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Maths-

General

Easy

Question

If a, b, c are lengths of the sides of a triangle, then $open parentheses a plus b plus c close parentheses to the power of 3 end exponent$ is

$3 (a + b - c) (b + c - a) (c + a - b)$
$9 (a + b - c) (b + c - a) (c + a - b)$
$27 (a + b - c) (b + c - a) (c + a - b)$
none of these.

The correct answer is: $27 open parentheses a plus b minus c close parentheses open parentheses b plus c minus a close parentheses open parentheses c plus a minus b close parentheses$

Since the sum of two sides of a triangle is greater than the third side.
$therefore a plus b greater than c text or end text a plus b minus c greater than 0$
$b plus c greater than a text or end text b plus c minus a greater than 0 c plus a greater than b text or end text c plus a minus b greater than 0 therefore fraction numerator open parentheses a plus b minus c close parentheses plus open parentheses b plus c minus a close parentheses open parentheses c plus a minus b close parentheses over denominator 3 end fraction greater or equal than open square brackets open parentheses a plus b minus c close parentheses open parentheses b plus c minus a close parentheses open parentheses c plus a minus b close parentheses close square brackets to the power of 1 divided by 3 end exponent$
$rightwards double arrow fraction numerator a plus b plus c over denominator 3 end fraction greater or equal than open square brackets open parentheses a plus b plus c close parentheses open parentheses b plus c minus a close parentheses open parentheses c plus a minus b close parentheses close square brackets to the power of 1 divided by 3 end exponent rightwards double arrow open parentheses a plus b plus c close parentheses to the power of 3 end exponent greater or equal than 27 open parentheses a plus b minus c close parentheses open parentheses b plus c minus a close parentheses open parentheses c plus a minus b close parentheses$

Related Questions to study

If a, b, c are +ve, then $a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent$ is

If a, b, c are +ve, then $a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent$ is

3 distinct integers are selected at random from 1, 2, 3,…, 20. The probability that the sum is divisible by 5 is

3 distinct integers are selected at random from 1, 2, 3,…, 20. The probability that the sum is divisible by 5 is

If $open vertical bar table row a b 0 row 0 a b row b 0 a end table close vertical bar equals 0$ , then

If $open vertical bar table row a b 0 row 0 a b row b 0 a end table close vertical bar equals 0$ , then

parallel

$not stretchy integral e to the power of sin invisible function application x end exponent. fraction numerator x cos to the power of 3 end exponent invisible function application x minus sin invisible function application x over denominator cos to the power of 2 end exponent invisible function application x end fraction d x$ is equal to

$not stretchy integral e to the power of sin invisible function application x end exponent. fraction numerator x cos to the power of 3 end exponent invisible function application x minus sin invisible function application x over denominator cos to the power of 2 end exponent invisible function application x end fraction d x$ is equal to

$not stretchy integral fraction numerator d x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction$ is equal to

$not stretchy integral fraction numerator d x over denominator sec to the power of 2 end exponent invisible function application x plus tan to the power of 2 end exponent invisible function application x end fraction$ is equal to

Let $f left parenthesis x right parenthesis equals not stretchy integral e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis d x$ . Then f decreases in the interval :

Let $f left parenthesis x right parenthesis equals not stretchy integral e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis d x$ . Then f decreases in the interval :

parallel

The function f(x) = | px − q|+ r|x|, $x element of left parenthesis negative infinity comma infinity right parenthesis$ ,where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :

The function f(x) = | px − q|+ r|x|, $x element of left parenthesis negative infinity comma infinity right parenthesis$ ,where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :

The number of solutions of the equation x³ + 2x² + 5x + 2 cos x = 0 in [0, 2 $pi$ ] is :

The number of solutions of the equation x³ + 2x² + 5x + 2 cos x = 0 in [0, 2 $pi$ ] is :

The distance between the origin and the normal to the curve y = e^2x + x² at the point x = 0 is :

The distance between the origin and the normal to the curve y = e^2x + x² at the point x = 0 is :

parallel

The function f(x) = (x² − 1) |x² − 3x + 2 | + cos | x |) is not differentiable at :

The function f(x) = (x² − 1) |x² − 3x + 2 | + cos | x |) is not differentiable at :

If x^y y^x = 1, then $fraction numerator d y over denominator d x end fraction$ is :

If x^y y^x = 1, then $fraction numerator d y over denominator d x end fraction$ is :

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

If g(x) is a polynomial such that g(x) g(y) = g(x) + g(y) + g(xy) − 2 for all real x and y and g(2) = 5, then $stack l i m with x rightwards arrow 2 below g ´ left parenthesis x right parenthesis$ is :

parallel

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

$CH subscript 3 CH equals CHCH subscript 3 plus KCl plus straight H subscript 2 straight O$ Dehydrohalogenation reaction of 2-chlorobutane gives 2-butene.
(R) Elimination reaction takes' place according to Saytzeff's rule.

Chemistry-General

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

(R) -CN is an ambident nucleophile, therefore, reaction gives both cyanide and isocyanide.

Chemistry-General

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

If 1,3-dibromopropane reacts with zinc and NaI, the product. obtained is : .

Chemistry-General

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