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If in a two digit number, the sum of both the digit is 3 times it's positive difference and the difference of both the didgits is 4, find the number.

In △ ABC, D is a point on BC such that BD: DC = 3 : 2. If area △ ABD = 45 sq cm, then area of △ ADC = ____ sq cm.

Find algebraic expressions which give the perimeters and areas of all rectangles with length 1 centimetre more than the breadth.

An open box A is made from a square piece of tin by cutting equal squares S at the corners and folding up the remaining flaps. Another open box B is made similarly using one of the squares S. If U and V are the volumes of A and B respectively, then which of the following is not possible?

The point where the tangent meets the circle is called ___

The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

1. 14

Kiran deposited Rs 200 per month for 36 months in a bank's recurring deposit account. If the bank pays interest at the rate of 10% per annum, find the amount she will get on maturity.

If P(A) and P(A') are complementary events and P(A) = 0.15, then P(A') = ?

Quotient and remainder of a polynomial when divided by $x+2$ are $2x-1$ and $3$ respectively. Find the polynomial.

From the given Frequency distribution table, find the Average Class Mark.

$\begin{array}{cc}\text{Class Internal}& \text{Frequency}\\ 0-10& 2\\ 10-20& 8\\ 20-30& 12\\ 30-40& 7\\ 40-50& 9\\ 50-60& 4\\ 60-70& 5\end{array}$

Let a pair of dice be thrown and the random variable $X$ be the sum of the numbers that appear on the two dice. Then the mean or expectation of $X$ is:

Two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centers, up to two places of decimal.

If the points (1,2), (0,0) and (a,b) are collinear, then the area of the triangle formed by these points is ____.

Find the volume of the sphere whose radius is 3 cm.

A metal block is in the shape of a cuboid measuring 4 cm x 4 cm x 3 cm. A hole of radius 1.5 cm is drilled through the block such that it is ⏊ to the sides of the cuboid that measure 4 cm x 4 cm. What % of original metal remains? (π = 3.14)

In the given figure, an equilateral triangle $ABC$ is inscribed in a circle. If $AB=2\sqrt{2}\text{cm}$ then the area of the circle is

What is the value of the polynomial

$x^2-3x+5$ at $x=3?$

The height of a tree is 10$\sqrt{3}$ m, if a boy looks at the top of the tree with an angle of elevation of ${30}^{\circ }$, find the distance between the boy and the tree.

In a $△ABC$, Let P and Q be points on AB and AC respectively such that PQ || BC. Prove that median AD bisects PQ [3 MARKS]

AB is divided in the ratio a:1 by a point which lies on the line x + y = 10. Find the value of a.

Question 1(i)
Evaluate:

$3^{-2}$

Identify the major sector and minor segment in the given figure:

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be `x` km/h form an equation and solve it to evaluate `x`.

The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A'', then coordinates of A'' will be