1
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The solution set of the inequalities $$4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$$ is represented by region

MHT CET 2023 14th May Morning Shift Mathematics - Linear Programming Question 34 English

A
$$\mathrm{S}_2$$ region
B
$$\mathrm{S}_1$$ region
C
$$\mathrm{S}_3$$ region
D
$$\mathrm{S}_4$$ region
2
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the line $$x-2 y=\mathrm{m}(\mathrm{m} \in \mathrm{Z})$$ intersects the circle $$x^2+y^2=2 x+4 y$$ at two distinct points, then the number of possible values of $m$ are

A
8
B
9
C
10
D
11
3
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$|\bar{a}+\bar{b}+\bar{c}|=1, \overline{\mathrm{c}}=\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})$$ and $$|\overline{\mathrm{a}}|=\frac{1}{\sqrt{3}},|\overline{\mathrm{b}}|=\frac{1}{\sqrt{2}},|\overline{\mathrm{c}}|=\frac{1}{\sqrt{6}}$$, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

A
$$\frac{\pi}{6}$$
B
$$\frac{\pi}{4}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{\pi}{2}$$
4
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation $$x^3+x-1=0$$ has

A
no real root.
B
exactly two real roots.
C
exactly one real root.
D
more than two real roots.
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