1
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^{2}\end{array}\right|=\frac{9}{8}(103 x+81)$$, then $$\lambda, \frac{\lambda}{3}$$ are the roots of the equation :

A
$$4 x^{2}+24 x-27=0$$
B
$$4 x^{2}-24 x+27=0$$
C
$$4 x^{2}-24 x-27=0$$
D
$$4 x^{2}+24 x+27=0$$
2
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the mean of 6 observations $$1,2,4,5, \mathrm{x}$$ and $$\mathrm{y}$$ be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :

A
$$\frac{10}{3}$$
B
$$\frac{8}{3}$$
C
$$\frac{7}{3}$$
D
3
3
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a continuous function satisfying $$\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0$$, then the value of $$\alpha$$ is :

A
$$-\sqrt{3}$$
B
$$\sqrt{2}$$
C
$$-\sqrt{2}$$
D
$$\sqrt{3}$$
4
JEE Main 2023 (Online) 11th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f$$ and $$g$$ be two functions defined by

$$f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ |x-1|, & x \geq 0\end{array}\right.$$ and $$\mathrm{g}(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ 1, & x \geq 0\end{array}\right.$$

Then $$(g \circ f)(x)$$ is :

A
continuous everywhere but not differentiable at $$x=1$$
B
differentiable everywhere
C
not continuous at $$x=-1$$
D
continuous everywhere but not differentiable exactly at one point
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