1
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1
Change Language

Suppose $$y=y(x)$$ be the solution curve to the differential equation $$\frac{d y}{d x}-y=2-e^{-x}$$ such that $$\lim\limits_{x \rightarrow \infty} y(x)$$ is finite. If $$a$$ and $$b$$ are respectively the $$x$$ - and $$y$$-intercepts of the tangent to the curve at $$x=0$$, then the value of $$a-4 b$$ is equal to _____________.

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2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1
Change Language

Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is ___________.

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3
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1
Change Language

The number of matrices $$A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$$, where $$a, b, c, d \in\{-1,0,1,2,3, \ldots \ldots, 10\}$$, such that $$A=A^{-1}$$, is ___________.

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4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Two projectiles are thrown with same initial velocity making an angle of $$45^{\circ}$$ and $$30^{\circ}$$ with the horizontal respectively. The ratio of their respective ranges will be :

A
$$1: \sqrt{2}$$
B
$$\sqrt{2}: 1$$
C
$$2: \sqrt{3}$$
D
$$\sqrt{3}: 2$$
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