Test Name | No. of Questions | Marks (of each) | Time | Take Test |
---|---|---|---|---|
Test-1 | 10 | 3 | 40 Minutes | |
Test-2 | 10 | 3 | 40 Minutes | |
Test-3 | 11 | 3 | 40 Minutes |
Question 1.

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is
Question 2.

If = 3(2 + √2), then find the value of
Question 3.

For some positive and distinct real numbers x, y and z if is the arithmetic mean of and , then the relationship which will always hold true, is?
Question 4.

The sum of all possible values of x satisfying the equation = 0, is
Question 5.

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If ambn = 144145, then the largest possible value of n - m is
Let a, b, m and n be natural numbers such that a > 1 and b > 1. If ambn = 144145, then the largest possible value of n - m is
Question 6.

Let n be any natural number such that 5n-1 < 3n+1. Then, the least integer value of m that satisfies 3n+1 < 2n+m for each such n, is?
Let n be any natural number such that 5n-1 < 3n+1. Then, the least integer value of m that satisfies 3n+1 < 2n+m for each such n, is?
Question 7.

If = 875/2401 and = ,for all non-zero real values of a and b, then the value of x + y is
Question 8.

For all possible integers n satisfying 2.25 ≤ 2 + 2n+2 ≤ 202, the number of integer values of 3 + 3n+1 is
For all possible integers n satisfying 2.25 ≤ 2 + 2n+2 ≤ 202, the number of integer values of 3 + 3n+1 is
Question 9.

In ‘n’ is a positive integer such that () ......... > 999, then the smallest value of n is
Question 10.

The number of real-valued solutions of the equation 2x + 2-x = 2 – (x – 2)² is
The number of real-valued solutions of the equation 2x + 2-x = 2 – (x – 2)² is
Question 11.

If x = , then which of the following equals 64?
Question 12.

If a, b, c are non-zero and 14a = 36b = 84c, then 6b( - ) is equal to
If a, b, c are non-zero and 14a = 36b = 84c, then 6b( - ) is equal to
Question 13.

How many pairs (a, b) of positive integers are there such that a ≤ b and ab = 42017?
How many pairs (a, b) of positive integers are there such that a ≤ b and ab = 42017?
Question 14.

If m and n are integers such that (√2)19 34 42 9m 8n = 3n 16m (64)1/4, then m is
If m and n are integers such that (√2)19 34 42 9m 8n = 3n 16m (64)1/4, then m is
Question 15.

If 5.55x = 0.555y = 1000, then the value of (1/x) − (1/y) is
If 5.55x = 0.555y = 1000, then the value of (1/x) − (1/y) is
Question 16.

If 5x - 3y = 13438 and 5x-1 + 3y+1 = 9686, then x + y equals
If 5x - 3y = 13438 and 5x-1 + 3y+1 = 9686, then x + y equals
Question 17.

Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is
Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is
Question 18.

If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is
If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is
Question 19.

If a and b are integers of opposite signs such that (a + 3)2 : b2 = 9 : 1 and (a - 1)2: (b - 1)2 = 4 : 1, then the ratio a2 : b2 is:
If a and b are integers of opposite signs such that (a + 3)2 : b2 = 9 : 1 and (a - 1)2: (b - 1)2 = 4 : 1, then the ratio a2 : b2 is:
Question 20.

If 92x–1 – 81x-1 = 1944, then x is
If 92x–1 – 81x-1 = 1944, then x is
Question 21.

If - 22x - 2 = 4x - 32x - 3, then x is
If - 22x - 2 = 4x - 32x - 3, then x is
Question 22.

If x = −0.5, then which of the following has the smallest value?
Question 23.

Which among 21/2, 31/3, 41/4 , 61/6 and 121/12 is the largest ?
Which among 21/2, 31/3, 41/4 , 61/6 and 121/12 is the largest ?
Question 24.

What are the values of x and y that satisfy both the equations?
2^(0.7x). 3^(−1. 25y) =
40.3x . 90.2y = 8 . (81)1/5
What are the values of x and y that satisfy both the equations?
2^(0.7x). 3^(−1. 25y) =
40.3x . 90.2y = 8 . (81)1/5
Question 25.

What values of x satisfy -2 0
Question 26.

Let x = Then x equals
Question 27.

Let y = What is the value of y?
Question 28.

If pqr = 1 then + + is equivalent to
Question 29.

Which of the following is true?
Question 30.

A, B and C are defined as follows.
A = 2.000004 ÷ [(2.000004)2 + (4.000008)]
B = 3.000003 ÷ [(3.000003)2 + (9.000009)]
C = 4.000002 ÷ [(4.000002)2 + (8.000004)]
Which of the following is true about the values of the above three expressions?
A, B and C are defined as follows.
A = 2.000004 ÷ [(2.000004)2 + (4.000008)]
B = 3.000003 ÷ [(3.000003)2 + (9.000009)]
C = 4.000002 ÷ [(4.000002)2 + (8.000004)]
Which of the following is true about the values of the above three expressions?
Question 31.

273 – 272 – 271 is the same as
273 – 272 – 271 is the same as