Correct Answer: $\frac{59}{48}$

Solution : Given: $\frac{4 \tan ^2 30^{\circ}+\sin ^2 30^{\circ} \cos ^2 45^{\circ}+\sec ^2 48^{\circ}-\cot ^2 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ}+\sin 37^{\circ} \cos 53^{\circ}+\tan 18^{\circ} \tan 72^{\circ}}$
We know that $\tan 30^{\circ} = \frac{1}{\sqrt{3}}$
$\sin 30^{\circ} = \frac{1}{2}$
$\cos 45^{\circ} = \frac{1}{\sqrt{2}}$
$\cos 37^{\circ} = \cos (90^{\circ} - 53^{\circ}) = \sin 53^{\circ}$
$\sin 37^{\circ} = \sin (90^{\circ} - 53^{\circ}) = \cos 53^{\circ}$
$\tan 18^{\circ} \tan 72^{\circ} = 1$ (since $18^{\circ}$ and $72^{\circ}$ are complementary angles)
Putting the values, we get:
$= \frac{4 (\frac{1}{\sqrt{3}})^2 + (\frac{1}{2})^2 (\frac{1}{\sqrt{2}})^2 + \sec ^2 48^{\circ} - \tan ^2 48^{\circ}}{\sin 53^{\circ} \sin 53^{\circ} + \cos 53^{\circ} \cos 53^{\circ} + 1}$
$= \frac{4 (\frac{1}{3}) + \frac{1}{8} +1}{(\sin ^2 53^{\circ} + \cos ^2 53^{\circ}) + 1}$
Since $\sin ^2 \theta + \cos ^2 \theta = 1$ for any angle $\theta$, the denominator becomes $1 + 1 = 2$.
So, the expression simplifies to:
$=\frac{4 (\frac{1}{3}) + \frac{1}{8} + 1}{2}$
$=\frac{ (\frac{4}{3}) + \frac{1}{8} + 1}{2}$
$=\frac{ (\frac{32+3+24}{24}) }{2}$
$=(\frac{59}{48})$
Hence, the correct answer is $(\frac{59}{48})$.

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Correct Answer: Tapti

Solution : The correct option is Tapti.

The Tapti River does not form a delta before it falls into the Arabian Sea. Unlike rivers like the Ganges, Mahanadi and Godavari, which form extensive deltas as they reach the coast, the Tapti flows directly into the Arabian Sea without creating a deltaic region.

Hi !

Preparing for JEE Mains can provide a solid foundation for appearing in other engineering entrance exams, including BITSAT.

Similarities:

1. Common Subjects: JEE Mains and BITSAT both cover physics, chemistry, and mathematics.
2. Math and Physics Emphasis: Both exams have a significant emphasis on mathematics and physics, requiring a strong understanding of these subjects.

Differences:

1. Exam Pattern: BITSAT has a different exam pattern compared to JEE Mains. BITSAT includes sections on English proficiency and logical reasoning, in addition to physics, chemistry, and mathematics.
2. Difficulty Level.

Hope this helps.

Regards,

Ishan

Hello Aspirant,

As you studying in 12th , I would suggest that if you are giving BITSAT then focus on 11th and 12th equally and before 2 months of the conduction of the examination you should start revising the syllabus for 11th and for MET I would suggest that focus more on the 12th syllabus because the level of the questions would be on a easier level than BITSAT.

Although BITSAT is also easy but the thing is for BITSAT you need speed and accuracy to answer your paper.

For BITSAT you can get through the link to get more details about the examination -

https://engineering.careers360.com/articles/bitsat-exam-pattern