1
MHT CET 2023 9th May Evening 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
all three real roots.
2
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The range of values of $$x$$ for which $$f(x)=x^3+6 x^2-36 x+7$$ is increasing in

A
$$(-\infty,-6) \cup(2, \infty)$$
B
$$(-6,2)$$
C
$$(-\infty,-2) \cup(6, \infty)$$
D
$$(-6,2]$$
3
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of the function $$f(x)=3 x^3-18 x^2+27 x-40$$ on the set $$\mathrm{S}=\left\{x \in \mathbb{R} / x^2+30 \leq 11 x\right\}$$ is

A
122
B
132
C
112
D
222
4
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A water tank has a shape of inverted right circular cone whose semi-vertical angle is $$\tan ^{-1}\left(\frac{1}{2}\right)$$. Water is poured into it at constant rate of 5 cubic meter/minute. The rate in meter/ minute at which level of water is rising, at the instant when depth of water in the tank is $$10 \mathrm{~m}$$ is

A
$$\frac{1}{5 \pi}$$
B
$$\frac{1}{15 \pi}$$
C
$$\frac{2}{\pi}$$
D
$$\frac{1}{10 \pi}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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