Algebra - Surds & Indices - Previous Year CAT/MBA Questions
The best way to prepare for Algebra - Surds & Indices is by going through the previous year Algebra - Surds & Indices cat questions. Here we bring you all previous year Algebra - Surds & Indices cat questions along with detailed solutions.
Click here for previous year questions of other topics.
It would be best if you clear your concepts before you practice previous year Algebra - Surds & Indices cat questions.
If is a whole number then which one of the statements below is consistent with it?
a = 3, b = 2, c = 1
a = 3, b = 1, c = 1
a = 2, b = 1, c = 2
a = 2, b = 1, c = 1
a = 1, b = 2, c = 2
Answer: Option A
Let us prime factorize all the terms under the cube root sign.
7a × (35)(b+1) × (20)(c+2) = 7a × 5b+1 × 7b+1 × 22(c+2) × 5c+2
= 22(c+2) × 5b+c+3 × 7a+b+1
We have to calculate cube-root of this expression, hence powers of all prime numbers should be divisible by 3 for cube-root to be a whole number.
∴ 2(c + 2), (b + c + 3) and (a + b + 1) all should be multiples of 3.
Only option (a) satisfies this given condition.
Hence, option (a).
If x = 8 - and y = 2 + √2, then is given by:
Answer: Option D
x = 8 − √32 = 8 − 4√2 = 4(2 − √2)
On rationalising, we get
= = =
∴ x + 1/y = x + x/8 = 9x/8
⇒ = = =
Hence option (d).
The highest number amongst and
None of the above
Answer: Option B
Since the powers are (1/2), (1/3), (1/4), raise them to their LCM i.e. 12.
Hence, the terms become (26)1/12; (34)1/12 and (43)1/12 i.e. (64)1/12; (81)1/12 and (64)1/12
Since 81 > 64, the largest value would be ∛3.
Hence, option (b).
The value of x for which the equation will be satisfied is:
Answer: Option D
Substituting values given in options, the equation is satisfied for x = 4.
Hence, option (d).
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.