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Category Archives: IIT JEE

IIT JEE

$\scriptscriptstyle (2\cos \theta + 3\sin \theta )x + (3\cos \theta – 5\sin \theta )y – (5\cos \theta – 2\sin \theta ) = 0$

January 20, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

$f(x) = \frac{{\sin 2x}}{{\sin \frac{x}{2}}}$

January 19, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

$\mathop {\lim }\limits_{x \to 0} \frac{{|x|}}{{\sqrt {{x^4} + 4{x^2} + 1} }}$

January 18, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

$(a + b + c)(b + c – a) = \lambda bc$

January 17, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

${}^{x – 1}{C_4} – {}^{x – 1}{C_3} – \frac{5}{4}{}^{x – 2}{P_2} < 0$

January 16, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

$y = \cos x\cos (x + 2) – {\cos ^2}(x + 1)$

January 15, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

IIT JEE

$\frac{3}{{{1^2}{{.2}^2}}} + \frac{5}{{{2^2}{{.3}^2}}} + \frac{7}{{{3^2}{{.4}^2}}} + ………..$

January 14, 2023 Engineer Manish Verma Leave a comment

Solution [.pdf]

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Blog Posts

  • ${\scriptscriptstyle 6 + f(x) = 2f( – x) + 3{x^2}\int\limits_{ – 1}^1 {f(t)dt}}$
  • $\scriptstyle f(x) = {\left( {\frac{x}{\pi }} \right)^x} + {\left( {\frac{\pi }{x}} \right)^x}$
  • $\scriptstyle \sqrt {7 – \sqrt {7 + \sqrt {7 – \sqrt {7 + …..} } } }$
  • $\scriptstyle f(x) = \int\limits_0^x {{\pi ^t}(t – e)(t – \pi )dt} $
  • $\scriptstyle 7f(x) + 5f\left( {\frac{1}{x}} \right) = x + 1$ …

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