Summation of Combination Terms MCQ Quiz in मराठी - Objective Question with Answer for Summation of Combination Terms - मोफत PDF डाउनलोड करा

Last updated on Apr 14, 2025

पाईये Summation of Combination Terms उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). हे मोफत डाउनलोड करा Summation of Combination Terms एमसीक्यू क्विझ पीडीएफ आणि बँकिंग, एसएससी, रेल्वे, यूपीएससी, स्टेट पीएससी यासारख्या तुमच्या आगामी परीक्षांची तयारी करा.

Latest Summation of Combination Terms MCQ Objective Questions

Top Summation of Combination Terms MCQ Objective Questions

Summation of Combination Terms Question 1:

Comprehension:

Direction: Consider , where a0, a1, a2, ....a4n are real numbers and n is positive integer on the basis of above information, answer the following question.

The correct statement is

  1. ar = an - r, 0 ≤ r ≤ n
  2. an - r = an + r, 0 ≤ r ≤ n
  3. ar = a2n - r, 0 ≤ r ≤ 2n
  4. ar = a4n - r, 0 ≤ r ≤ 4n

Answer (Detailed Solution Below)

Option 4 : ar = a4n - r, 0 ≤ r ≤ 4n

Summation of Combination Terms Question 1 Detailed Solution

Calculation:

Given,

The equation is

We are asked to determine the correct relationship between the coefficients in the expansion of .

The expansion of is given by:

From the structure of the binomial expansion of , we can observe that the coefficients follow a symmetry. Specifically, the coefficients on opposite ends of the expansion are equal. That is:

This symmetry implies that:

and so on.

Therefore, the correct statement is:

Hence, the correct answer is Option (4) 

Summation of Combination Terms Question 2:

Comprehension:

Direction: Consider , where a0, a1, a2, ....a4n are real numbers and n is positive integer on the basis of above information, answer the following question.

The value of a4n-1 is

  1. 2n
  2. 2n2 + 4n
  3. 2n + 3
  4. 2n2 + 3n

Answer (Detailed Solution Below)

Option 1 : 2n

Summation of Combination Terms Question 2 Detailed Solution

Calculation:

Given,

The equation is

We need to find the value of , which is the coefficient of in the expansion of .

We first replace x by in the given expression to get the equation:

We then modify the expression as follows:

By comparing the coefficients, we obtain:

Thus, the value of is equal to the coefficient of x  in the expansion of , which is .

Hence, the value of is .

Hence, the correct answer is Option (1) 

Summation of Combination Terms Question 3:

Comprehension:

Direction: Consider , where a0, a1, a2, ....a4n are real numbers and n is positive integer on the basis of above information, answer the following question.

The value of a2 is

Answer (Detailed Solution Below)

Option 3 :

Summation of Combination Terms Question 3 Detailed Solution

Calculation:

Given,

The equation is

We need to find the value of , which is the coefficient of in the expansion of .

The equation is expanded as follows:

We are interested in the coefficient of .

From the binomial expansion, we have:

Hence, the correct answer is Option (3) 

Summation of Combination Terms Question 4:

The value of  is

Answer (Detailed Solution Below)

Option 3 :

Summation of Combination Terms Question 4 Detailed Solution

Given:

Series is 

Concept Used:

Calculation:

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