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Maths-

General

Easy

Question

Let $f left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent plus 12 x plus 3 close parentheses left parenthesis x minus a right parenthesis over denominator left parenthesis x minus a right parenthesis end fraction$ If range of f(x) is a proper subset of the set of real numbers, then the most exhaustive set in which a lies is

$(- ¥, 7) ㅌ (8, ¥)$
$(- \neq, 7] E [8, ¥)$
$(- \infty, \frac{1}{2}] \cup [\frac{5}{2}, \infty)$
$(- \infty, \frac{1}{2}) \cup (\frac{5}{2}, \infty)$

The correct answer is: $open parentheses negative infinity comma fraction numerator 1 over denominator 2 end fraction close parentheses union open parentheses fraction numerator 5 over denominator 2 end fraction comma infinity close parentheses$

Related Questions to study

If $open parentheses b to the power of 2 end exponent minus 4 a c close parentheses to the power of 2 end exponent open parentheses 1 plus 4 a to the power of 2 end exponent close parentheses less than 64 a to the power of 2 end exponent comma a less than 0 comma$ then maximum value of quadratic expression $a x to the power of 2 end exponent plus b x plus c$ is always less than

If $open parentheses b to the power of 2 end exponent minus 4 a c close parentheses to the power of 2 end exponent open parentheses 1 plus 4 a to the power of 2 end exponent close parentheses less than 64 a to the power of 2 end exponent comma a less than 0 comma$ then maximum value of quadratic expression $a x to the power of 2 end exponent plus b x plus c$ is always less than

Analyze the following graph of $f to the power of ´ end exponent left parenthesis x right parenthesis$ the which is incorrect about $f left parenthesis x right parenthesis text for end text alpha less than x less than beta$

Analyze the following graph of $f to the power of ´ end exponent left parenthesis x right parenthesis$ the which is incorrect about $f left parenthesis x right parenthesis text for end text alpha less than x less than beta$

If one root is square of other root of equation $x to the power of 2 end exponent plus p x plus q equals 0 comma q element of R$ then condition on

If one root is square of other root of equation $x to the power of 2 end exponent plus p x plus q equals 0 comma q element of R$ then condition on

parallel

Statement -1 : There exists only one real value of ‘k’ for which the real roots of the equation $k x to the power of 3 end exponent plus 3 x to the power of 2 end exponent minus 3 x plus 1 equals 0$ are in H.P. because
Statement - 2 : For a cubical equation $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0 comma$ if b, c and d are non zero real and constant, then we can have only one real value of ‘a’ for which all real roots of $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0$ are in H.P.

Statement -1 : There exists only one real value of ‘k’ for which the real roots of the equation $k x to the power of 3 end exponent plus 3 x to the power of 2 end exponent minus 3 x plus 1 equals 0$ are in H.P. because
Statement - 2 : For a cubical equation $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0 comma$ if b, c and d are non zero real and constant, then we can have only one real value of ‘a’ for which all real roots of $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d equals 0$ are in H.P.

Consider a triangle ABC. BE and CF are the medians drawn through the angular points B and C respectively and G is the centroid of the $capital delta$ ABC.
Statement – 1: If the points, A, E, G, F are concyclic then $angle A$ must be acute. because
Statement – 2: The medians of a triangle divide triangle into area wise two equal parts.

Consider a triangle ABC. BE and CF are the medians drawn through the angular points B and C respectively and G is the centroid of the $capital delta$ ABC.
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Statement – 2: The medians of a triangle divide triangle into area wise two equal parts.

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