NIMCET 2015 — Mathematics PYQ

Q: How do I solve NIMCET 2015 Mathematics questions?

Practice NIMCET 2015 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

If $x, y,$ and $z$ are three consecutive positive integers, then $\log(1 + xz)$ is:

Choose the correct answer:

Explanation

Since $x, y,$ and $z$ are three consecutive positive integers, we can write them in terms of $y$ :

$x = y - 1$

$z = y + 1$

Now, substitute these into the expression:

1 + xz = 1 + (y - 1)(y + 1)

Apply the algebraic identity $(a - b)(a + b) = a^2 - b^2$ :

1 + xz = 1 + (y^2 - 1)

1 + xz = y^2

Now, take the logarithm of the expression:

\log(1 + xz) = \log(y^2)

Using the property of logarithms $\log(a^n) = n\log a$ :

\log(y^2) = 2\log y

Correct Option: (d)