1
JEE Advanced 2018 Paper 1 Offline
Numerical
+3
-0
The value of $${({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}}$$ is ....................
2
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
Let f : R $$\to$$ R be a differentiable function such that f(0) = 0, $$f\left( {{\pi \over 2}} \right) = 3$$ and f'(0) = 1.

If $$g(x) = \int\limits_x^{\pi /2} {[f'(t)\text{cosec}\,t - \cot t\,\text{cosec}\,t\,f(t)]dt}$$

for $$x \in \left( {0,\,{\pi \over 2}} \right]$$, then $$\mathop {\lim }\limits_{x \to 0} g(x)$$ =
3
JEE Advanced 2016 Paper 1 Offline
Numerical
+3
-0

Let $$\alpha$$, $$\beta$$ $$\in$$ R be such that $$\mathop {\lim }\limits_{x \to 0} {{{x^2}\sin (\beta x)} \over {\alpha x - \sin x}} = 1$$. Then 6($$\alpha$$ + $$\beta$$) equals _________.

4
JEE Advanced 2015 Paper 2 Offline
Numerical
+3
-1
Let m and n be two positive integers greater than 1. If $$\mathop {\lim }\limits_{\alpha \to 0} \left( {{{{e^{\cos \left( {{\alpha ^n}} \right)}} - e} \over {{\alpha ^m}}}} \right) = - \left( {{e \over 2}} \right)$$\$ then the value of $${m \over n}$$ is _________.