1
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
2
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
$$(\mathrm{m}-\mathrm{r}+1)!\mathrm{r}$$ !
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$$ and $$\theta=\frac{2 \pi}{7}$$, then $$A^{100}=A \times A \times \ldots .(100$$ times) is equal to

A
$$ \left(\begin{array}{cc} \cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta \end{array}\right) $$
B
$$ \left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right) $$
C
$$ \left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right) $$
D
$$ \left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right) $$
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2 k}$$ is equal to

A
25
B
45
C
0
D
44
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