1
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that

$${{QA} \over {AR}} = {{RB} \over {BP}} = {{PC} \over {CQ}} = {1 \over 2}$$. Then $${{Area(\Delta PQR)} \over {Area(\Delta ABC)}}$$ is equal to :

A
$$\frac{5}{2}$$
B
4
C
2
D
3
2
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x) = \left\{ {\matrix{ {{x^2}\sin \left( {{1 \over x}} \right)} & {,\,x \ne 0} \cr 0 & {,\,x = 0} \cr } } \right.$$

Then at $$x=0$$

A
$$f$$ is continuous but $$f'$$ is not continuous
B
$$f$$ and $$f'$$ both are continuous
C
$$f$$ is continuous but not differentiable
D
$$f'$$ is continuous but not differentiable
3
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1
Change Language

Let $$\lambda \in \mathbb{R}$$ and let the equation E be $$|x{|^2} - 2|x| + |\lambda - 3| = 0$$. Then the largest element in the set S = {$$x+\lambda:x$$ is an integer solution of E} is ______

Your input ____
4
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1
Change Language

The shortest distance between the lines $${{x - 2} \over 3} = {{y + 1} \over 2} = {{z - 6} \over 2}$$ and $${{x - 6} \over 3} = {{1 - y} \over 2} = {{z + 8} \over 0}$$ is equal to ________

Your input ____
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