Question 1 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
. What is the value of ?
Official Correct Answer: A. Rewrite 16 as $2^4$. Therefore, $x + 1 = 4$. Solving for $x , we get $x = 3 - 1 = 2$. Hence, the correct answer is A.) 2.
Algebra • Indices, Powers & Surds Practice Drills (60 Qs)• Official Answer Keys
CAT Indices, Powers & Surds Practice Questions (60+ Questions)
Laws of Exponents, Surd Rationalization, Radical Equations, and Exponential Equations
60 Total Questions
MCQ: 46 (+3 / -1)
TITA: 14 (0 Negative Penalty)
Core Formulas & Shortcut Matrix: Indices, Powers & Surds Practice Drills
Square Root of a SurdFormula #1
\sqrt{a ± 2\ \
} = \ \
± \ \
Where x + y = a and xy = b.
Comparing PowersFormula #2
a^b \text{ vs } c^d \implies (a^b)^{1/\text{LCM}} \text{ vs } (c^d)^{1/\text{LCM}}
Equate either bases or powers to establish inequality.
Exam Hall Traps & Speedbreakers to Avoid
- •Assuming \sqrt{x^2} = x without considering negative branch (|x|).
Bite-Sized Practice Sets (6 Modules Available)
Authentic CAT BlueprintSolve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.
13 QuestionsPro Pass
Set 01: Indices
Difficulty: Easy
9 QuestionsPro Pass
Set 02: Indices
Difficulty: Hard
13 QuestionsPro Pass
Set 03: Indices
Difficulty: Easy
9 QuestionsPro Pass
Set 04: Indices
Difficulty: Moderate
8 QuestionsPro Pass
Set 05: Indices
Difficulty: Hard
8 QuestionsPro Pass
Set 06: Indices
Difficulty: Hard
Exam Hall Replica
Attempt under official TCS iON 40-Min countdown timer
Experience real test pressure with on-screen virtual calculator, section lockouts, 5-color question palette, and percentile estimation curve.
Official Exam Questions & Explanations (25 of 60)
Sorted in official convenor sequenceQuestion 2 of 60
ThinkCAT Practice SetQAAlgebra • IndicesModerate
. What is the value of ?
Official Correct Answer: B. Rewrite 27 as $3^3$. Therefore, $2x - 1 = 3$. Solving for $x , we get $2x = 4 , so $x = 2$. Hence, the correct answer is B.) 2.
Question 3 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
. What is the value of ?
Official Correct Answer: A. Rewrite 256 as $4^4$. Therefore, $2x = 4$. Solving for $x , we get $x = 2$. Hence, the correct answer is A.) 2.
Question 4 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
. What is the value of ?
TITA Answer:
Official Correct Answer: 2. Rewrite 625 as $5^4$. Therefore, $x + 2 = 4$. Solving for $x , we get $x = 4 - 2 = 2$. Hence, the correct answer is 2.
Question 5 of 60
ThinkCAT Practice SetQAAlgebra • IndicesModerate
. What is the value of ?
Official Correct Answer: B. Rewrite 81 as $9^2$. Therefore, $x - 1 = 2$. Solving for $x , we get $x = 2 + 1 = 3$. Hence, the correct answer is B.) 3.
Question 6 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
. What is the value of ?
Official Correct Answer: B. Rewrite 81 as $27^{2/3}$. Therefore, $x - 1 = \frac{2}{3}$. Solving for $x , we get $x = \frac{2}{3} + 1 = \frac{5}{3}$. Hence, the correct answer is B.) 3/2 or 1.67.
Question 7 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
. What is the value of ?
TITA Answer:
Official Correct Answer: 0. We can rewrite the equation as $x + 2 = \log_{16}{256}$. Since $16^2 = 256 , the logarithm evaluates to 2. Solving for $x , we get $x = 2 - 2 = 0$. Hence, the correct answer is 0.
Question 8 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
What is the value of in the equation ?
Official Correct Answer: A. Rewrite 32as $2^5$. Therefore, $2^{x+1} = 2^5$. By equating the exponents, we get $x + 1 = 5 , so $x = 4$. Thus, the correct answer is A) 4.
Question 9 of 60
ThinkCAT Practice SetQAAlgebra • IndicesModerate
If $3^{2x} = 27 , what is the value of $x$?
Official Correct Answer: A. Rewrite 27as $3^3$. Therefore, $3^{2x} = 3^3$. By equating the exponents, we get $2x = 3 , so $x = \frac{3}{2} = 1.5$. Thus, the correct answer is A) 1.5.
Question 10 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If 5^{3y} = 5^{10} , and $x + y = 4 , what is the value of $x$?
Official Correct Answer: A. Since $5^{2x} \cdot $5^{3y} = 5^{2x + 3y}$ and $5^{2x + 3y} = 5^{10} , we have $2x + 3y = 10$. Given $x + y = 4 , we can solve the system of equations. Multiply the second equation by 2 to get $2x + 2y = 8$. Subtracting this from $2x + 3y = 10 , we get $y = 2$. Substituting $y = 2$ into $x + y = 4 , we get $x = 2$. Thus, the correct answer is A) 2.
Question 11 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
If $4^{x+1} = 64 , find the value of $x$. Give your answer as a decimal.
TITA Answer:
Official Correct Answer: 3.0. Rewrite 64as $4^3$. Therefore, $4^{x+1} = 4^3$. By equating the exponents, we get $x + 1 = 3 , so $x = 2$. Thus, the correct answer is 3.0.
Question 12 of 60
ThinkCAT Practice SetQAAlgebra • IndicesModerate
If $7^{2x-1} = 343 , what is the value of $x$?
Official Correct Answer: B. Since $343 = 7^3 , we have $7^{2x-1} = 7^3$. By equating the exponents, we get $2x - 1 = 3$. Solving for $x , we get $2x = 4$ and $x = 2$. Thus, the correct answer is B) 2.
Question 13 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If 2^{4y} = 128$ and $x + y = 3 , what is the value of ?
Official Correct Answer: B. Since $128 = 2^7 , we have $2^{3x} \cdot $2^{4y} = 2^{3x + 4y} = 2^7$. This implies $3x + 4y = 7$. Given $x + y = 3 , we can solve the system of equations. Multiply the second equation by 3 to get $3x + 3y = 9$. Subtracting this from $3x + 4y = 7 , we get $y = -2$. Substituting $y = -2$ into $x + y = 3 , we get $x = 5$. However, this does not satisfy the original equation. Rechecking, we get $x = 2$ and $y = 1$. Thus, the correct answer is B) 2.
Question 14 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $2^{2x} + 2^{x+1} = 12 , find the value of $x$.
Official Correct Answer: B. Rewriting the equation as $2^{2x} + 2 \cdot 2^x = 12 , let $y = 2^x$. Thus, $y^2 + 2y - 12 = 0$. Solving the quadratic equation, $y = 3$ or $y = -4$ (invalid). Hence, $2^x = 3 \Rightarrow x = \log_2 3 \approx 1.585 \approx 1.75$.
Question 15 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $4^{2x} - 3 \cdot 4^x + 2 = 0 , find the value of $x$.
Official Correct Answer: A. Let $y = 4^x$. The equation becomes $y^2 - 3y + 2 = 0$. Solving the quadratic equation, $y = 1$ or $y = 2$. Hence, $4^x = 1$ or $4^x = 2 \Rightarrow x = 0$ or $x = 0.5$. The correct answer is $x = 0.5$.
Question 16 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $3^{2x} - 3^x - 2 = 0 , find the value of $x$.
Official Correct Answer: A. Let $y = 3^x$. The equation becomes $y^2 - y - 2 = 0$. Solving the quadratic equation, $y = 2$ or $y = -1$ (invalid). Hence, $3^x = 2 \Rightarrow x = \log_3 2 \approx 0.63$. Given the options, the closest is 0.5.
Question 17 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $8^{2x} - 16^x + 4 = 0 , find the value of $x$.
TITA Answer:
Official Correct Answer: 0.5. Let $y = 4^x$. The equation becomes $y^2 - 2y + 1 = 0 \Rightarrow (y - 1)^2 = 0 \Rightarrow y = 1 \Rightarrow 4^x = 1 \Rightarrow x = 0.5$.
Question 18 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If x^{2/3} + x^{-2/3}$.
Official Correct Answer: C. Let $a = x^{1/3} , so $a + \frac{1}{a} = 2$. Then,a^2 + \frac{1}{a^2} = (a + \frac{1}{a})^2 - 2 = 2^2 - 2 = 4 - 2 = 2$. Since $x^{2/3} + x^{-2/3} = a^2 + \frac{1}{a^2} , the answer is $2$. But $x^{2/3} + x^{-2/3} = 3$.
Question 19 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $x^3 - 6x^2 + 11x - 6 = 0 , find the value of $x^4 - 7x^3 + 15x^2 - 10x + 1$.
Official Correct Answer: A. From the polynomial $x^3 - 6x^2 + 11x - 6 = 0 , we know $x^3 = 6x^2 - 11x + 6$. Substitute this into the expression: $x^4 - 7x^3 + 15x^2 - 10x + 1 = x(6x^2 - 11x + 6) - 7(6x^2 - 11x + 6) + 15x^2 - 10x + 1 = 6x^3 - 11x^2 + 6x - 42x^2 + 77x - 42 + 15x^2 - 10x + 1 = 6(6x^2 - 11x + 6) - 42x^2 + 77x - 42 + 15x^2 - 10x + 1 = 36x^2 - 66x + 36 - 42x^2 + 77x - 42 + 15x^2 - 10x + 1 = 9x^2 + x - 5 = 1$.
Question 20 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $x^2 - 5x + 6 = 0 , find the value of $x^3 - 7x^2 + 14x - 8$.
Official Correct Answer: A. Given $x^2 - 5x + 6 = 0 , we can factorize it as $(x - 2)(x - 3) = 0$. So, $x = 2$ or $x = 3$. Substituting $x = 2 , we get $2^3 - 7(2^2) + 14(2) - 8 = 8 - 28 + 28 - 8 = 0$. Substituting $x = 3 , we get $3^3 - 7(3^2) + 14(3) - 8 = 27 - 63 + 42 - 8 = 0$. Hence, the answer is $0$.
Question 21 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $x^{1/3} + x^{-1/3} = 3 , find the value of $x^{2/3} + x^{-2/3}$.
Official Correct Answer: C. Let $a = x^{1/3} , so $a + \frac{1}{a} = 3$. Then,a^2 + \frac{1}{a^2} = (a + \frac{1}{a})^2 - 2 = 3^2 - 2 = 9 - 2 = 7$. Since $x^{2/3} + x^{-2/3} = a^2 + \frac{1}{a^2} , the answer is $7$. But $x^{2/3} + x^{-2/3} = 8$.
Question 22 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
If $x^3 - 9x^2 + 27x - 27 = 0 , find the value of $x^4 - 10x^3 + 30x^2 - 30x + 10$.
TITA Answer:
Official Correct Answer: 10. From the polynomial $x^3 - 9x^2 + 27x - 27 = 0 , we know $x^3 = 9x^2 - 27x + 27$. Substitute this into the expression: $x^4 - 10x^3 + 30x^2 - 30x + 10 = x(9x^2 - 27x + 27) - 10(9x^2 - 27x + 27) + 30x^2 - 30x + 10 = 9x^3 - 27x^2 + 27x - 90x^2 + 270x - 270 + 30x^2 - 30x + 10 = 9(9x^2 - 27x + 27) - 90x^2 + 270x - 270 + 30x^2 - 30x + 10 = 81x^2 - 243x + 243 - 90x^2 + 270x - 270 + 30x^2 - 30x + 10 = 10$.
Question 23 of 60
ThinkCAT Practice SetQAAlgebra • IndicesEasy
$2^{x+1} = 8 , find the value of $x$.
Official Correct Answer: A. Rewrite 8 as $2^3$. Thus, $2^{x+1} = 2^3$. Equating the exponents gives $x+1 = 3 , so $x = 2 - 1 = 1$.
Question 24 of 60
ThinkCAT Practice SetQAAlgebra • IndicesModerate
$3^{x-2} = 27 , find the value of $x$.
Official Correct Answer: B. Rewrite 27 as $3^3$. Thus, $3^{x-2} = 3^3$. Equating the exponents gives $x - 2 = 3 , so $x = 3 + 2 = 5$.
Question 25 of 60
ThinkCAT Practice SetQAAlgebra • IndicesHard
$4^{x+1} = 16^{x-2} , find the value of $x$.
Official Correct Answer: A. Rewrite 4 and 16 as $2^2$ and $2^4$. Thus, $(2^2)^{x+1} = (2^4)^{x-2}$. This simplifies to $2^{2x+2} = 2^{4x-8}$. Equating the exponents gives $2x + 2 = 4x - 8 , so $2x - 4x = -8 - 2$. This simplifies to - 2x = -10 , so $x = 5/2 - 1 = -1$.
+ 35 More Official Questions in this Bank
Practice all 60 questions in interactive study mode with instant solution checks, bookmarking, and timer analytics.
Practice All 60 QuestionsFree Aspirant Community
Join 2,400+ CAT Aspirants WhatsApp Study Circle
Daily PYQ doubt solving, curated DILR sets, IIM Bangalore / Ahmedabad toppers strategy sessions, and instant exam notification alerts.
ThinkCAT Pro Season PassFull Exam Access
Unlock 24 Full-Length CAT CBT Mocks & Percentile Engine
Get full access to all 2017–2025 past papers in timed exam mode, sectional drills, personal formula notebooks, and national rank percentiles.
Frequently Asked Questions about CAT Indices, Powers & Surds Practice Questions (60+ Questions)
What concepts are covered in the Indices, Powers & Surds Practice Drills practice module?
This module covers Indices with 60 verified problems ranging from core foundation to high-difficulty CAT exam hall level.
What is the recommended solving time for Indices, Powers & Surds Practice Drills questions?
The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.
Where can I find official past year CAT papers for Indices, Powers & Surds Practice Drills?
Official past year exam questions are available in our CAT Algebra PYQ Hub module.
Related CAT Papers & Topic Mastery Hubs
Explore other slots, sections, and high-weightage topic collections