Which one set of letters when placed sequentially in the blanks will complete the following series correctly ?
a _ c a _ b _ a _ _ b c _ a b _ c c _ a a b _ c _
A's speed = 24 x (5/18) m/s = 20/3 m/s
Time taken by A to cover 500 m = 500/(20/3) = 75 sec
.'. Time taken by B to cover 460 m = (75+15) = 90 sec.
Hence, B's speed = (460/90) x (18/5) = 92/5 m/s = 18.4 km/h
Correct Option 5)
A bag contains 5 Blue, 6 Green, 3 Yellow and 4 Red balls. If four balls are selected at random, then what is the probability that there exist at least two red balls ?
Total ways of selecting 4 balls out of 18 = 18C4 = 3060
Out of the 4 balls at least 2 red colour is possible when, there are (2 Red+2 Non-Red) or (3 Red + 1 Non-Red) Or All Four Red
.'. Ways of selecting at least 2 red balls = (4C2 x 14C2) + (4C3 x 14C1) + 4C4 = 546 + 56 + 1 = 603
Hence, required probability = 603/3060 = 67/340
Correct Option 7)
In a school, a student can opt the language subject out of English, Hindi and Sanskrit either single or in a combination. 50 students opted English, 62 Hindi and 42 Sanskrit. If there are total 78 students and only 12 opted for all three languages, then the number of students who opted for exactly two languages is
The average weight of a group of boys is 48 kg. If 8 boys of average weight 51 kg leave and 3 boys of average weight 42 kg join the group, then the average weight of group decreases by 1 kg 50 gm. Find the initial number of boys in a group
Let there are 'n' boys in a group initially, then their total weight=48n
When, 8 boys of average weight 51 kg leave and 3 boys of average weight 42 kg join the group, then of boys left = n-8+3 = n-5
New average of a group = (48n - 8*51 + 3*42) / (n-5) = (48 - 1.05)
48n - 408 + 126 = 46.95n - 234.75
1.05n = 47.25
n = 45
Correct Option 5)
A retailer sells two items having cost prices Rs. 1200 and Rs. 1500 respectively. He offers discount of 8% on both items. The ratio between the marked price of these items is 8:9 respectively. If the total profit earned by a retailer is Rs. 428, then the difference between the marked price (in Rs) of two items is
Given, CP are Rs. 1200 and Rs. 1500
Let the MP be 8x and 9x respectively.
Then with 8% discounts, MP are (92/100)*8x and (92/100)*9x
.'. Profits are (92/100)*8x - 1200 and (92/100)*9x - 1500
Given, sum of profits = 428
â‡’ (92/100)*8x - 1200 + (92/100)*9x - 1500 = 428
(23/25)*17x = 3128
x = 200
Hence, difference of marked price = 9x - 8x = x = 200
Correct Option 9)
Given, arithmetic sequence 57, 54, 51, ....., k. Here first term a=57, Difference d=-3, Last term=k, Sum of all terms=-123
Sum of the n terms of an A.P. = (n/2)[2a + (n-1)d]
-123 = (n/2)[2*57 + (n-1)*(-3)]
â‡’ nÂ² - 39n - 82 = 0
(n-41)(n+2) = 0
Considering positive value of number of terms, n=41 â‡’ k=41th term of the series.
Now, n th term of an AP = a + (n-1)d
.'. k = 57 + 40*(-3) = -63
A number of light bulbs were purchased to illuminate a house. However, only 3/5 of them were needed and 72 leftover light bulbs were returned. If only 70% of the cost of those returned, or Rs. 11088, was reimbursed, how much money was spent on illuminating the house?
Bulbs used=3/5 .'. Bulbs returned=2/5
Let total bulbs=x, then (2/5)*x=72 â‡’ x=180
We know that Rs. 11088 represents 70% of the cost of 72 bulbs
.'. Full cost of 72 bulbs=(100/70)*11088=15840
Cost per bulb=15840/72=220
And cost which was not recovered=15840-11088=4752
Total cost = Cost(108 used bulbs) + Cost not recovered = 108*220 + 4752 = 28512 Rs.
It cost Rs. 1089 to paint all the surfaces of a cube at the rate of Rs. 1.5 per meter sq. If the same cube is cut to form three cuboids of equal volumes, then the cost of painting all the surfaces of any two of the cuboids so formed at the 50% more rate is
Surface area of a cube = 6aÂ², where a=side
Cost of painting = Surface Area*Rate per meter sq.
1089 = 6aÂ²*1.5
â‡’ aÂ²=121 or a=11
When the cube is cut to form three cuboids of equal volume, one of the edge (side) will be divided into 3 equal parts.
Then, sides of each cuboid are 11/3, 11 and 11 m.
.'. Surface area of a cuboid = 2*[(11/3)*11 + (11/3)*11 + 11*11] = 1210/3
New cost of painting = (150/100)*1.5 = 9/4/m sq.
Hence cost of painting 2 cuboids = 2*(9/4)*(1210/3) = 1815
Correct Option 5)
There is nothing more deceptive thing in mathematics than an obvious fact.
Conan.O.Doyle
Students attend our lectures, not because the mathematics we teach â€˜makes lots of funâ€™ for us, but because they believe they can learn some essential knowledge from us. And each of our young students has only one life to live. We should therefore be a