1
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^\frac{p}{q}= p^{\left(\frac{p}{q}-1\right)}$. Then,

A

$q^p = p^q$

B

$q^p = p^{2q}$

C

$ \sqrt{q} = \sqrt{p}$

D
$\sqrt[p]{q}=\sqrt[q]{p}$
2
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Which one of the given options is a possible value of x in the following sequence?

3, 7, 15, x, 63, 127, 255

A

35

B

40

C

45

D

31

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

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

A

51

B

49

C

50

D

55

4
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+2
-0.83

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.

From the ancient Athenian arena to the modern Olympic stadiums, athletics ___(i)___ the potential for a spectacle. The crowd ___(ii)___ with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps ___(iii)___ in an abrupt stop on his left foot. As his body ___(iv)___ like a door turning on a hinge, the javelin is launched skyward at a precise angle.

A

(i) hold (ii) waits (iii) culminates (iv) pivot

B

(i) holds (ii) wait (iii) culminates (iv) pivot

C

(i) hold (ii) wait (iii) culminate (iv) pivots

D

(i) holds (ii) waits (iii) culminate (iv) pivots

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