The largest positive integer for which x-4x-2 - x-1x-5 - 0 is

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Inequalities Involving Modulus Function

The largest p...

Question

The largest positive integer for which $\frac{(x - 4) (x - 2)}{(x - 1) (x - 5)} \leq 0$ is

2

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5

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4

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Solution

The correct option is D $4$
The above-given inequality changes signs across $1, 2, 4, 5.$
The expression is negative in the intervals: $(1, 2]$ and $[4, 5)$
and positive in all other intervals.
Hence, the largest integer for which it is satisfies given equation is $4$ .

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Similar questions

Q. The largest negative integer for which

\frac{(x - 4) (x - 2)}{(x - 1) (x - 5)} > 0

Q. The largest negative integer for which the inequality

\frac{(x - 3) (x - 2)}{(x - 1) (x - 5)} > 0

holds true is

The least positive integer n for which ${(\frac{1 + i}{1 - i})}^{n} = \frac{2}{π} (s e c^{- 1} \frac{1}{x} + s i n^{- 1} x), x \neq 0, - 1 \leq x \leq 1$ is:

Q. Find the periods for the given 1-5 functions
1.

cos (3 x + 5) + 7

tan 5 x

cos (\frac{4 x + 9}{5})

| sin x |

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(n any positive integer)

Q. Solve for x:

(i)

\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3}; x \neq 2, 4

(ii)

\frac{1}{x} - \frac{1}{x - 2} = 3, x \neq 0, 2

(iii)

x + \frac{1}{x} = 3, x \neq 0

(iv)

\frac{16}{x} - 1 = \frac{15}{x + 1}, x \neq 0, - 1

(v)

\frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6}, x \neq 3, - 5

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The largest positive integer for which (x−4)(x−2)(x−1)(x−5)≤0 is

The correct option is D 4The above-given inequality changes signs across 1,2,4,5.The expression is negative in the intervals: (1,2] and [4,5)and positive in all other intervals. Hence, the largest integer for which it is satisfies given equation is 4.

The largest positive integer for which $\frac{(x - 4) (x - 2)}{(x - 1) (x - 5)} \leq 0$ is

The correct option is D $4$
The above-given inequality changes signs across $1, 2, 4, 5.$
The expression is negative in the intervals: $(1, 2]$ and $[4, 5)$
and positive in all other intervals.
Hence, the largest integer for which it is satisfies given equation is $4$ .