Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The question consists of two statements- assertion (A) and reason (R).

Assertion (A): The value of $(25) 3 + (− 16) 3 + (− 9) 3$ is 10800.

Reason (R): If a + b + c = 0, then $a 3 + b 3 + c 3 = 3 a b c$ .

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

Both assertion (A) and reason (R) are true and reason (R) is a correct explanation of assertion (A).

Both assertion (A) and reason (R) are true but reason (R) is not a correct explanation of the assertion(A).

Assertion (A) is true and reason (R) is false.

Assertion (A) is false and reason (R) is true.

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given data,
If a + b + c = 0, then

.
Considering,

(25) 3 + − 16 3 + − 9 3

As we know, f (a) = 0 if (x-a) is a factor of the quadratic equation f(x).
Let a =25, b=(-16) and c=(-9)
Using the formula,

a^{3} + b^{3} + c^{3} - 3 abc = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - bc - ca)

Now, using the assertion given,

25^{3} + {(- 16)}^{3} + {(- 9)}^{3} = 10800

Substituting the value of a, b, and c in the formula, we get,
(25)3+(-16)3+(-9)3-3(25)(-16)(-9)=(25-16-9)[252+162+92-25×(-16)-(-16)×(-9)-(-9)×25× (-16)-(-16)×(-9)-(-9)×25
Substituting the value again,

a + b + c = 25 - 16 - 9 = 0

{(25)}^{3} + {(- 16)}^{3} + {(- 9)}^{3} - 3 (25) (- 16) (- 9) = 0

{(25)}^{3} + {(- 16)}^{3} + {(- 9)}^{3} = 3 (25) (- 16) (- 9)

15625 - 4096 - 729 = 3 \times 3600

10800 = 10800

Therefore, both the assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
Hence, option 1 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!