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1. What is the product of the irrational roots of the equation (2x-1)(2x-3)(2x-5)(2x-7)=9?
Answer: Option A
Explanation:Let 2x - 4 = y
=> (y + 3) (y + 1) (y - 1) (y - 3) = 9
=> (y^2 - 1) (y^2 - 9) = 9
=> y^4 - 10y^2 + 9 = 9
=> y^2 (y^2 - 10) = 0
=> y = 0 or ± √(10)
=> 2x - 4 = ± √(10)
=> x = (1/2) [4 ± √(10)]
=> product of the irrational roots
= (1/2)^2 * [4 + √(10)] [4 - √(10)]
= (1/4) * 6
= 3/2.
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2. The total population of a village is 5000. The number of males and females increases by 10% and 15% respectively and consequently the population of the village becomes 5600. what was the number of males in the village ?
Answer: Option B
Explanation:Lets Assume males and females as x and y respectively.
So total Population (x+y)=5000 -----------(1)
Incresed by 10% and 15%
so (x+(10x/100))+(y+15y/100)=5600
=> 110x/100+115y/100=5600
By Solving eq. (1) & (2)
y=2000 x=3000 (i.e Male population)
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3. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Answer: Option C
Explanation:n(s)= probability of drawing three balls out off 15 balls = 15c3
= (15*14*13)/(3*2*1)
= 455
n(E) = probability of getting red ball = 5c3
= (5*2*1)/(3*2*1)
=10
P(getting red ball)= n(E)/n(s)
= 10/455
= 2/91
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4. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer: Option C
Explanation:The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
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5. 6 people A,B,C,D,E and F sit around a table for dinner. Since A does not like C, he doesn't sit either opposite or beside C.B and F always like to sit opposite each other.
If A is beside F then who is are the two neighbours of B?
Answer: Option C
Explanation:ShortCut By :: SurabhiAs shown in this diagram , D and E are two neighbours of B.
As shown in this diagram , D and E are two neighbours of B.
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6. 6 people A,B,C,D,E and F sit around a table for dinner. Since A does not like C, he doesn't sit either opposite or beside C.B and F always like to sit opposite each other.
If D is adjacent to F then who is adjacent to C?
7. Complete the sequence A, E ,I ,M ,Q ,U , _ , _
Answer: Option B
Explanation:Y,C
after 3 letters of A then E arrives similarly after 3 letters of U then Y arrives and after 3 letters of Y then C arrives
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8. If
9. A person travels 6km towards west, then travels 5km towards north ,then finally travels6km towards west. Where is he with respect to his starting position?
10. If "football" is "cricket" ,"cricket" is "basketball" ,"basketball" is "volleyball","volleyball" is "khokho" and "khokho" is cricket, which is not a ball game?