1
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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2
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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3
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
$$\sqrt{3}: 2$$
4
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $$4^{\text {th }}$$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $$1 \mathrm{~mm}$$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and $$6^{\text {th }}$$ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :

A
3.02 cm
B
3.06 cm
C
3.10 cm
D
3.20 cm
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