Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geomatics Engineering Or Surveying

Engineering Mechanics

Hydrology

Transportation Engineering

Strength of Materials Or Solid Mechanics

Reinforced Cement Concrete

Steel Structures

Irrigation

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude

1

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P (X = 2) equals :

A

$$25 \over 169$$

B

$$49\over 169$$

C

$$24 \over 169$$

D

$$52 \over 169$$

P (X = 1) means out of two drawn cards one card is ace.

and P(X = 2) means both the drawn cards are ace.

$$ \therefore $$ P(X = 1) = first card is ace or 2nd card is ace.

= A $$-$$ $$+$$ $$-$$ A

= $${4 \over {52}} \times {{48} \over {52}} + {{48} \over {52}} \times {4 \over {52}}$$

= $$2 \times {4 \over {52}} \times {{48} \over {52}}$$

P(X = 2) =First and second both cards arc ace.

= A A

= $${4 \over {52}} \times {4 \over {52}}$$

$$ \therefore $$ P(X = 1) + P(X = 2)

= $$2 \times {4 \over {52}} \times {{48} \over {52}} + {4 \over {52}} \times {4 \over {52}}$$

= $${{25} \over {169}}$$

and P(X = 2) means both the drawn cards are ace.

$$ \therefore $$ P(X = 1) = first card is ace or 2nd card is ace.

= A $$-$$ $$+$$ $$-$$ A

= $${4 \over {52}} \times {{48} \over {52}} + {{48} \over {52}} \times {4 \over {52}}$$

= $$2 \times {4 \over {52}} \times {{48} \over {52}}$$

P(X = 2) =First and second both cards arc ace.

= A A

= $${4 \over {52}} \times {4 \over {52}}$$

$$ \therefore $$ P(X = 1) + P(X = 2)

= $$2 \times {4 \over {52}} \times {{48} \over {52}} + {4 \over {52}} \times {4 \over {52}}$$

= $${{25} \over {169}}$$

2

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :

A

$${{21} \over {49}}$$

B

$${{27} \over {49}}$$

C

$${{26} \over {49}}$$

D

$${{32} \over {49}}$$

5 Red and 2 green balls

P(one red ball) = $${5 \over 7}$$

P(one green ball) = $${2 \over 7}$$

**Case I : **

If drawn ball is green than a red ball is added

$$\left( {\matrix{ {6{\mathop{\rm Re}\nolimits} d} \cr {1\,Green} \cr } } \right)$$ P (red ball) = $${6 \over 7}$$

**Case II : **

If drawn ball is red than a green ball is added

$$\left( {\matrix{ {4{\mathop{\rm Re}\nolimits} d} \cr {3\,Green} \cr } } \right)$$ P (red ball) = $${4 \over 7}$$

P (2^{nd} red ball) = $${5 \over 7}$$ $$ \times {4 \over 7} + {2 \over 7} \times {6 \over 7}$$ = $${{32} \over {49}}$$

P(one red ball) = $${5 \over 7}$$

P(one green ball) = $${2 \over 7}$$

If drawn ball is green than a red ball is added

$$\left( {\matrix{ {6{\mathop{\rm Re}\nolimits} d} \cr {1\,Green} \cr } } \right)$$ P (red ball) = $${6 \over 7}$$

If drawn ball is red than a green ball is added

$$\left( {\matrix{ {4{\mathop{\rm Re}\nolimits} d} \cr {3\,Green} \cr } } \right)$$ P (red ball) = $${4 \over 7}$$

P (2

3

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, ……, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is -

A

$${{19} \over {36}}$$

B

$${{15} \over {72}}$$

C

$${{13} \over {36}}$$

D

$${{19} \over {72}}$$

$$P\left( A \right) = {1 \over 2} \times {{11} \over {36}} + {1 \over 2} \times {2 \over 9} = {{19} \over {72}}$$

4

If the probability of hitting a target by a shooter, in any shot, is $${1 \over 3}$$, then the minimum number of independent
shots at the target required by him so that the probability of hitting the target atleast once is greater than $${5 \over 6}$$
is -

A

4

B

6

C

5

D

3

$$1 - {}^n{C_0}{\left( {{1 \over 3}} \right)^0}{\left( {{2 \over 3}} \right)^n} > {5 \over 6}$$

$${1 \over 6} > {\left( {{2 \over 3}} \right)^n}\,\, \Rightarrow \,\,0.1666 > {\left( {{2 \over 3}} \right)^n}$$

$${n_{\min }} = 5$$

$${1 \over 6} > {\left( {{2 \over 3}} \right)^n}\,\, \Rightarrow \,\,0.1666 > {\left( {{2 \over 3}} \right)^n}$$

$${n_{\min }} = 5$$

Number in Brackets after Paper Name Indicates No of Questions

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Trigonometric Functions & Equations *keyboard_arrow_right*

Properties of Triangle *keyboard_arrow_right*

Inverse Trigonometric Functions *keyboard_arrow_right*

Complex Numbers *keyboard_arrow_right*

Quadratic Equation and Inequalities *keyboard_arrow_right*

Permutations and Combinations *keyboard_arrow_right*

Mathematical Induction and Binomial Theorem *keyboard_arrow_right*

Sequences and Series *keyboard_arrow_right*

Matrices and Determinants *keyboard_arrow_right*

Vector Algebra and 3D Geometry *keyboard_arrow_right*

Probability *keyboard_arrow_right*

Statistics *keyboard_arrow_right*

Mathematical Reasoning *keyboard_arrow_right*

Functions *keyboard_arrow_right*

Limits, Continuity and Differentiability *keyboard_arrow_right*

Differentiation *keyboard_arrow_right*

Application of Derivatives *keyboard_arrow_right*

Indefinite Integrals *keyboard_arrow_right*

Definite Integrals and Applications of Integrals *keyboard_arrow_right*

Differential Equations *keyboard_arrow_right*

Straight Lines and Pair of Straight Lines *keyboard_arrow_right*

Circle *keyboard_arrow_right*

Conic Sections *keyboard_arrow_right*