Question

JEE Maths - Questions for people to try

Answer 1

Q.1)
Let a->, b-> and c-> be three non zero vectors such that no two of them are collinear and \[(\vec a \times \vec b) \times \vec c=\frac{1}{3}|\vec b||\vec c|\vec a\]. If theta is the angle betweens vectors b-> and c->, then value of sin theta is
1) \[\frac{2}{3}\]
2) \[\frac{-2\sqrt{3}}{3}\]
3)\[\frac{2\sqrt{2}}{3}\]\[\frac{-\sqrt{2}}{3}\]
Q.2)Let O be the vertex and Q be any point on the parabola, x^2=8y. If the point P divides the line segment OQ internally in the ratio 1: 3, then the locus of P is:
1)\[y^{2}=2x\]
2.)\[ x^2=2y\]
3.)\[x^2=y\]
4.)\[y^{2}=x\]
Q.3)
If the angles of elevation of the top of a tower from three collinear points A,B and C, on a line leading to the foot of the tower are, 30, 45 and 60 respectively, then the ratio AB:AC is,
1.)\[1:\sqrt{3}\]
2.)\[2:3\]
3.)\[\sqrt{3}:1\]
4.)\[\sqrt{3}:\sqrt{2}\]
Q.4)The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0), is:
1.) 820
2.) 780
3.) 901
4.) 869
I'll post more when people have solved these :)

Answer 2

ahh one at a time which one u want help with?

Answer 3

I don't want help, I'm sharing these questions for people to try

Answer 4

Nope I didn't qualify man I had no preparation

Answer 5

for the first one:\[(\vec a \times \vec b) \times \vec c = \vec b ( \vec a \bullet \vec c) - \vec a (\vec b \bullet \vec c)\]
\[ \vec a \bullet \vec c = 0\]
\[- \vec a (\vec b \bullet \vec c) = - \vec a|\vec b||\vec c| \cos \theta = \frac{\vec a}{3}|\vec b||\vec c| \]

ie 3.)

Answer 6

Nice, nice