Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is :

• $\frac{7}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^5\mathrm{C}_3 + {}^6\mathrm{C}_4}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^5\mathrm{C}_2 {}^6\mathrm{C}_2}{{}^{11}\mathrm{C}_7}$

• $\frac{{}^6\mathrm{C}_3 {}^5\mathrm{C}_4}{{}^{11}\mathrm{C}_7}$

In a book of 500 pages, it is found that there are 250 typing errors. Assume that Poisson law holds for the number of errors per page. Then,the probability that a random sample of 2 pages will contain no error, is :

• e ^{- 3}

• e ^{- 5}

• e ^{- 1}

• e ^{- 2}

The transformed equation of x² + 6xy + 8y² = 10 when the axes are rotated through an angle $\frac{\mathrm{\pi }}{4}$is :

• 15x² - 14xy + 3y² = 20

• 15x² + 14xy - 3y² = 20

• 15x² + 14xy + 3y² = 20

• 15x² - 14xy - 3y² = 20

The lines x - y - 2 = 0, x + y - 4 = 0 and x + 3y = 6 meet in the common point :

• (1, 2)

• (2, 2)

• (3, 1)

• (1, 1)

The equation of the line passing through the point of intersection of the lines x - 3y + 2 = 0 and 2x + 5y - 7 = 0 and perpendicular to the line 3x + 2y + 5 = 0 is :

• 2x - 3y + 1 = 0

• 6x - 9y + 11 = 0

• 2x - 3y + 5 = 0 

• 3x - 2y + 1 = 0

36.

Let O be the origin and A be a point on the curve y = 4x. Then the locus of the mid point of OA is :

• x² = 4y

• x² = 2y

• y² = 16x

• y² = 2x

The lines represented by the equation x² - y² - x + 3y - 2 = 0 are :

• x + y - 1 = 0, x - y + 2 = 0

• x - y - 2 = 0, x + y + 1 = 0

• x + y + 2 = 0, x - y - 1 = 0

• x + y - 1 = 0, x + y - 2 = 0

The centroid of the triangle formed by the pair of straight lines 12x² - 20xy + 7y² = 0 and the line 2x - 3y + 4 = 0 is :

• $\left(- \frac{7}{3}, \frac{7}{3}\right)$

• $\left(- \frac{8}{3}, \frac{8}{3}\right)$

• $\left(\frac{8}{3}, \frac{8}{3}\right)$

• $\left(\frac{4}{3}, \frac{4}{3}\right)$

If OA is equally inclined to OX, OY and OZ and if A is $\sqrt{3}$units from the origin, then A is :

• (3, 3, 3)

• (- 1, 1, - 1)

• (- 1, 1, 1)

• (1, 1, 1)

The number of common tangents to the two circles x² + y - 8x + 2y = 0 and x² + y² - 2x - 16y + 25 = 0 is :

• 1

• 2

• 3

• 4