GATE XE exam:gate PYQs & Answers — Page 39

Questions 381–390 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 39 of 178

A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.

The minimum number of such cuts required is

Your answerChoose one option.

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In the

array shown below, each cell of the first three rows has either a cross (X) or a number.

Diagram for Engineering Sciences question 10

The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is

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Let

with

. If

represents the Fourier series of

, then the value of

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Let

be a non-zero quadratic polynomial satisfying the differential equation

where

is a real constant. If

, then the value of the integral

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There are four cities, namely,

and

. The cities are directly connected by four roads as shown in the picture given below, that is,

is connected with

, and

is connected with

. The probability of any road getting blocked is

. Let

be the event of traveling from

via

and

be the event of traveling from

via

. Then, which of the following statements is correct?

Diagram for Engineering Sciences question 13

Your answerChoose one option.

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Assume that

is continuous on

and differentiable on

such that

for some

. If

, and

is expressed in terms of

and

, then the value of

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Let

be a

matrix whose eigenvalues are 2, 3, 4 and let

be the identity matrix of order 3. If

for some integer

, then the value of

is _____

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For some integer

, the differential equation

is transformed into

, where

and

. Then, the value of

is _____

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The approximate value (rounded off to two decimal places) of the integral

using the Trapezoid rule with step-size

, is _____

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Consider

, where

and

. Which of the following statements is correct?

Your answerChoose one option.

is periodic

is not periodic

for all

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GATE XE exam:gate PYQs

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