1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{p} x+\mathrm{r}=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the equation $x^2-q x+r=0$. Then the value of r is

A
$\frac{2}{9}(\mathrm{p}-\mathrm{q})(2 \mathrm{q}-\mathrm{p})$
B
$\frac{2}{9}(\mathrm{q}-\mathrm{p})(2 \mathrm{p}-\mathrm{q})$
C
$\frac{2}{9}(q-2 p)(2 q-p)$
D
$\frac{2}{9}(2 p-q)(2 q-p)$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation $(\operatorname{cosp}-1) x^2+(\operatorname{cosp}) x+\sin p=0$ in the variable $x$, has real roots. Then p can take any value in the interval

A
$(0,2 \pi)$
B
$(-\pi, 0)$
C
$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
D
$(0, \pi)$
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation $(\operatorname{cosp}-1) x^2+(\cos p) x+\operatorname{sinp}=0$ in the variable $x$, has real roots. Then p can take any value in the interval

A
$(0,2 \pi)$
B
$(-\pi, 0)$
C
$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
D
$(0, \pi)$
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.
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12