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Question 1 of 5
1. Question
Q1-Let x and y be positive integers such that x˃y. The expression 3x + 2y and 2x +3y, when divided by 5 leave remainders 2 and 3, respectively. What is the remainder when (x-y), is divided by 5?
Correct
Ans: a
We have, 3x+2y is divided by 5 remainder is 2.
∴3x+2y=5q+2 ……………………..(1)
And 2x +3y is divided by 5 remainder is 3.
∴2x + 3y = 5m+3 ……………………..(2)
Subtract Eq. (2 ) from Eq.(1) , we get
x-y = 5(q-m)-1
x-y=5(q-m)-5+4
x-y=5(q-m-1)+4
∴x-y is divided by 5 remainder is 4.
Incorrect
Ans: a
We have, 3x+2y is divided by 5 remainder is 2.
∴3x+2y=5q+2 ……………………..(1)
And 2x +3y is divided by 5 remainder is 3.
∴2x + 3y = 5m+3 ……………………..(2)
Subtract Eq. (2 ) from Eq.(1) , we get
x-y = 5(q-m)-1
x-y=5(q-m)-5+4
x-y=5(q-m-1)+4
∴x-y is divided by 5 remainder is 4.
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Question 2 of 5
2. Question
If (x + 1) is the HCF of Ax2 + Bx +C and Bx2+Ax + C, where A # B, then the value of C is
Correct
Ans: C
Since, (x + 1) is the HCF of Ax2 + Bx + C and Bx2+ Ax +C
∴A(-1)++ B(-1)+C = 0
⇒ A-B+C = 0 ⇒ C = B- A
or B(-1)2+ A(-1) + C = 0
⇒ B – A+C=0 ⇒C = A-B
Because A# B
∴C = A-B
Incorrect
Ans: C
Since, (x + 1) is the HCF of Ax2 + Bx + C and Bx2+ Ax +C
∴A(-1)++ B(-1)+C = 0
⇒ A-B+C = 0 ⇒ C = B- A
or B(-1)2+ A(-1) + C = 0
⇒ B – A+C=0 ⇒C = A-B
Because A# B
∴C = A-B
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Question 3 of 5
3. Question
In a fire range, 4 shooters are firing at the respective targets. The first, the second, the third and fourth shooters hit the target once in every 5 s, 6 s, 7s and 8 s, respectively. If all of them hit their target at 9 : 00 am, when will they hit their target together again?
Correct
Ans-c
Time after which they will hit the target again together
= LCM (5, 6, 7 and 8)
= 5 × 3 × 7 × 2 × 4
= 840 s
They will hit target together = 840/60 = 14 min.
So, they will hit together again at 9:14 am.
Incorrect
Ans-c
Time after which they will hit the target again together
= LCM (5, 6, 7 and 8)
= 5 × 3 × 7 × 2 × 4
= 840 s
They will hit target together = 840/60 = 14 min.
So, they will hit together again at 9:14 am.
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Question 4 of 5
4. Question
The number 58129745812974 is divisible by
Correct
Ans: a
Number 58129745812974 is divisible by 11 as the difference of sum of all digits at even and odd places is 0.
Incorrect
Ans: a
Number 58129745812974 is divisible by 11 as the difference of sum of all digits at even and odd places is 0.
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Question 5 of 5
5. Question
When a ball bounces, it rise to 2/3 of the height from which it fell. If the ball is dropped from a height of 36 m, then how high will it rise at the third bounce?
Correct
Ans: a
After first bounce, height of ball = (2/3)1 x36
And after third bounce, height of ball = (2/3)3 x36
= (8/27)x36 =[ (8/4)/3] = 32/3m = =10(2/3)m
Hence, the required height at third bounce is 10(2/3)m.
Incorrect
Ans: a
After first bounce, height of ball = (2/3)1 x36
And after third bounce, height of ball = (2/3)3 x36
= (8/27)x36 =[ (8/4)/3] = 32/3m = =10(2/3)m
Hence, the required height at third bounce is 10(2/3)m.
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