Mathematics Test 41

Result

Mathematics Test 41

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

If the function f (x) = 2x³ − 9ax² + 12a² x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p² = q, then a equals

A
3

B
1

C
2

D
1/2

Solution

Clearly f″ (x) > 0 for x = 2a ⇒ q = 2a < 0 for x = a ⇒ p = a
or p² = q ⇒ a = 2.
Hence, (C) is the correct answer.
Question 2
4 / -1

The remainder left out when 8²ⁿ – (62)²ⁿ⁺¹ is divided by 9 is

A
0

B
2

C
7

D
8

Solution

8²ⁿ – (62)^{2n + 1}
⇒ (9 – 1)²ⁿ– (63 – 1)^{2n + 1}
⇒ (²ⁿC₀ 9²ⁿ – ²ⁿC₁ 9^{2n – 1}+ ….. + ²ⁿC_2n) – (^{2n + 1}C₀ 63^{2n + 1}– ^{2n + 1}C₁63²ⁿ + …. – ^{2n +1}C_{2n + 1} )
⇒²ⁿC_2n+ ^{2n +1}C_{2n + 1} + (²ⁿC₀ 9²ⁿ – ²ⁿC₁ 9^{2n – 1}+ ….. )– (^{2n + 1}C₀ 63^{2n + 1}– ^{2n + 1}C₁ 63²ⁿ + …. )
⇒2 + multiple of 9

Hence, option B is correct.