Assertion (A) : The third term in the expansion of $(2 x + \frac{1}{x^{2}})^{m}$ does not contain x. The value of x for which that term equal to the second term in the expansion of $(1 + x^{3})^{30}$ is $4$
Reason (R) : $(a + x)^{n} = n \sum r = 0 C_{r} a^{n - r} x^{r}$

Both A and R are individually true and R is the correct explanation of A.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Both A and R are individually true and R is not correct explanation of A.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A is true but R is false

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A is false but R is true

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C A is false but R is true
It is given that the third term is independent of $x$ .
Therefore
$T_{3} =^{m} C_{2} 2^{m - 2} x^{m - 3 r}$
Hence $m - 3 r = 0$
$m - 6 = 0$
$m = 6$
$T_{2} =^{6} C_{2} 2^{6 - 2}$
$= 2^{3} (30) =$ second term in $(1 + x^{3})^{30}$
$T_{2} =^{30} C_{1} x^{3}$
Hence
$^{30} C_{1} x^{3} = 2^{3} (30)$
$30 x^{3} = 30 (8)$
$x^{3} = 8$
$x = 2$
Hence A is false.

Suggest Corrections

Similar questions

DIRECTIONS (Qs. 52 AND 53): The following item consist of two statements: one labelled as the Assertion a) and the other as Reason (R). You are to examine these two statements carefully and select the answers to these items using the codes given below:

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

53. Assertion a): Saluva Narasimha put an end to the old dynasty and assumed the royal title.

Reason

(R): He wanted to save the kingdom from further degeneration and disintegration. [2003]

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

52. Assertion a): Shah Alam II spent the initial years as an emperor far away from his capital.

Reason

(R): There was always a lurking danger of foreign invasion from the north-west frontier. [2003]

Q. Assertion (A)
8th term from the end of the AP 18, 14, 10, 6, ..., −30 is −2.

Reason (R)
The nth term from the end of an AP with last term l and common difference d is l −(n − 1)d.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Q. Assertion(A): Some algae are unicellular.
Reason(R): They belong to the kingdom Monera.

Q. Assertion (A)
Sum of first n positive integers is given by

S_{n} = \frac{1}{2} n (n + 1) .

Reason (R)
In an AP with first term a and common difference d, the sum of nth terms is given by

S_{n} = \frac{n}{2} [2 a + (n - 1) d] .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Join BYJU'S Learning Program

Assertion (A) : The third term in the expansion of (2x+1x2)m does not contain x. The value of x for which that term equal to the second term in the expansion of (1+x3)30 is 4Reason (R) : (a+x)n=n∑r=0Cran−rxr

The correct option is C A is false but R is trueIt is given that the third term is independent of x.ThereforeT3=mC22m−2xm−3rHence m−3r=0m−6=0m=6T2=6C226−2=23(30)= second term in (1+x3)30T2=30C1x3Hence30C1x3=23(30)30x3=30(8)x3=8x=2Hence A is false.

Assertion (A) : The third term in the expansion of $(2 x + \frac{1}{x^{2}})^{m}$ does not contain x. The value of x for which that term equal to the second term in the expansion of $(1 + x^{3})^{30}$ is $4$
Reason (R) : $(a + x)^{n} = n \sum r = 0 C_{r} a^{n - r} x^{r}$