A 20 m long ladder is placed against a wall such that it reaches a height of 10 m. What is the angle the ladder makes with the ground?
If n(A) = 4 and n(B) = 3, what is the number of possible relations from A to B?
In a class of 120 students, 90 students passed in History, 65 students passed in Sociology and 30 students failed in both the subjects. How many students passed in both the subjects?
How many terms are there in the G.P. 3, 6, 12, ..., 384?
What is the unit digit of \(137^{13} \times 13!\) ?
What is the remainder when \(17^{200}\) is divided by 18?
What is the average of the first 15 odd numbers?
Find the one which does not belong to that group ?
Find the one which does not belong to that group ?
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
The true discount on a bill due 9 months hence at 12% per annum is Rs. Find the amount of the bill and its present worth.
Raj decides to sell his watch at 5% discount. But his brother buys it from him and he gives his brother 8% discount. Due to this Raj gets Rs. 45 less in the profit. What was the marked price of the watch?
The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.
At what time between 5.30 & 6 will the hands of a watch be at right angle?
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Ariver 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic metres) is
The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
Two trains for Delhi leave Jaipur at 8:30 am and 9:00 am and travel at 60 km/hr and 75 km/hr respectively. How many km from Jaipur will the two trains meet?
A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
A 20 m long ladder is placed against a wall such that it reaches a height of 10 m. What is the angle the ladder makes with the ground?
Your Answer : (Not Answered)
Correct Answer : A
The ladder is the hypotenuse (20 m) and the height on the wall is the opposite side (10 m).
Let θ be the angle with the ground.
\(\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{10}{20} = \frac{1}{2}\).
The angle whose sine is 1/2 is 30°.
If n(A) = 4 and n(B) = 3, what is the number of possible relations from A to B?
Your Answer : (Not Answered)
Correct Answer : D
A relation from A to B is a subset of the Cartesian product A × B.
The number of elements in the Cartesian product is n(A × B) = n(A) × n(B) = 4 × 3 = 12.
The number of possible relations is the number of possible subsets of A × B, which is the size of its power set.
Number of relations = \(2^{n(A \times B)} = 2^{12} = 4096\).
In a class of 120 students, 90 students passed in History, 65 students passed in Sociology and 30 students failed in both the subjects. How many students passed in both the subjects?
Your Answer : (Not Answered)
Correct Answer : C
Total students = 120.
Number of students who failed in both subjects = 30.
Number of students who passed in at least one subject = Total students - Failed in both = 120 - 30 = 90.
So, n(H ∪ S) = 90.
Given n(H) = 90 and n(S) = 65.
Using the formula n(H ∪ S) = n(H) + n(S) - n(H ∩ S):
90 = 90 + 65 - n(H ∩ S)
n(H ∩ S) = 155 - 90 = 65.
So, 65 students passed in both subjects.
How many terms are there in the G.P. 3, 6, 12, ..., 384?
Your Answer : (Not Answered)
Correct Answer : B
Here, \(a=3, r=2, a_n=384\). We use the formula \(a_n = ar^{n-1}\). \(384 = 3 \times 2^{n-1} \Rightarrow 128 = 2^{n-1}\). Since \(128 = 2^7\), we have \(2^7 = 2^{n-1}\). Equating the powers gives \(7=n-1\), so \(n=8\). There are 8 terms.
What is the unit digit of \(137^{13} \times 13!\) ?
Your Answer : (Not Answered)
Correct Answer : A
We look at the unit digit of each part of the product. The unit digit of 13! is 0, because 13 is greater than 5, so 13! contains factors of 2 and 5. Any number multiplied by a number ending in 0 will also end in 0. Therefore, the unit digit of the entire expression is 0, regardless of the unit digit of \(137^{13}\).
What is the remainder when \(17^{200}\) is divided by 18?
Your Answer : (Not Answered)
Correct Answer : A
We can use the remainder theorem. \(17\) can be written as \((18 - 1)\). So, we need to find the remainder of \((18-1)^{200} \div 18\).
Using the binomial expansion, every term except the last one will have 18 as a factor. The last term is \((-1)^{200}\).
\((-1)^{200} = 1\).
So the remainder is 1.
What is the average of the first 15 odd numbers?
Your Answer : (Not Answered)
Correct Answer : A
The sum of the first n odd numbers is \(n^2\).
The average of the first n odd numbers is \(\frac{\text{Sum}}{n} = \frac{n^2}{n} = n\).
So, the average of the first 15 odd numbers is 15.
Find the one which does not belong to that group ?
Your Answer : (Not Answered)
Correct Answer : B
Part, Cart, Dart and Mart are rhyming words, but Trap does not sound similarly.
Find the one which does not belong to that group ?
Your Answer : (Not Answered)
Correct Answer : C
20 = 4⊃2; + 4, 42 = 6⊃2; + 6, 58 = 7⊃2; + 9, 72 = 8⊃2; + 8 and 90 = 9⊃2; + 9.
20, 42, 72 and 90 can be expressed in n2 + n form but not 58.
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
The true discount on a bill due 9 months hence at 12% per annum is Rs. Find the amount of the bill and its present worth.
Your Answer : (Not Answered)
Correct Answer : D
No answer description available for this question.
Raj decides to sell his watch at 5% discount. But his brother buys it from him and he gives his brother 8% discount. Due to this Raj gets Rs. 45 less in the profit. What was the marked price of the watch?
Your Answer : (Not Answered)
Correct Answer : A
No answer description available for this question.
The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
At what time between 5.30 & 6 will the hands of a watch be at right angle?
Your Answer : (Not Answered)
Correct Answer : A
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand must gain 40 min
55 min. spaces are gained in 60 min.
40 min. spaces would be gained in (60/55 × 40) min. = 43 7/11 min.
Required time = 43(7/11) min. past 5.
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
Ariver 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic metres) is
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
Your Answer : (Not Answered)
Correct Answer : C
No answer description available for this question.
How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
Your Answer : (Not Answered)
Correct Answer : D
No answer description available for this question.
Two trains for Delhi leave Jaipur at 8:30 am and 9:00 am and travel at 60 km/hr and 75 km/hr respectively. How many km from Jaipur will the two trains meet?
Your Answer : (Not Answered)
Correct Answer : B
No answer description available for this question.
A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Your Answer : (Not Answered)
Correct Answer : C
Let present age of the son \(=x\) years
Then, present age of the man is \((x+24)\) years
Given that, in 2 years, man's age will be twice the age of his son
\(\Rightarrow \) \((x+24)+2=2(x+2)\)
\(\Rightarrow \) \(x=22\)
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
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