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The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

A doorway is decorated as shown in the figure. There are 4 semi circles. BC, the diameter of the larger circle is of length 84 cm. Centres of 3 semi circles lie on BC. ∆ ABC is isosceles with AB = AC. If BO = OC, find the area of shaded region.

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ∼ ΔECF

A cardboard rectangle is cut out and the midpoint of one side is joined to the other ends to make a triangle. If you randomly put a dot in the rectangle, what is the probability that it would be within the triangle?

Find the centroid of the triangle with vertices A$(x_1,y_1)$, B$(x_2,y_2)$ and C$(x_3,y_3)$.

Two numbers are in the ratio 2 : 3. If 9 is added to each, they will be in the ratio 3 : 4. Find the numbers.

A jar containing $2695c{m}^3$ of juice is used to fill smaller hemispherical bowls having radius 3.5 cm. Find the number of bowls that can be filled.

The complete set of values of 'k' for which $\frac{x^2-x}{1-kx}$ attains all real values is

The equation of a line AB is 2x - 2y + 3 = 0, its slope is ______.

In the figure below, is any side of ΔABC parallel to X axis? If so, the side is ______

$2$ cubes each of volume $64c{m}^3$ are joined end to end. Find the surface area of the resulting cuboids.

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

The base PQ of two equilateral triangles PQR and PQR' with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R' of the triangles.

A cone of maximum volume is carved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the cone carved out correct to 1 d.p. (π = 3.14)

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5cm and height 4 cm.How many bottles are needed to empty the bowl?

A circle of diameter 13 cm has two chords of length 12 cm and 5 cm. If both the chords lie in the same semi-circle, what is the distance between the chords?

△ ABC and △ ABD have the same base AB and are between the same parallels. If area △ ABC = 150 sq cm, then area of △ ABD = ____ sq cm.

What do the images below represent?

Krishna Kulkarni has not kept proper books of accounts. Prepare the statement of profit or loss for the year ending December 31, 2005 from the following information:

$\begin{array}{ccc}\text{Items}& \text{Jan 1, 2005 (Rs.)}& \text{Dec 31, 2005 (Rs.)}\\ \text{Cash in hand}& 10,000& 36,000\\ \text{Debtors}& 20,000& 80,000\\ \text{Creditors}& 10,000& 46,000\\ \text{Bills receivable}& 20,000& 24,000\\ \text{Bills payable}& 4,000& 42,000\\ \text{Car}& \underset{–}{}& 80,000\\ \text{Stock}& 40,000& 30,000\\ \text{Furniture}& 8,000& 48,000\\ \text{Investment}& 40,000& 50,000\\ \text{Bank Balance}& 1,00,000& 90,000\end{array}$

The following adjustements were made-

(a) Krishna withdrew cash Rs 5,000 per month for private use.

(b) Depreciation 5% on car and furniture 10%.

(c) Outstanding rent Rs.6,000.

(d) Fresh capital introduced during the yaer Rs.30,000.

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

If two identical solid cubes each of volume 64 cm³ are joined end to end, then the total surface area of the resulting cuboid is:

Which among the following is a factor of $x^2+\frac{x}{6}-\frac{1}{6}?$

With respect to the roots of $x^2–2x–3=0$, we can say that

If ${\sin }^{-1}(-\frac{\sqrt{3}}{2})+{\cos }^{-1}(-\frac{1}{2})={\tan }^{-1}x,$ then the value of $x$ is equal to

The figure obtained when a rectangular sheet is rolled up is

For what value of k, the system of equations x+y-4=0 and 2x+ky-3=0 has no solution.