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Calculus
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Differential Equations
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1
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833

Let p = ln(x), q = ln(x3) and r = ln(x5), where x > 1. Which of the following statements is/are correct? 

I. p, q and r are in AP.

Il. p, q and r can never be in GP.

Select the answer using the code given below.  

1
I only 
2
II only 
3
Both I and II
4
Neither I nor II 
2
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Let x >1, y >1, z >1 be in GP. Then $\rm \frac{1}{1+ln x}, \frac{1}{1+lny}, \frac{1}{1+\ln z}$ are
1
in AP
2
in GP
3
in HP
4
neither in AP nor in GP nor in HP 
3
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
If the sum of the first n terms of a series is n(2n+1), then what is the nth term?
1
4n - 1
2
4n
3
4n + 1
4
4n + 3
4
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p2 : q2. Which one of the following is correct?
1
The first term is equal to the common difference
2
The first term is equal to twice the common difference
3
The common difference is equal to twice the first term
4
The first term is equal to square of the common difference