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Question 1 of 5
1. Question
With a uniform speed, a car covers a distance in 8 h. Had the speed been increased by 4 km/h, the Same distance could have been covered in 7h and 30 min. What is the distance covered?
Correct
Ans: b
Let the distance between A and B be x km.
Case l Given, distance= xkm, speed= V km/h
and time =8h
Because Speed = Distance/Time
Because V = x/8
Case 2 If speed = (V + 4) km/h
And time = 7 (1/2)h = 15/2 h
Because V + 4 = (x/(15/2))
V+4 = (2x/15) ⇒ (x/8) + 4 = 2x/15 [ From Eq. (1)]
(2x/15) – (x/8) = 4 ⇒ x/ 120 = 4
∴x = 480 km
Incorrect
Ans: b
Let the distance between A and B be x km.
Case l Given, distance= xkm, speed= V km/h
and time =8h
Because Speed = Distance/Time
Because V = x/8
Case 2 If speed = (V + 4) km/h
And time = 7 (1/2)h = 15/2 h
Because V + 4 = (x/(15/2))
V+4 = (2x/15) ⇒ (x/8) + 4 = 2x/15 [ From Eq. (1)]
(2x/15) – (x/8) = 4 ⇒ x/ 120 = 4
∴x = 480 km
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Question 2 of 5
2. Question
Jar has ‘X’ L of mixture of apple juice and water the respective ratio of 5:1 and jar B has X’ L of mixture of mango juice and water in the respective ratio of 21 : 30. 30 L mixture was taken from jar and jar B each and mixed in jar C. If 12 L mixture was taken out from jar C, what was the final quantity of water in jar C?
Correct
Ans: c
Quantity of juice in jar A = 5/6 and
Quantity of water in jar A = 1/6
Now quantity of Mango – juice in jar
B=21/51
and quantity of water in jar B =30/ 51
Now, quantity of juice in jar C = Mixture in A and B
=5/6= 21/51 = 255=126/306=381/306
and quantity of water in jar
C=1/6+ 30 /51 = 51+180 /306 = 231 /306
Ratio of mixture in jar
C=381/306 + 231/306= 612/306= 2/1 = 2 : 1
Quantity of juice in 12 lit , of 2 mixture
= 2/ (2+1)x12 = 8 lit
Quantity of water = 12-8 = 4 lit
Incorrect
Ans: c
Quantity of juice in jar A = 5/6 and
Quantity of water in jar A = 1/6
Now quantity of Mango – juice in jar
B=21/51
and quantity of water in jar B =30/ 51
Now, quantity of juice in jar C = Mixture in A and B
=5/6= 21/51 = 255=126/306=381/306
and quantity of water in jar
C=1/6+ 30 /51 = 51+180 /306 = 231 /306
Ratio of mixture in jar
C=381/306 + 231/306= 612/306= 2/1 = 2 : 1
Quantity of juice in 12 lit , of 2 mixture
= 2/ (2+1)x12 = 8 lit
Quantity of water = 12-8 = 4 lit
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Question 3 of 5
3. Question
If 16 *8 n+2 = 2m, then m is equal to
Correct
Ans: d
Given that, 16 *8 n+2 = 2m
(2)4 *23(n+2) = 2m
2(4+3n+6) = 2m
2(3n+10)=2m
On comparing powers, we get
3n+10 = m
m = 3n+10
Incorrect
Ans: d
Given that, 16 *8 n+2 = 2m
(2)4 *23(n+2) = 2m
2(4+3n+6) = 2m
2(3n+10)=2m
On comparing powers, we get
3n+10 = m
m = 3n+10
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Question 4 of 5
4. Question
Consider the following statements
- Every integer is a rational number
- Every rational number is a real number
Which of the above statement(s) is /are correct?
Correct
Ans: c
- It is true that every integer is a rational number.
E.g. Set of integers, Z = [……..,13/1 , -2/1, -1/1, 0/1, 1/1, 2/1, 3/1,…….]
Which is of the form p/q, which also show rational numbers.
- It is also true that every rational number is a real number because a real number does not contain I (iota).
So, both statements are true.
Incorrect
Ans: c
- It is true that every integer is a rational number.
E.g. Set of integers, Z = [……..,13/1 , -2/1, -1/1, 0/1, 1/1, 2/1, 3/1,…….]
Which is of the form p/q, which also show rational numbers.
- It is also true that every rational number is a real number because a real number does not contain I (iota).
So, both statements are true.
-
Question 5 of 5
5. Question
The value of [1/(1 *4)] +[1/(4* 7)]+[1/(7* 10)]+……+[1/(16 * 19)], is
Correct
Ans: b
We have, [1/(1 *4)] +[1/(4*7)]+[1/(7* 10)]+……+[1/(16 * 19)]
Then nth term of 1.4.7,……is (3n-2) and of 4,7,10…….is(3n+1)
Hence, [1/(1 *4)] +[1/(4* 7)]+[1/(7* 10)]+……+[1/(16 * 19)]
= =
=1/3[(1/1-1/4)+(1/4-1/7)+….+(1/16-1/9)]
=1/3(1-1/9)=1/3 * 18/19 = 6/19
Incorrect
Ans: b
We have, [1/(1 *4)] +[1/(4*7)]+[1/(7* 10)]+……+[1/(16 * 19)]
Then nth term of 1.4.7,……is (3n-2) and of 4,7,10…….is(3n+1)
Hence, [1/(1 *4)] +[1/(4* 7)]+[1/(7* 10)]+……+[1/(16 * 19)]
= =
=1/3[(1/1-1/4)+(1/4-1/7)+….+(1/16-1/9)]
=1/3(1-1/9)=1/3 * 18/19 = 6/19
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