Lakshya Education MCQs

Question: A beats B by 150 m in a race of 1000 m. B beats C by 100 m in a 1200m race. Approx by how many meters can A beat C in a race of 500 m?
Options:
A.110 m
B.150m
C.90 m
D.130 m
E.33128
Answer: Option A
: A

We can solve this question using ratios as follows:


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Question 1. Nupur and Sheetal play a game "eight time coin throw”. If the fair coin shows heads, Nupur gets a point & if it shows tails, Sheetal gets a point. After eight throws, they compare their scores. What is the probability that the game will be a tie?
  1.    18
  2.    19
  3.    35128
  4.    7128
  5.    33128
Answer: Option C
: C

For a tie, there would be 4 heads and 4 tails. Probability of "4” heads in 8 throws can be found using nCr pr qnr = 8C4(12)4(12)4 = 35128
Question 2. I usually take 72 minutes to reach college. On one fateful day, after traveling 13rd of the distance, I realized that I left my ID card at home and returned to pick it up and then went back to college. To reach on time, I increased my speed by 30 kmph from the point I turned back home till the time I reached college. Assuming that no time was lost at home, what is my usual speed?
  1.    20 kmph
  2.    30 kmph
  3.    10 kmph
  4.    15 kmph
  5.    33128
Answer: Option B
: B

Go from answer options .
Take a middle answer option.
Normal speed = 30kmph
Then distance between college and home = 30 ×7260=36 km
Also, since time =72 minutes, Speed = 30 kmph.
Distance travelled before leaving back =13 of 36 =12 km and 24 minutes.
Therefore, time wasted = 24 minutes. Time left to reach = 72 - 24 =48 minutes.
New Speed = 30+30=60 kmph
Distance ot be traveled = 48 km
Time taken =4860×60=48 minutes. Hence answer = option b.
Question 3. In an exciting finish to a T - 20 cricket match between MI and RCB, the MIs require 10 runs in the last 3 balls to win. If any one of the scores 0, 1, 2, 3, 4, 6 can be made from a ball and no wides or no-balls are bowled then in how many different sequences can batsmen make exactly 10?
  1.    36
  2.    21
  3.    35
  4.    22
  5.    33128
Answer: Option B
: B

A + B + C = 10, Where 0 ≤ A, B, C ≤ 6
Number of solution of given equation is (13C23×5C2). But A, B and C are not equal to 5. Number of cases which are not possible (5, 5, 0), (1, 4, 5) and (2, 3, 5). Total number of cases which are not possible = 3 + 6 + 6= 15. Total number of different sequences = 13C23×5C2- 15 = 21
Question 4. The figure below shows the plan of a town. A person "X" rides his bicycle from house at A to office at B, taking the shortest route.

The number of shortest paths that he can choose is: 



 
  1.    168
  2.    336
  3.    208
  4.    308
Answer: Option B
: B

Number of ways "X” can go from A to C= 8C3 and from C to B= 4C2. Then the total number of shortest paths that he can choose is 8C3 ×4C2 = 336
Question 5. In a public school there is an increase in number of admissions every year. The number of students in 2000 was 780 and it increased to 3000 in the year 2005. Find the annual increase?
  1.    25%
  2.    31%    
  3.    39%
  4.    20%
  5.    33128
Answer: Option B
: B

We need to use Compound Annual Growth Rate (CAGR) for this question :
Conventionally, CAGR is computed using the formula [(FinalInitial)1n1]
Using the reverse gear approach ,we can obtain the answer much faster
FinalInitial=30007803.8

We need to look for something close to 3.8 in the answer options
here n = 5.
Choose a middle answer option,assuming the answer is 30%

(1.3)5=(1.3)2×(1.3)3=17×17×1.3=3.75.
Hence, the answer will be slightly higher than this = 31%
Option (b)

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