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Question 1. For what values of x will the following inequality hold true 3|a1|+a27>0 ?
  1.    (−∞,−5)∪(2,∞)
  2.    (−∞,−1)∪(2,∞)
  3.    (−∞,−1)∪(4,∞)
  4.    (−∞,−5)∪(4,∞)
Answer: Option B
: B

Let a = 3. the inequality holds good as 3(2)+9-7>0
Options c & d are eliminated.
Let a= -2, the inequality holds good as 3(3)+4-7>0
Option a is eliminated Answer = b

Question 2. There are 170 people each one of them likes at least one of the fruits, 60 like grapes, 40 like papaya, 50 like watermelon and 70 like pomegranate. If there are exactly 10 people who like all four fruits. Then, find the maximum number of people who like only watermelon: -
  1.    40
  2.    30
  3.    35
  4.    38
Answer: Option A
: A

Maximum possible value is 40.
Option(a). The distribution in this case is as follows.

Question 3. If Y is a prime number greater than 10000 and it leaves a remainder of 2 when divided by 3, then what remainder does Y leave on division by 6?

___

: The number is of the form 3y+ 2 and as it is a prime number, it is odd.
y is odd and is of the form 2k+1.
3y+ 2 = 3(2k+ 1) + 2 = 6k+5

The number leaves a remainder of 5 when divided by 6.

Question 4. A hare completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. The hare then cycles up the mountain (the same distance) at an average speed of (x - 8) meters per second. If the ride up the mountain took 135 seconds longer than its run down the mountain, what was the hare's average speed, in meters per second, during its downhill run?
  1.    10
  2.    15
  3.    20
  4.    25
Answer: Option C
: C

Approach : Reverse gear
Since the difference in time is given, and

Time=DistanceSpeed

300x8300x±10=135
Now going from answer options, we can easily substitute and see which value satisfies this equation. Option (c) is the correct answer choice.

Question 5. Disha wants to paint her room a unique brown. For that she uses a certain violet paint which contains 30% blue pigment and 70% red pigment by weight. She mixes that violet paint with a certain green paint which contains 50% blue pigment and  50% yellow pigment. When these paints are mixed to produce the brown paint which she uses, it contains  40% blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?

 
  1.    2.8 gms
  2.    3.5 gms
  3.    4 gms
  4.    5.3 gms
Answer: Option B
: B

Use allegation Considering only the blue pigment in all the paints


Thus, 5gms of each paint is used .Weight of red paint =710×5=3.5 gms.Option (b)


Question 6. A GP consists of 500 terms. Sum of the terms occupying the odd places is P1 and the sum of the terms occupying the even places is P2. Find the common ratio?
  1.    p2p1
  2.    p1p2
  3.    p2+p2p1
  4.    p2+p1p2
Answer: Option A
: A

Consider a simple GP = 2, 4 with two terms Sum of terms occupying the odd places =2 and sum of terms occupying the even places =4 Thus, common ratio = 2 =p2p1.