Instructions

For the following questions answer them individually

Question 51

Let r and c be real numbers. If r and -r are roots of $$5x^{3} + cx^{2} - 10x + 9 = 0$$, then c equals

Question 52

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is

Question 53

Suppose for all integers x, there are two functions f and g such that $$f(x) + f (x - 1) - 1 = 0$$ and $$g(x ) = x^{2}$$. If $$f\left(x^{2} - x \right) = 5$$, then the value of the sum f(g(5)) + g(f(5)) is

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 54

In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 55

Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All

Question 56

In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was

Question 57

On day one, there are 100 particles in a laboratory experiment. On day n, where $$n\ge2$$, one out of every n articles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

Question 58

The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

Question 59

For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is

Question 60

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Backspace

789

456

123

0.-

Clear All

Submit
789

456

123

0.-

Clear All