1
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33
What is the value of $\left(\frac{3^{81}}{27^4}\right)^{1 / 3}$ ?
A
$3^{13}$
B
$3^{96}$
C
$3^{23}$
D
$3^{69}$
2
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

The decimal number system uses the characters 0, 1, 2, ... , 8, 9, and the octal number system uses the characters 0, 1, 2, ... , 6, 7.

For example, the decimal number 12 ( = 1 × 101 + 2 × 100) is expressed as 14 ( = 1 × 81 + 4 × 80) in the octal number system.

The decimal number 108 in the octal number system is

A

168

B

108

C

150

D

154

3
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

A

₹2,500.00

B

₹1,975.40

C

₹2,250.00

D

₹2,548.80

4
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

If, for non-zero real variables $x$, $y$, and real parameter $a > 1$,

$x : y = (a + 1) : (a - 1)$,

then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

A

$2a : (a^2 + 1)$

B

$a : (a^2 + 1)$

C

$2a : (a^2 - 1)$

D

$a : (a^2 - 1)$

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