2 Marks

Question 12 Marks

Find the area of the region in the first quadrant enclosed by X -axis, line $x=\sqrt{3} y$ and the circle $x^2+y^2=4$.

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Question 22 Marks

Ten eggs are drawn successively will replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.

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SELF

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Question 32 Marks

Abag contains 4 red and 4 black balls. Another bag contains 2 red and 6 black balls. One of two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Answer

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Question 42 Marks

Find the equation of the plane which contains the line of intersection of the planes $\vec{r} \cdot(\hat{i}+2 \hat{j}+3 \hat{k})-4=0, \quad \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})+5=0$ and which is perpendicular to the plane $\vec{r} \cdot(5 \hat{i}+3 \hat{j}-6 \hat{k})+8=0$.

Answer

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Question 52 Marks

Show that the point $A (1,-2,-8), B (5,0,-2)$ and $C (11,3,7)$ are collinear and find the ration in which B divides AC .

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SELF

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Question 62 Marks

Find the area enclosed by the parabola $4 y=3 x^2$ and line $2 y=3 x+12$.

Answer

SELF