1). Find the number of words formed with the letters of the word 'BOOKS' beginning with B and ending with S.
a) 15 ways
b) 14 ways
c) 6 ways
d) 12 ways
e) None of these
2). A box contains 5 Sony, 6 Samsung and 4 Sandisk pen drives. 3 pen drives are drawn at random. What is the probability that they are not of the same company?
a) 12/455
b) 501/455
c) 418/455
d) 91/455
3). The base of a triangular field is 660 metres and height 440 metres. If the charges for watering the field are at the rate of Rs.26.5 per sq hectometre, find the total cost to water the triangular field.
a) Rs. 389.69
b) Rs. 384.78
c) Rs. 588.69
d) RS. 374.78
e) None of these
4). In a mixture of milk and water the proportion of milk by weight was 70%. If in a 250-gm mixture 100 gm water was added, what would be the percentage of water?
a) 50%
b) 40%
c) 60%
d) 70%
e) 45%
5). Two pipes can fill a tank in 28 and 24 minutes respectively and a waste pipe can empty 5 gallons per minute. All three pipes working together can fill the tank in 16 minutes. How much time is taken by the waste pipe to empty the full tank?
a) 50 min
b) 57 1/2 min
c) 66 1/2min
d) 67.2 min
e) 65.2 min
Directions (Q. 6-10): What value should come in place of question mark (?) in the following questions?
6). [3√(2197+3x13x14x27+2744) / (196+364+169)]1/3 = ?
a) 27
b) 1/9
c) 9
d) 1/3
e) 1/27
7). (28/9) × (17/8) ÷ (153/6) + [1 41/45] = ?
a) 1 23/135
b) 2 23/135
c) 3 27/29
d) 2 29/135
e) None of these
8). 28% of 3540 + 26% of 4550 + 24% of 5060 = ?
a) 3488.5
b) 3833.6
c) 3388.6
d) 3500
e) None of these
9). [(8 1/3) ÷ (175/27)] / (2 5/14) – (1 1/28) = ?
a) 36/37
b) 35/37
c) 35/36
d) 37/35
e) None of these
10). √(0.2304) x0.012x16 =?
a) 0.09467
b) 0.02216
c) 0.9858
d) 0.09565
e) None of these
Solution With Answer Key:
1). E)
We have to arrange 3 letters (O, O and K) out of which 'O' occurs two times. So, reqd no. = 3! / 2! = 3 ways
2). E)
The total number of pen drives = 5 + 6 + 4 = 15
n(S)= 15C3 = (15x14x13) / (3×2) = 455
Now, 3 pen drives out of 15 pen drives can be drawn in 455 ways.
If all 3 pen drives are of the same company
It Can be done in 5C3 + 6C3 + 4C3 = 10 + 20 + 4 = 34 ways
Probability that all 3 pen drives are not of the same company = 1 – (34/455) = (421/455)
3). B)
Area of the field
= (Base x Height) / 2 = (660 x 440)/2 sq metre
= (660 x 440)/( 2x100x100) sq metre
= 14.52 sq hectmetres
Cost of watering 1 sq hectometre = Rs.26.5
Cost of watering the field = 26.5 x 14.52 = Rs.384.78
4). A)
Proportion of milk in the mixture =250 x (70/100) = 175gm
Water = 75 gm
After 100 gm water added in mixture the percentage of water = (75 +100) / (250+100) x 100
= (175/350) x 100 = 50%
5). D)
Let the capacity of the tank be 336 litres
LMC of (28, 24 and 16 = 336)
Waste pipe empties the tank in (12 + 14 - 21) 5 litres per minute
Waste pipe empties the tank in (336/5) = 67.2 minutes
6). D)
We know that
a3 + 3ab (a+b) + b3 = (a+b)3
? = [ 3√(2197+3x13x14x27+2744) / (196+364+169)]1/3
= [ 3√(13+14)3 /729]1/3
= (27/729)1/3 = 1/3
7). B)
? = (28/9) × (17/8) × (6/153) × (1 41/45)
= (7/27) + (86/45) = (35 + 258) / 135 = 293/135 = 2 23/135
8). C)
Solving by breaking method,
? = 20% of 3540 + 8% of 3540 + 20% of 4550 + 6% of 4550 + 20% of 5060 + 4% of 5060
= 708 + 283.2 + 910 + 273 + 1012 + 202.4
= 3388.6
9). A)
[(25/3)×(27/175)] / {(2-1) + [(5/14) – (1/28)]}
= (9/7) / {1+ [(10-1)/28] } = (9/7) / (37/28)
= (9/7) × (28/37) = 36/37
10). E)
? = √(0.23.4) x 0.012 x 16 = 0.48 x 0.012 x 16 = 0.09216
