1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$$ where $$\mathrm{ac} \neq 0$$, then $$\mathrm{P}(x) \cdot \mathrm{Q}(x)=0$$ has (a, b, c, d are real)

A
2 real roots
B
at least two real roots
C
4 real roots
D
no real root
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{N}$$ be the number of quadratic equations with coefficients from $$\{0,1,2, \ldots, 9\}$$ such that 0 is a solution of each equation. Then the value of $$\mathrm{N}$$ is

A
29
B
39
C
90
D
81
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$a, b, c$$ are distinct odd natural numbers, then the number of rational roots of the equation $$a x^2+b x+c=0$$

A
must be 0
B
must be 1
C
must be 2
D
cannot be determined from the given data
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The numbers $$1,2,3, \ldots \ldots, \mathrm{m}$$ are arranged in random order. The number of ways this can be done, so that the numbers $$1,2, \ldots \ldots ., \mathrm{r}(\mathrm{r}<\mathrm{m})$$ appears as neighbours is

A
$$(m-r)$$ !
B
$$(\mathrm{m}-\mathrm{r}+1)$$ !
C
$$(\mathrm{m}-\mathrm{r})!\mathrm{r}$$ !
D
$$(\mathrm{m}-\mathrm{r}+1)!\mathrm{r}$$ !
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