Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 20 ] :
The value of \(2\sin 15° \cos 15°\) is:
Your Answer : (Not Answered)
Correct Answer : B
This expression is in the form of the double angle identity \(\sin(2A) = 2\sin A \cos A\).
Here, A = 15°.
The expression equals \(\sin(2 \times 15°) = \sin(30°)\).
The value of \(\sin 30°\) is 1/2.
What is the cardinality of the set of all vowels in the English alphabet?
Your Answer : (Not Answered)
Correct Answer : C
The set of vowels in the English alphabet is A = {a, e, i, o, u}.
The cardinality of a set is the number of elements it contains.
The set A has 5 elements. Therefore, its cardinality is 5.
In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics?
Your Answer : (Not Answered)
Correct Answer : B
Let M be the set for Math teachers and P for Physics teachers.
n(M ∪ P) = 20, n(M) = 12, n(M ∩ P) = 4.
We use the formula n(M ∪ P) = n(M) + n(P) - n(M ∩ P).
20 = 12 + n(P) - 4
20 = 8 + n(P)
n(P) = 12.
A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in:
Your Answer : (Not Answered)
Correct Answer : A
LCM of 18 and 24 is 72. Total work = 72 units. A's rate=4, B's rate=3 units/day. Work done in 8 days together = \((4+3) \times 8 = 56\) units. Remaining work = 72 - 56 = 16 units. Time for B to finish this = 16 / 3 = 5 1/3 days.
If the sum of 5 terms of an A.P. is 75, find the 3rd term.
Your Answer : (Not Answered)
Correct Answer : B
For an A.P. with an odd number of terms, the sum is equal to the number of terms multiplied by the middle term. Here, the sum of 5 terms is 75. The middle term is the 3rd term. So, \(5 \times a_3 = 75 \Rightarrow a_3 = 75/5 = 15\).
What is the remainder when \(1! + 2! + 3! + ... + 100!\) is divided by 8?
Your Answer : (Not Answered)
Correct Answer : A
We need to find the remainder of the sum when divided by 8. Let's look at the remainders of the first few factorials. \(1! = 1\) (rem 1). \(2! = 2\) (rem 2). \(3! = 6\) (rem 6). \(4! = 24\). Since 24 is a multiple of 8, the remainder is 0. For any \(n \ge 4\), \(n!\) contains the factors 4 and 2, so it is a multiple of 8. The remainder for all subsequent factorials will be 0. We only need to sum the remainders of the first three factorials: \(1 + 2 + 6 = 9\). The remainder of \(9 \div 8\) is 1.
A differential equation not depending on x(variable) is called
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
Your Answer : (Not Answered)
Correct Answer : A
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Your Answer : (Not Answered)
Correct Answer : A
No answer description available for this question.
P can run 100m in 20 second and Q in 25 seconds. P beats Q by
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
A field with equal sides of 40m is full of grass. One cow is tied to each corner of the field by a rope of 14m. How much grass will not be eaten by those 4 cows?
Your Answer : (Not Answered)
Correct Answer : A
No answer description available for this question.
A mixture consists of some amount of sandalwood oil and 240 liters of water. It is priced at Rs. 275 per liter. Sandalwood oil is priced Rs. 325 per liter. How much oil is there in the mixture?
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
Your Answer : (Not Answered)
Correct Answer : A
Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Your Answer : (Not Answered)
Correct Answer : C
M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Your Answer : (Not Answered)
Correct Answer : C
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Rohit covers one-fourth of the total distance at 20 km/hr, one-fourth at 10 km/h and rest of his journey at 80 km/h. Find Rohit’s average speed for the whole distance?
Your Answer : (Not Answered)
Correct Answer : A
No answer description available for this question.
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Your Answer : (Not Answered)
Correct Answer : D
| Part filled by (A + B) in 1 minute = |  |
1 | + | 1 |  |
= | 1 | . |
| 60 | 40 | 24 |
Suppose the tank is filled in x minutes.
| Then, | x | |
1 | + | 1 | |
= 1 |
| 2 | 24 | 40 |
 |
x | x | 1 | = 1 |
| 2 | 15 |
x = 30 min.
The value of \(5^{\frac{1}{4}}\times(125)^{0.25}\) is:
Your Answer : (Not Answered)
Correct Answer : C
\(5^{0.25}\times(5^3)^{0.25}=5^1=5\)
Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay ?
Your Answer : (Not Answered)
Correct Answer : B
Let the present ages of Ajay and Vijay be ' \(A\) ' and ' \(V\) ' years respectively.
\(\Rightarrow A-8= \frac{4}{3}\left ( V-8 \right )\) and \( A + 8 =\frac{6}{5}\left ( V-8 \right )\)
\(\Rightarrow\frac{3}{4}\left ( A-8 \right )= V-8\) and \(\frac{5}{6}\left ( A+8 \right )=V+8\)
\(V=\frac{3}{4}\left ( A-8 \right ) + 8=\frac{5}{6}\left ( A+8 \right )-8\)
\(\Rightarrow \frac{3}{4}A-6+8=\)\(\frac{5}{6}A + \frac{20}{3}- 8\)
\(\Rightarrow 10 -\frac{20}{3}=\)\(\frac{10}{12}A -\)\(\frac{9}{12}A\)
\(\Rightarrow \) \(\frac{10}{3}=\) \(\frac{A}{12}\)
\(\Rightarrow A = 40\)