1
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then
A
I(p) > J(p)
B
I(p) $$ \le $$ J(p)
C
I(p) < J(p) in $$\left[ {0,{p \over 2}} \right]$$ and I(p) > J(p) in $$\left[ {{p \over 2},\infty } \right]$$
D
I(p) < J(p) in $$\left[ {{p \over 2},\infty } \right]$$ and I(p) > J(p) in $$\left[ {0,{p \over 2}} \right]$$
2
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\overrightarrow \alpha $$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta $$ = $$\widehat i - \widehat j - \widehat k$$ and $${\overrightarrow \gamma }$$ = $$ - \widehat i - \widehat j - \widehat k$$ be three vectors. A vector $$\overrightarrow \delta $$, in the plane of $$\overrightarrow \alpha $$ and $$\overrightarrow \beta $$, whose projection on $${\overrightarrow \gamma }$$ is $${1 \over {\sqrt 3 }}$$, is given by
A
$$ - \widehat i - 3\widehat j - 3\widehat k$$
B
$$\widehat i - 3\widehat j - 3\widehat k$$
C
$$ - \widehat i + 3\widehat j + 3\widehat k$$
D
$$\widehat i + 3\widehat j - 3\widehat k$$
3
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\overrightarrow \alpha $$, $${\overrightarrow \beta }$$, $${\overrightarrow \gamma }$$ be the three unit vectors such that $$\overrightarrow \alpha .\overrightarrow \beta = \overrightarrow \alpha .\overrightarrow \gamma = 0$$ and the angle between $$\overrightarrow \beta $$ and $$\overrightarrow \gamma $$ is 30$$^\circ$$. Then $$\overrightarrow \alpha $$ is
A
2($$\overrightarrow \beta $$ $$ \times $$ $$\overrightarrow \gamma $$)
B
$$-$$ 2($$\overrightarrow \beta $$ $$ \times $$ $$\overrightarrow \gamma $$)
C
$$ \pm $$ 2($$\overrightarrow \beta $$ $$ \times $$ $$\overrightarrow \gamma $$)
D
($$\overrightarrow \beta $$ $$ \times $$ $$\overrightarrow \gamma $$)
4
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let z1 and z2 be complex numbers such that z1 $$ \ne $$ z2 and |z1| = |z2|. If Re(z1) > 0 and Im(z2) < 0, then $${{{z_1} + {z_2}} \over {{z_1} - {z_2}}}$$ is
A
one
B
real and positive
C
real and negative
D
purely imaginary
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