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

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is ___________.

Your Input ________

Correct Answer is **77**

First find all possible words and then subtract words
from each case that have both R together.

FARMER (6)

A, E, F, M, R, R

FARMER (6)

A, E, F, M, R, R

A | |||||
---|---|---|---|---|---|

E | |||||

F | A | E | |||

F | A | M | |||

F | A | R | E | ||

F | A | R | M | E | R |

2

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________.

Your Input ________

Correct Answer is **576**

Total possible words = 6! = 720

When 4 consonants are together (V, W, L, S)

such cases = 3! ⋅ 4! = 144

All consonants should not be together

= Total $$-$$ All consonants together,

= 6! $$-$$ 3! 4! = 576

When 4 consonants are together (V, W, L, S)

such cases = 3! ⋅ 4! = 144

All consonants should not be together

= Total $$-$$ All consonants together,

= 6! $$-$$ 3! 4! = 576

3

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is ____________.

Your Input ________

Correct Answer is **100**

5 | a | b | b | a | 5 |

For divisible by 55 it shall be divisible by 11 and 5 both, for divisibility by 5 unit digit shall be 0 or 5 but as the number is six digit palindrome unit digit is 5.

A number is divisible by 11 if the difference between sum of the digits in the odd places and the sum of the digits in the even places is a multiple of 11 or zero.

Sum of the digits in the even place = a + b + 5

Sum of the digits in the odd places = a + b + 5

Difference between the two sums = (a + b + 5 ) - (a + b + 5) = 0

0 is divisible by 11.

Hence, 5abba5 is divisible by 11.

So, required number = 10 $$\times$$ 10 = 100

4

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______________.

Your Input ________

Correct Answer is **52**

(i) When '0' is at unit place

Number of numbers = 20

(ii) When 4 or 6 are at unit place

Number of numbers = 32

Total three digit even number = 20 + 32 = 52

Number of numbers = 20

(ii) When 4 or 6 are at unit place

Number of numbers = 32

Total three digit even number = 20 + 32 = 52

Number in Brackets after Paper Name Indicates No of Questions

JEE Main 2021 (Online) 1st September Evening Shift (1) *keyboard_arrow_right*

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Straight Lines and Pair of Straight Lines *keyboard_arrow_right*

Circle *keyboard_arrow_right*

Conic Sections *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*

Trigonometric Functions & Equations *keyboard_arrow_right*

Properties of Triangle *keyboard_arrow_right*

Inverse Trigonometric Functions *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*