1
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
Let $$a$$ and $$b$$ two non-collinear unit vectors. If $$u = a - \left( {a\,.\,b} \right)\,b$$ and $$v = a \times b,$$ then $$\left| v \right|$$ is
A
$$\left| u \right|$$
B
$$\,\left| u \right| + \left| {u\,.\,a} \right|$$
C
$$\,\left| u \right| + \left| {u\,.\,b} \right|$$
D
$$\left| u \right| + u.\left( {a + b} \right)$$
2
IIT-JEE 1999
Subjective
+10
-0
Let $$u$$ and $$v$$ be units vectors. If $$w$$ is a vector such that $$w + \left( {w \times u} \right) = v,$$ then prove that $$\left| {\left( {u \times v} \right) \cdot w} \right| \le 1/2$$ and that the equality holds if and only if $$u$$ is perpendicular to $$v .$$
3
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
$$\int\limits_{\pi /4}^{3\pi /4} {{{dx} \over {1 + \cos x}}} $$ is equal to
A
$$2$$
B
$$-2$$
C
$$1/2$$
D
$$-1/2$$
4
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
If two distinct chords, drawn from the point (p, q) on the circle $${x^2}\, + \,{y^2} = \,px\, + \,qy\,\,(\,where\,pq\, \ne \,0)$$ are bisected by the x - axis, then
A
$${p^2}\, = \,\,{q^2}$$
B
$$\,{p^2}\, = \,\,8\,{q^2}$$
C
$${p^2}\, < \,\,8\,{q^2}$$
D
$${p^2}\, > \,\,8\,{q^2}$$.
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