1
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Let A be a symmetric matrix such that $$\mathrm{|A|=2}$$ and $$\left[ {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr } } \right]A = \left[ {\matrix{ 1 & 2 \cr \alpha & \beta \cr } } \right]$$. If the sum of the diagonal elements of A is $$s$$, then $$\frac{\beta s}{\alpha^2}$$ is equal to __________.

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2
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is $$\frac{1}{\sqrt m}$$, the value of m is -

A
2
B
16
C
8
D
4
3
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

A
40 N
B
20 N
C
5 N
D
10 N
4
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The equation of a circle is given by $$x^2+y^2=a^2$$, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : $${(x - At)^2} + {\left( {y - {t \over B}} \right)^2} = {a^2}$$. The dimensions of t is given as $$[\mathrm{T^{-1}]}$$.

A
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT^{-1}]}$$
B
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT]}$$
C
$$\mathrm{A=[LT],B=[L^{-1}T^{-1}]}$$
D
$$\mathrm{A=[L^{-1}T],B=[LT^{-1}]}$$
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