.5
1998
25
0.25
42
2.3
25
1.5
65
3
40
1.5
1999
30
1.5
48
2.5
30
2.0
68
3
45
2
2000
27
1.5
41
2.1
26
1.75
72
3.5
50
2.5
In the case of Q type of computers, in which year was the ratio of rejection to production the highest among the given years?
Directions: Study the following table carefully and answer the questions given below Number of Five Types of Computers Produced and Rejected (for defects) by a Company Over the Years (in thousand)
Computer Year
P
Q
R
S
T
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
1995
20
2
50
3
15
0.5
80
5
60
4
1996
35
3
45
2
20
0.55
75
4
58
4
1997
15
0.5
40
2.5
17
0.75
58
2
62
3.5
1998
25
0.25
42
2.3
25
1.5
65
3
40
1.5
1999
30
1.5
48
2.5
30
2.0
68
3
45
2
2000
27
1.5
41
2.1
26
1.75
72
3.5
50
2.5
In the case of T type of computers, in which year was the ratio of rejection to production the lowest among the given years?
Directions: Study the following table carefully and answer the questions given below Number of Five Types of Computers Produced and Rejected (for defects) by a Company Over the Years (in thousand)
Computer Year
P
Q
R
S
T
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
Produced
Reject
1995
20
2
50
3
15
0.5
80
5
60
4
1996
35
3
45
2
20
0.55
75
4
58
4
1997
15
0.5
40
2.5
17
0.75
58
2
62
3.5
1998
25
0.25
42
2.3
25
1.5
65
3
40
1.5
1999
30
1.5
48
2.5
30
2.0
68
3
45
2
2000
27
1.5
41
2.1
26
1.75
72
3.5
50
2.5
What was the difference in number of R type of computers rejected between year 1996 and year among the given years 1997?
Directions: Study the following graph and answer the questions given below.
If in April the crude oil price would have been lesser than the given by Rs. 223 per metric tonne, then how much would have been the percentage increase in