The plane passing through the point (4, –1, 2) and parallel to the lines {{x + 2} \over 3} = {{y - 2} \over { - 1}} = {{z + 1} \over 2} and {{x - 2} \over 1} = {{y - 3} \over 2} = {{z - 4} \over 3} also passes through the point -

Let A be a point on the line $$\overrightarrow{r}=\left(1-3\mu \right)\hat{i}+\left(\mu -1\right)\hat{j}+\left(2+5\mu \right)\hat{k}$$ and B(3, 2, 6) be a point in the space. Then the value of $$\mu$$ for which the vector $$\overrightarrow{AB}$$ is parallel to the plane x $$-$$ 4y + 3z = 1 is -

On which of the following lines lies the point of intersection of the line, {{x - 4} \over 2} = {{y - 5} \over 2} = {{z - 3} \over 1} and the plane, x + y + z = 2 ?

The plane containing the line {{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z - 1} \over 3} and also containing its projection on the plane 2x + 3y $$-$$ z = 5, contains which one of the following points ?

The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle {\pi \over 4} with the plane y $$-$$ z + 5 = 0 are :

Two lines {{x - 3} \over 1} = {{y + 1} \over 3} = {{z - 6} \over { - 1}} and {{x + 5} \over 7} = {{y - 2} \over { - 6}} = {{z - 3} \over 4} intersect at the point R. The reflection of R in the xy-plane has coordinates :

If the point (2, $$\alpha$$, $$\beta$$) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2$$\alpha$$ – 3$$\beta$$ is equal to

The perpendicular distance from the origin to the plane containing the two lines, {{x + 2} \over 3} = {{y - 2} \over 5} = {{z + 5} \over 7} and {{x - 1} \over 1} = {{y - 4} \over 4} = {{z + 4} \over 7}, is :

A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is :

The length of the perpendicular from the point (2, –1, 4) on the straight line, {{x + 3} \over {10}}= {{y - 2} \over {-7}} = {{z} \over {1}} is :

The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points ?

If the standard deviation of the numbers –1, 0, 1, k is $$\sqrt{5}$$ where k > 0, then k is equal to

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2 , (x2 – 4)2 ,....., (x50 – 4)2 is :

If for some x $$\in$$ R, the frequency distribution of the marks obtained by 20 students in a test is : .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-s6z2{text-align:center} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-hgcj{font-weight:bold;text-align:center} Marks 2 3 5 7 Frequency (x + 1)2 2x - 5 x2 - 3x x then the mean of the marks is

The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then {y \over x} is equal to

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :