# GATE Questions

Q:

What is the value of P in the following Equation ?

$\fn_jvn \left ( 19 \right )^{2.5}x\left ( 19 \right )^{p}=\left ( 19 \right )^{7}$

 A) 3.9 B) 4.1 C) 3.7 D) 4.5

Explanation:

Given euation is

$\fn_jvn \left ( 19 \right )^{2.5}x\left ( 19 \right )^{p}=\left ( 19 \right )^{7}$

Here it is in the form of $\fn_jvn a^{m}xa^{n} = a^{\left ( m+n \right )}$

Here m = 2.5 , n = p, m+n = 7

=> 2.5 + p = 7

=> p = 7 - 2.5

=> p = 4.5

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Q:

What should come in place of x in the following equation?

$\inline \fn_jvn \frac{x}{\sqrt{128}}=\frac{\sqrt{162}}{x}$

 A) 13 B) 12 C) 17 D) 16

Explanation:

$\inline \fn_jvn \frac{x}{\sqrt{128}}=\frac{\sqrt{162}}{x}$

Then x2 = $\inline \fn_jvn \sqrt{162x128}$

= $\inline \fn_jvn \sqrt{64x2x18x9}$

= Sqrt of 82 x 62 x 32

= 8 x 6 x 3

x2  = 144.

x = $\inline \fn_jvn \sqrt{144}$ = 12.

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Q:

One fathom is equal to how many meters ?

 A) 1.7699 B) 2.0210 C) 1.8288 D) 2.1212

Explanation:

One fathom = 1.8288 meters = 6 feet

A fathom is a unit of length used especially for measuring the depth of water.

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Q:

Maneela lent Rs. 8000 partly at the rate of 5% and partly at the rate of 6% per annum simple interest. The total interest she get after 2 years is Rs. 820, then in which ratio will Rs. 8000 is to be divided?

 A) 7:1 B) 13:5 C) 15:7 D) 2:7

Explanation:

Maneela lent Rs. 8000 in two parts,

2 210
Q:

What value will come in place of question mark (?) in following number series?

12        16         32          68         ?

 A) 198 B) 164 C) 132 D) 118

Explanation:

Given series is

12        16         32          68         ?

Here it follows a pattern that,

12

12 + (2x2) = 16

16 + (4x4) = 32

32 + (6x6) = 68

68 + (8x8) = 132