Test 01

In a party of 150 persons, 75 persons take tea, 60 persons take coffee and 50 persons take milk. 15 of them take both tea and coffee, but no one taking milk takes tea. If each person in the party takes at least one drink, then what is the number of persons taking milk only?

Consider the following numbers : 1. 437 2. 797 3. 1073

How many of the above numbers are prime?

A, B, C, D and E enter into a business. They invest money in the ratio \(2:3:4:5:6\). However, the time invested by them is in the ratio \(6:5:4:3:2\). If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit?

If the roots of the equation \( x^{2}-b x+c=5 \) differ by 5, then which one of the following is correct?

What is the remainder when \( 65^{99} \) is divided by 11?

What is the largest power of 10 that divides the product \( 29 \times 28 \times 27 \times \ldots 2 \times 1 \)?

What is the largest number which divides both \( 2^{35}-1 \) and \( 2^{91}-1 \)?

A can do a certain work at twice the speed of B. Further, B can do the same work at 1.5 times the speed of C. All of them together can finish the work in 12 days. In how many days can C alone finish the work?

Twelve percent of bananas bought by a fruit vendor got lost during transportation. On selling the remaining bananas, the vendor's overall profit turned out to be \(4\%\). If the vendor had not lost any bananas and had sold them at the price of the remaining bananas, what would have been his profit percentage?

If \(a, b, c\) are non-zero real numbers such that \(a+b+c=0\), then what are the roots of the equation \(ax^2 + bx + c = 0\)?

The time taken by a train to cross a man travelling in another train is 10 seconds, when the other train is travelling in the opposite direction. However, it takes 20 seconds if both the trains are travelling in the same direction. The length of the first train is 200 m and that of the second train is 150 m. What is the speed of the first train?

The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number?

If \( a, b, c, d, e \) and \( f \) satisfy \( 2 \mathrm{a}=3 \mathrm{~b}=6 \mathrm{c}=9 \mathrm{~d}=12 \mathrm{e}=18 \mathrm{f} \), then what is the value of \( (a+b) /(c+d+e+f) \) ?

Consider the following statements:
1. If n is a natural number, then the number \(\frac{n(n^2+2)}{3}\) is also a natural number.
2. If m is an odd integer, then the number \(\frac{m^4+4m^2+11}{16}\) is an integer.
Which of the statements given above is/are correct?

In a business dealing, A owes B ₹ 20,000 payable after 5 years, whereas B owes A ₹ 12,000 payable after 4 years. They want to settle it now at the rate of 5% simple interest. Who gives how much money in this settlement?

Average marks in Mathematics of Section A comprising 30 students is 65 and that of Section B comprising 35 students is 70. What are the average marks (approximately) of both the sections if it was detected later that an entry of 47 marks was wrongly made as 74?

When every even power of every odd integer (greater than 1) is divided by 8, what is the remainder?

What is the largest 5-digit number, which leaves remainder 7, when divided by 18 as well as by 11?

It is given that 5 does not divide \(n-1\), \(n\) and \(n+1\), where n is a positive integer. Which one of the following is correct?

If the positive square root of \( (5+3 \sqrt{2})(5-3 \sqrt{2}) \) is \( \alpha \), then what is the positive square root of \( 8+2 \alpha \) ?

Two sections, X and Y, have average scores of 80 and 75 respectively. Section X has 25 students and section Y has 30 students. If a score of 90 was incorrectly recorded as 60 in section X, what is the corrected average score of both sections combined?

A class of 50 students has an average score of 72. If a score of 55 was mistakenly recorded as 85, what is the corrected average score of the class?

In a school, the average marks of two classes, A and B, are 68 and 74 respectively. Class A has 40 students and class B has 45 students. If it was later found that a score of 50 in class A was wrongly recorded as 80, what is the new average of both classes combined?