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Detailed Solution for Test: Algebra - 2 - Question 1

Test: Algebra - 2 - Question 2

Let x and y be positive real numbers such that

log_{5} (x + y) + log_{5} (x – y) = 3, and log_{2} y – log_{2} x = 1 – log_{2} 3. Then xy equals

(2019)

Detailed Solution for Test: Algebra - 2 - Question 2

Test: Algebra - 2 - Question 3

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

(2019)

Detailed Solution for Test: Algebra - 2 - Question 3

Test: Algebra - 2 - Question 4

If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?

(2019)

Detailed Solution for Test: Algebra - 2 - Question 4

Test: Algebra - 2 - Question 5

Let A be a real number. Then the roots of the equation x^{2} – 4x – log_{2}A = 0 are real and distinct if and only if

(2019)

Detailed Solution for Test: Algebra - 2 - Question 5

Detailed Solution for Test: Algebra - 2 - Question 6

Test: Algebra - 2 - Question 7

Let a_{1}, a_{2}, ... be integers such that a_{1} – a_{2} + a_{3} – a_{4} + ... + (–1)^{n–1}. an = n, for all n ≥ 1.

Then a_{51} + a_{52} + . . . + a_{1023} equals

(2019)

Detailed Solution for Test: Algebra - 2 - Question 7

Test: Algebra - 2 - Question 8

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

(2018)

Detailed Solution for Test: Algebra - 2 - Question 8

Test: Algebra - 2 - Question 9

If x is a positive quantity such that 2^{x} = 3log _{5}^{2}, then × is equal to

(2018)

Detailed Solution for Test: Algebra - 2 - Question 9

Test: Algebra - 2 - Question 10

Given that X^{2018}Y^{2017} = 1/2 and X^{2016}Y^{2019} = 8, the value of x^{2} + y^{3} is

(2018)

Detailed Solution for Test: Algebra - 2 - Question 10

Detailed Solution for Test: Algebra - 2 - Question 11

Test: Algebra - 2 - Question 12

If log2(5 + log_{3} a) = 3 and log5(4a + 12 + log_{2} b) = 3, then a + b is equal to

(2018)

Detailed Solution for Test: Algebra - 2 - Question 12

Test: Algebra - 2 - Question 13

Let a_{1}, a_{2}...., a_{2n} be an arithmetic progression with a_{1} = 3 and a_{2} = 7. If a_{1} + a_{2} + ... + a_{3n }= 1830, then what is the smallest positive integer m such that m(a_{1} + a_{2 }+ ... + a_{n}) > 1830?

(2017)

Detailed Solution for Test: Algebra - 2 - Question 13

Test: Algebra - 2 - Question 14

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

(2017)

Detailed Solution for Test: Algebra - 2 - Question 14

Detailed Solution for Test: Algebra - 2 - Question 15

Test: Algebra - 2 - Question 16

The value of log _{0.008} √5 + log _{√3} 81 - 7 is equal to

(2017)

Detailed Solution for Test: Algebra - 2 - Question 16

Detailed Solution for Test: Algebra - 2 - Question 17

Test: Algebra - 2 - Question 18

Two positive real numbers, a and b, are expressed as the sum of m positive real numbers and n positive real numbers respectively as follows:

a = s_{1} + s_{2} +…+ s_{m} and b = t_{1} + t_{2} +…+ t_{n}

If [a] = [s_{1}] + [s_{2}] +…+ [s_{m}] + 4 and [b] = [t_{1} ] + [t_{2} ] +…+ [t_{n}] + 3,

Where [x] denotes the greatest integer less than or equal to x, what is the minimum possible value of m + n?

(2016)

Detailed Solution for Test: Algebra - 2 - Question 18

Test: Algebra - 2 - Question 19

P_{1}, P_{2}, P_{3}, ..., P_{11} are 11 friends. The number of balls with P_{1 }through P_{11} in that order is in an Arithmetic Progression. If the sum of the number of balls with P_{1}, P_{3}, P_{5}, P_{7}, P_{9} and P_{11} is 72, what is the number of balls with P_{1}, P_{6} and P_{11} put together?

(2014)

Detailed Solution for Test: Algebra - 2 - Question 19

Test: Algebra - 2 - Question 20

If log_{3}2, log_{3}(2^{x} – 5) and log_{3} are in Arithmetic Progression, then x is equal to

(2014)

Detailed Solution for Test: Algebra - 2 - Question 20

Test: Algebra - 2 - Question 21

A ray of light along the line gets reflected on the x-axis to become a ray along the line

(2014)

Detailed Solution for Test: Algebra - 2 - Question 21

Test: Algebra - 2 - Question 22

If where p ≤ n, then the maximum value of X for n = 8 is :

(2014)

Detailed Solution for Test: Algebra - 2 - Question 22

Test: Algebra - 2 - Question 23

If x + y = 1, then what is the value of (x^{3} + y^{3} + 3xy)?

(2012)

Detailed Solution for Test: Algebra - 2 - Question 23

Test: Algebra - 2 - Question 24

If log_{16}5 = m and log_{5}3 = n, then what is the value of log_{3}6 in terms of ‘m’ and ‘n’?

(2011)

Detailed Solution for Test: Algebra - 2 - Question 24

Test: Algebra - 2 - Question 25

If a = b^{2} = c^{3} = d^{4} then the value of log_{a} (abcd) would be :

(2010)

Detailed Solution for Test: Algebra - 2 - Question 25

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