1
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$f: R \rightarrow R$$ be a function such that $$f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R \text {, }$$ then $$f(2)$$ equals

A
30
B
$$-$$2
C
$$-$$4
D
8
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A radioactive substance, with initial mass $$m_0$$, has a half-life of $$h$$ days. Then, its initial decay rate is given by

A
$$\frac{m_0}{h} \log 2$$
B
$$m_0 h \log 2$$
C
$$-\frac{m_0}{h} \log 2$$
D
$$-m_0 h \log \cdot 2$$
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The abscissae of two points $$A$$ and $$B$$ are the roots of the equation $$x^2+2 a x-b^2=0$$ and their ordinates are roots of the equation $$y^2+2 p y-q^2=0$$. Then, the equation of the circle with $$A B$$ as diameter is given by

A
$$x^2+y^2-2 a x-2 p y+\left(b^2+q^2\right)=0$$
B
$$x^2+y^2-2 a x-2 p y-\left(b^2+q^2\right)=0$$
C
$$x^2+y^2+2 a x+2 p y+\left(b^2+q^2\right)=0$$
D
$$x^2+y^2+2 a x+2 p y-\left(b^2+q^2\right)=0$$
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The incentre of the $$\triangle A B C$$, whose vertices are $$A(0,2,1), B(-2,0,0)$$ and $$C(-2,0,2)$$, is

A
$$\left(-\frac{3}{2}, \frac{1}{2}, 1\right)$$
B
$$\left(\frac{3}{2}, \frac{1}{2}, 1\right)$$
C
$$\left(-\frac{3}{2},-\frac{1}{2},-1\right)$$
D
$$\left(\frac{3}{2},-\frac{1}{2},-1\right)$$
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