1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
Change Language
The least positive integral value of $\alpha$, for which the angle between the vectors $\alpha \hat{i}-2 \hat{j}+2 \hat{k}$ and $\alpha \hat{i}+2 \alpha \hat{j}-2 \hat{k}$ is acute, is ___________.
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2
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
Change Language
If $\alpha$ satisfies the equation $x^2+x+1=0$ and $(1+\alpha)^7=A+B \alpha+C \alpha^2, A, B, C \geqslant 0$, then $5(3 A-2 B-C)$ is equal to ____________.
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3
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1
Change Language
A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let

$a=P(X=3), b=P(X \geqslant 3)$ and $c=P(X \geqslant 6 \mid X>3)$. Then $\frac{b+c}{a}$ is equal to __________.
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4
JEE Main 2024 (Online) 27th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2 t^2 \hat{j}+5 \hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1 \mathrm{~s}$$ will be :

A
$$16 \mathrm{~m} / \mathrm{s}$$ in $$y$$-direction
B
$$4 \mathrm{~m} / \mathrm{s}$$ in $$x$$-direction
C
$$9 \mathrm{~m} / \mathrm{s}$$ in $$\mathrm{z}$$-direction
D
$$4 \mathrm{~m} / \mathrm{s}$$ in $$y$$-direction
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