JEE 2016 SAMPLE questions

Are you preparing for the engineering entrance exams? Well this math quiz would be the perfect for you. The Maths test could serve as JEE 2016 sample questions for maths.

JEE 2016 Sample Questions for Mathematics

Each of the questions is followed by four/five options. Once you solve the question, scroll down to see the answer and a detailed explanation.

All the best!!

JEE 2016 Sample Questions No. 1: ((x+4)/(x-3))<2 is satisfied when x satisfies

a. (-∞,3)

b. (3,10)

c. (-∞,3)∪(10,∞)

d. (10,∞)

e. None of these

Answer 1: c

hint 1

 

JEE 2016 Sample Questions No.2: If x>0, λ>0 and λx+(1/x)-1 is always non negative, then the least value of λ is

a. 1

b. ½

c. 0

d. 1/4

e. None of these

Answer 2: d

hint2

JEE 2016 Sample Questions No.3: If the product of n positive numbers is 1 then their sum is

a. A positive integer

b. Divisible by n

c. Equal to n+(1/n)

d. Never less than n

e. None of these

Answer 3: d

hint3

 

JEE 2016 Sample Questions No.4: Solution of |x-1|+|x−2|≥4 is

a. (2,3)∪[(7/2),∞)

b. (-∞,(-1/2)]∪[(7/2),∞)

c. (-∞,∞)

d. (1,∞)

Answer 4: b

hint4

 

JEE 2016 Sample Questions No.5: For log3(x2 – 2) < log3 (3/2 |x| – 1) x must lie in the interval

a. (-2,-√2)

b. (-√2,2)

c. (-√2,-1)

d. (-2,-√2)∪ (√2,2)

e. None of these

Answer 5: d

hint5

 

JEE 2016 Sample Questions No.6: Solution of (|x|-1)/(|x|-2) ≥ 0, x ∈ R, x ≠ ±2 is

a. (0, ∞)

b. (-1, 0) ∪ (1, 3)

c. (-2, ∞)

d. [-1,1] ∪ (-∞, -2) ∪ (2, ∞)

Answer 6: d

hint6

 

JEE 2016 Sample Questions No.7: Solution of (x-1)2 (x+4) < 0 is

a. (-∞,1)

b. (-∞,-4)

c. (-1,4)

d. (1,4)

e. None of these

Answer 7: b

hint7

 

JEE 2016 Sample Questions No.8: The minimum value of  ((b+c)/a)+((c+a)/b)+((a+b)/c) (for real positive numbers a,b,c) is

a. 1

b. 2

c. 4

d. 6

e. None of these

Answer 8: d

hint8

 

JEE 2016 Sample Questions No.9: Solution of 0<|3x+1|<(1/3) is

a. (-(4/9),-(2/9))

b. (-(4/9),-(2/9))-{-(1/3)}

c. [-(4/9),-(2/9)]

d. [-(4/9),-(2/9)]-{-(1/3)}

e. None of these

Answer 9: b

hint9

 

JEE 2016 Sample Questions No.10: If x2 +6x-27 > 0 and x2 –3x-4 < 0, then

a. x >3

b. x < 4

c. 3 < x < 4

d. x=7/2

e. None of these

Answer 10: c
hint10

 

JEE 2016 Sample Questions No.11: The number of integral solution of (x+8)/(x+2)≥2 is

a. 3

b. 4

c. 5

d. 6

e. None of these

Answer 11: d

hint11

 

JEE 2016 Sample Questions No.12: A solution is to be kept between 77°F and 86°F. The range in temperature in degree Celsius, if the Celsius/ Fahrenheit (F) conversion formula is F= 9/5C+32, is

a. 20 < C< 25

b. 25 < C < 30

c. 20 < C< 24

d. 30 < C< 33

e. None of these

Answer 12: b

hint12

 

JEE 2016 Sample Questions No.13: The solution set of the inequations 2x-1 ≤ 3 and 3x+1 ≥ -5 is

a. (-2,2)

b. [-2,2]

c. (-∞, -2]  ∪ [2, ∞)

d. (-∞, -2)  ∪ (2, ∞)

e. None of these

Answer 13: b

hint13

 

JEE 2016 Sample Questions No.14: The number of positive integer solutions of  24x < 100 is

a. 4

b. 5

c. 3

d. 2

e. None of these

Answer 14: a

hint14

 

JEE 2016 Sample Questions No.15: The solution set of |x-1| + |x-2| + |x-3| < 6 is

a. ϕ

b. (1,3)

c. (-6,6)

d. (0,4)

e. None of these

Answer 15: e

hint15

 

JEE 2016 Sample Questions No.16: The number of solutions of the linear inequations x ≥ 0 , y ≥ 0 , 2x + y ≤ 2 and x + y ≥ 3 is

a. 0

b. 1

c. 3

d. Infinite

e. None

Answer 16: e

hint16

 

JEE 2016 Sample Questions No.17:The number of integral x-3/x+5 > 0 and -7 <x< 5 is

a. 0

b. 1

c. 2

d. 3

e. None of these

Answer 17: c

hint17

 

JEE 2016 Sample Questions No.18: The solution set of |x+1| + |x-1| < 2 is

a. (-1,1)

b. (0,1)

c. (-1,0)

d. (-½, ½)

e. None of these

Answer 18: a

hint18

 

JEE 2016 Sample Questions No.19: If |x-5|<1 then the range of f(x)=x/x+10 is

a. (3/7, ¼)

b. (2/7, 3/8)

c. (0, ∞)

d. (1, ∞)

e. None of these

Answer 19: b

maths question

 

JEE 2016 Sample Questions No.20: The solution set of |3x-2| <1 is

a. [1, 1)

b. [1, 3)

c. [1/3, 3]

d. (1/3, 1)

e. None of these

Answer 20: d

hint20

 

JEE 2016 Sample Questions No.21: A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution then the quantity in litres of the 2% solution to be added is x where

a. 240 < x < 300

b. 300<x<1000

c. 320 < x < 1280

d. 400 < x < 1600

e. None of these

Answer 21: c

hint21

 

JEE 2016 Sample Questions No.22: The IQ of a person is calculated using the formula IQ=MA/CA*100 where MA is the Mental Age CA is Chronological Age. If 80≤IQ≤140 for a group of 12 year old children the range of their mental age is

a. 9.6 ≤ MA ≤ 16.8

b. 9 ≤ MA ≤ 16

c. 10 ≤ MA ≤ 16.8

d. 9.6 ≤ MA < 16

e. None of these

Answer 22: a

maths questions

 

JEE 2016 Sample Questions No.23: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cms, the minimum length of the shortest side is

a. 7 cms

b. 8.5 cms

c. 10 cms

d. 9 cms

e. None of these

Answer 23: d

maths question

 

JEE 2016 Sample Questions No.24: The number of integer solutions of |2x-3| < 1 is

a. 1

b. 0

c. 2

d. 4

e. None of these

Answer 24: b

maths question

 

JEE 2016 Sample Questions No.25: The set of solutions of the linear inequations x ≥ 0, y ≥ 0, x+2y ≤ 2 and 2x + y ≤ 2 is

a. A triangular region

b. A square region

c. A quadrangular region

d. A pentagonal region

e. None of these

Answer 25: c

HINT25

This test is from the chapter Linear Inequalities in the Maths.

4 Tips on How to Practice for Entrance Exams

  • Try and solve the quiz in 25 minutes, so that you get accustomed to the entrance exam time restraints and increase your speed gradually.
  • As almost all entrances have negative marking, it is advisable that you mark only those answers you are sure about.
  • To a certain extent, elimination among the options help. But that requires practice of more and more numericals.
  • At times guess work for a few questions work. But this is a highly subjective thing. So you need to practice with tests. Review each test with its answers. You can then see which of your guesses work and which are disastrous. And thus you devise your exam strategy.

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Happy Learning!!