CUET · MATHS · PYQ PAPER 2023

Let us consider an annuity whose periodic payment is ₹ R payable at the end of each payment period for ' \(n ^{\prime}\) periods, interest paid r% per period or \(i=\frac{r}{100}\), so the amount.

A \(A=R\left[\frac{(1+i)^n-1}{i}\right]\)
B \(A=R\left[\frac{(1-i)^n-1}{i}\right]\)
C \(A=R\left[\frac{(1+i)^n}{i}-1\right]\)
D \(A=R\left[i^{n-1}-1\right]\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(A=R\left[\frac{(1+i)^n-1}{i}\right]\)

Step-by-step Solution

Detailed explanation

The correct formula for the future amount A of an ordinary annuity is:\(A=R\left[\frac{(1+i)^n-1}{i}\right]\) This matches Option A, representing the sum of a geometric series for n periodic payments R at interest rate i. (A) \(A=R\left[\frac{(1+i)^n-1}{i}\right]\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II

List-I	List-II
(A) The minimum value of \(f(x)=(2 x-1)^2+3\)	(I) 4
(B) The maximum value of \(f(x)=-\|x+1\|+4\)	(II) 10
(C) The minimum value of \(f(x)=\sin (2 x)+6\)	(III) 3
(D) The maximum value of \(f(x)=-(x-1)^2+10\)	(IV) 5

Choose the correct answer from the options given below:

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The greatest integer function defined by \(f(x)=[2 x], 0 < x < 2\)

CUET 2023 Medium

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