21.

Find x and y if $\left[\begin{array}{cc}\mathrm{x}& 3\mathrm{x}\\ \mathrm{y}& 4\mathrm{y}\end{array}\right]\left[\begin{array}{c}2\\ 1\end{array}\right] = \left[\begin{array}{c}5\\ 12\end{array}\right]$

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots:

x² + (p – 3)x + p = 0.

In the figure alongside, OAB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion. (Take $\mathrm{\pi } = \frac{22}{7}$).

A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.

Find the mean of the following distribution by step deviation method:

Using a ruler and compasses only:

(i) Construct a triangle ABC with the following data:
AB = 3.5 cm, BC = 6 cm and $\angle$ABC = 120$°$

(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure $\angle$BCP.

The marks obtained by 120 students in a test are given below:

Draw an ogive for the given distribution on a graph sheet.

Use suitable scale for ogive to estimate the following:

(i) The median.

(ii) The number of students who obtained more than 75% marks in the test.

(iii) The number of students who did not pass the test if minimum marks required to pass is 40.

In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3, 4) on AB divides it in the ratio 2:3. Find the coordinates of A and B.

Using the properties of proportion, solve for x, given

$\frac{{\mathrm{x}}^{4 }+ 1}{2{\mathrm{x}}^2} = \frac{17}{8}$