For the frequency distribution :
Variate (x) :      x₁   x₂   x₃ ....  x₁₅
Frequency (f) : f₁    f₂   f₃ ...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and
$$\sum\limits_{i = 1}^{15} {{f_i}} $$ > 0, the standard deviation cannot be :

Let P be a point on the parabola, y² = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is $${4 \over 3}$$, then :

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :

The area (in sq. units) of the region

{ (x, y) : 0 $$ \le $$ y $$ \le $$ x² + 1, 0 $$ \le $$ y $$ \le $$ x + 1,

$${1 \over 2}$$ $$ \le $$ x $$ \le $$ 2 } is :