Test Name | No. of Questions | Marks (of each) | Time | Take Test |
---|---|---|---|---|
Test-1 | 12 | 3 | 40 Minutes | |
Test-2 | 12 | 3 | 40 Minutes | |
Test-3 | 13 | 3 | 40 Minutes |
Question 1.
If x and y are positive real numbers such that = 4 and , then x + y equals?
Question 2.
For some positive ral number x, if + = 16/ 3 , then the value of is
Question 3.
For a real number x, if 1/ 2 , , and are in arithmetic progression, then the common difference is
Question 4.
The number of distinct integer values of n satisfying < 0, is
Question 5.
If 5 - + 4 = , then 100x equals
Question 6.
log2 [3 + ] - 2 = 0, then 4x equals
Question 7.
For a real number a, if = 4, then a must lie in the range
Question 8.
If y is a negative number such that , then y equals
Question 9.
If log₄ 5 = (log₄ y)(log₆ √5), then y equals
Question 10.
The value of , for 1 < a ≤ b cannot be equal to
Question 11.
equals .
Question 12.
If = A, = -B and = 1/3, then equals
Instructions
Let x and y be positive real numbers such that log5(x + y) + log5(x - y) = 3, and log2y - log2x = 1 - log23. Then xy equals
Let x and y be positive real numbers such that log5(x + y) + log5(x - y) = 3, and log2y - log2x = 1 - log23. Then xy equals
Question 13.
Question 14.
The real root of the equation + - 21 = 0 is
Question 15.
Let A be a real number. Then the roots of the equation - 4x - = 0 are real and distinct if and only if
Instructions
If x is a real number, then is a real number if and only if
If x is a real number, then is a real number if and only if
Question 16.
Instructions
If x is a positive quantity such that 2x = , then x is equal to
If x is a positive quantity such that 2x = , then x is equal to
Question 17.
Instructions
If log1281 = p, then 3((4-p)/(4+p)) is equal to
If log1281 = p, then 3((4-p)/(4+p)) is equal to
Question 18.
Instructions
If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to
If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to
Question 19.
Instructions
If p3 = q4 = r5 = s6, then the value of logs(pqr) is equal to
If p3 = q4 = r5 = s6, then the value of logs(pqr) is equal to
Question 20.
Instructions
The smallest integer n for which 4n > 1719 holds, is closest to
The smallest integer n for which 4n > 1719 holds, is closest to
Question 21.
Instructions
- + - + - + ?
- + - + - + ?
Question 22.
Instructions
Suppose, log3x = log12y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6G is equal to:
Suppose, log3x = log12y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6G is equal to:
Question 23.
Instructions
The value of log0.008√5 + log√381 – 7 is equal to:
The value of log0.008√5 + log√381 – 7 is equal to:
Question 24.
Instructions
If x is a real number such that log35 = log5(2 + x), then which of the following is true?
If x is a real number such that log35 = log5(2 + x), then which of the following is true?
Question 25.
Instructions
If log (2a × 3b × 5c) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57), and log (2 × 32 × 54), then a equals
If log (2a × 3b × 5c) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57), and log (2 × 32 × 54), then a equals
Question 26.
Instructions
If logyx = a × logzy = b × logxz = ab, then which of the following pairs of values for (a, b) is not possible?
If logyx = a × logzy = b × logxz = ab, then which of the following pairs of values for (a, b) is not possible?
Question 27.
Instructions
If x ≥ y and y > 1, then the value of the expression
(x/y) + (y/x) can never be
If x ≥ y and y > 1, then the value of the expression
(x/y) + (y/x) can never be
Question 28.
Instructions
Let u = (log2 x)2 – 6 log2 x + 12 where x is a real number. Then the equation xu = 256, has
Let u = (log2 x)2 – 6 log2 x + 12 where x is a real number. Then the equation xu = 256, has
Question 29.
Instructions
If log3 2, log3 (2x − 5), log3 (2x − 7/2) are in arithmetic progression, then the value of x is equal to
If log3 2, log3 (2x − 5), log3 (2x − 7/2) are in arithmetic progression, then the value of x is equal to
Question 30.
Question 31.
If 1/3 \log_{3} N = 1 + 5 , then
Instructions
If log10 x - log10 x^(1/2) = 2 logx 10, then a possible value of x is given by:
If log10 x - log10 x^(1/2) = 2 logx 10, then a possible value of x is given by:
Question 32.
Instructions
What is the sum of n terms in the series
log m + log (m^2 / n) + log (m^3 / n^2) + log (m^4 / n^3) .......+ log (m^n / n^(n-1)) ?
What is the sum of n terms in the series
log m + log (m^2 / n) + log (m^3 / n^2) + log (m^4 / n^3) .......+ log (m^n / n^(n-1)) ?
Question 33.
Instructions
Directions: Each question is followed by two statements I and II. Mark:
1. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
2. if the question can be answered by using either statement alone.
3. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. if the question cannot be answered even by using both the statements together.
What is the distance x between two cities A and B in integral number of kilometres?
I. x satisfies the equation =
II. x ≤ 10 km
Directions: Each question is followed by two statements I and II. Mark:
1. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
2. if the question can be answered by using either statement alone.
3. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. if the question cannot be answered even by using both the statements together.
What is the distance x between two cities A and B in integral number of kilometres?
I. x satisfies the equation =
II. x ≤ 10 km
Question 34.
Instructions
If log2 [log7 (x2 - x + 37)] = 1, then what could be the value of ‘x’?
If log2 [log7 (x2 - x + 37)] = 1, then what could be the value of ‘x’?
Question 35.
Instructions
If log7 log5 ((x+5)^(1/2) + x^(1/2)) = 0, find the value of x.
If log7 log5 ((x+5)^(1/2) + x^(1/2)) = 0, find the value of x.
Question 36.
Instructions
log6 216 is
log6 216 is