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

A unit vector in XY-plane making an angle $$45^{\circ}$$ with $$\hat{i}+\hat{j}$$ and an angle $$60^{\circ}$$ with $$3 \hat{i}-4 \hat{j}$$ is

A
$$ \frac{13}{14} \hat{i}+\frac{1}{14} \hat{j} $$
B
$$ \frac{1}{14} \hat{i}+\frac{13}{14} \hat{j} $$
C
$$ \frac{13}{14} \hat{\mathrm{i}}-\frac{1}{14} \hat{\mathrm{j}} $$
D
$$ \frac{1}{14} \hat{i}-\frac{13}{14} \hat{j} $$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be given by $$\mathrm{f}(x)=\left|x^2-1\right|$$, then

A
f has a local minima at $$x= \pm 1$$ but no local maxima
B
f has a local maxima at $$x=0$$, but no local minima
C
$$\mathrm{f}$$ has a local minima at $$x= \pm 1$$ and a local maxima at $$x=0$$
D
f has neither any local maxima nor any local minima
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If $$a_n$$ and $$b_n$$ be the $$n^{\text {th }}$$ term of A.P. and G.P. respectively then

A
$$a_n>b_n$$ for all $$n>2$$
B
$$a_n< b_n$$ for all $$n>2$$
C
$$a_n=b_n$$ for some $$n>2$$
D
$$a_n=b_n$$ for some odd $$n$$
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If for the series $$a_1, a_2, a_3$$, ...... etc, $$\mathrm{a}_{\mathrm{r}}-\mathrm{a}_{\mathrm{r}+\mathrm{i}}$$ bears a constant ratio with $$\mathrm{a}_{\mathrm{r}} \cdot \mathrm{a}_{\mathrm{r}+1}$$; then $$\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3 \ldots .$$. are in

A
A.P.
B
G.P.
C
H.P.
D
Any other series
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