IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q7

Algebra Level 4

The set (not necessarily exhaustive) of the real values of x x satisfying x 2 − 3 x + 2 > 0 x^2-3x+2>0 and x 2 − 3 x − 4 ≤ 0 x^2-3x-4\leq0 is given by the union of which of the following options?

  • (A) ( − ∞ , − 1 ] (-\infty,\ -1]
  • (B) [ − 1 , 4 ] [-1,\ 4]
  • (C) [ 1 , 2 ] [1,\ 2]
  • (D) [ 4 , ∞ ) [4,\ \infty)

Enter your answer as a 4 digit string of 1s and 9s, using 1 for correct option, 9 for wrong. For example, 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .


The answer is 9999.

Shubhamkar Ayare by Shubhamkar Ayare , 22, India

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1 solution

Rohit Sachdeva
Jan 20, 2017

First equation factorizes to:

( x − 1 ) ( x − 2 ) > 0 (x-1)(x-2)>0

Its solution set is: ( − ∞ (-\infty , 1) U (2 , ∞ ) \infty)

Second equation factorizes to:

( x + 1 ) ( x − 4 ) ≤ 0 (x+1)(x-4)\leq 0

Its solution set is: [-1 , 4]

The intersection of these two solution sets gives:

[-1 , 1) U (2 , 4]

As we can see from options, union of none of the options gives the above result.

Hence 9999

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