1
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = $$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma $$. If $$\widehat \beta $$ is not parallel to $$\widehat \gamma $$, then the angle between $$\widehat \alpha $$ and $$\widehat \beta $$ is
A
$${{5\pi } \over 6}$$
B
$${{\pi } \over 6}$$
C
$${{\pi } \over 3}$$
D
$${{2\pi } \over 3}$$
2
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is
A
0
B
1
C
2
D
$$-$$ 4
3
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves $${1 \over 2}$$ unit vertically up and reaches P2, then it moves $${1 \over 4}$$ unit horizontally to right and reaches P3, then it moves $${1 \over 8}$$ unit vertically down and reaches P4, then it moves $${1 \over 16}$$ unit horizontally to right and reaches P5 and so on. Let Pn = (xn, yn) and $$\mathop {\lim }\limits_{n \to \infty } {x_n} = \alpha $$ and $$\mathop {\lim }\limits_{n \to \infty } {y_n} = \beta $$. Then, ($$\alpha$$, $$\beta$$) is
A
(2, 3)
B
$$\left( {{4 \over 3},{2 \over 5}} \right)$$
C
$$\left( {{2 \over 5},1} \right)$$
D
$$\left( {{4 \over 3},3} \right)$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is
A
1
B
$${{1 \over 2}}$$
C
0
D
$${{3 \over 2}}$$
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