1
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1
Change Language

Let $$M = \left[ {\matrix{ 0 & { - \alpha } \cr \alpha & 0 \cr } } \right]$$, where $$\alpha$$ is a non-zero real number an $$N = \sum\limits_{k = 1}^{49} {{M^{2k}}} $$. If $$(I - {M^2})N = - 2I$$, then the positive integral value of $$\alpha$$ is ____________.

Your input ____
2
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1
Change Language

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8{x^2} - 2x$$ and $$g(f(x)) = 4{x^2} + 6x + 1$$, then the value of $$f(2) + g(2)$$ is _________.

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3
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

A
10 m
B
20 m
C
30 m
D
40 m
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27$$^\circ$$C).

(Given : coefficient of linear thermal expansion of gold $$\alpha$$L = 1.4 $$\times$$ 10$$-$$5 K$$-$$1)

A
125.7$$^\circ$$C
B
91.7$$^\circ$$C
C
425.7$$^\circ$$C
D
152.7$$^\circ$$C
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