If the line of intersection of the planes $$ax+by=3$$ and $$ax+by+cz=0$$, a $$>0$$ makes an angle $$30^{\circ }$$ with the plane $$y-z+2=0$$, then the direction cosines of the line are :

The foot of the perpendicular from a point on the circle $$x^2+y^2=1,z=0$$ to the plane $$2x+3y+z=6$$ lies on which one of the following curves?

Let the lines $$\frac{x-1}{\lambda }=\frac{y-2}{1}=\frac{z-3}{2}$$ and $$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda }$$ be coplanar and $$\mathrm{P}$$ be the plane containing these two lines. Then which of the following points does NOT lie on P?

A plane P is parallel to two lines whose direction ratios are $$-2,1,-3$$ and $$-1,2,-2$$ and it contains the point $$(2,2,-2)$$. Let P intersect the co-ordinate axes at the points $$\mathrm{A},\mathrm{B},\mathrm{C}$$ making the intercepts $$\alpha ,\beta ,\gamma$$. If $$\mathrm{V}$$ is the volume of the tetrahedron $$\mathrm{OABC}$$, where $$\mathrm{O}$$ is the origin, and $$\mathrm{p}=\alpha +\beta +\gamma$$, then the ordered pair $$(\mathrm{V},\mathrm{p})$$ is equal to :

If the foot of the perpendicular from the point $$\mathrm{A}(-1,4,3)$$ on the plane $$\mathrm{P}:2x+\mathrm{m}y+\mathrm{n}z=4$$, is $$\left(-2,\frac{7}{2},\frac{3}{2}\right)$$, then the distance of the point A from the plane P, measured parallel to a line with direction ratios $$3,-1,-4$$, is equal to :

Let $$Q$$ be the foot of perpendicular drawn from the point $$P(1,2,3)$$ to the plane $$x+2y+z=14$$. If $$R$$ is a point on the plane such that $$\angle PRQ=60^{\circ }$$, then the area of $$△PQR$$ is equal to :

If $$(2,3,9),(5,2,1),(1,\lambda ,8)$$ and $$(\lambda ,2,3)$$ are coplanar, then the product of all possible values of $$\lambda$$ is:

Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be {24 \over 5} and $$194\frac{2}{5}$$ respectively. If the mean and variance of the first 4 observation are {7 \over 2} and a respectively, then (4a + x5) is equal to:

The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :

Let $$\{a_n{\}}_{n=0}^{\infty }$$ be a sequence such that $$a_0=a_1=0$$ and $$a_{n+2}=2a_{n+1}-a_n+1$$ for all n $$\ge$$ 0. Then, \sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}} is equal to:

The sum of the infinite series 1 + {5 \over 6} + {{12} \over {{6^2}}} + {{22} \over {{6^3}}} + {{35} \over {{6^4}}} + {{51} \over {{6^5}}} + {{70} \over {{6^6}}} + \,\,..... is equal to :

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is :

Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = {1 \over {1296}} and A2 + A4 = {7 \over {36}}, then the value of A6 + A8 + A10 is equal to

Let S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,...... Then 4S is equal to

If a1, a2, a3 ...... and b1, b2, b3 ....... are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4 b4 is equal to -

$$x=\sum _{n=0}^{\infty }{a}^n,y=\sum _{n=0}^{\infty }{b}^n,z=\sum _{n=0}^{\infty }{c}^n$$, where a, b, c are in A.P. and |a|