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If the Cartesian product A $\times$ A has 32 elements among which few elements are found to be (-2, -1), (0, -1), (1, 0), (-2, 2). Find set A.

Find the lengths of the medians of a $△ABC$ whose vertices are A(0,-1), B(2,1) and C(0, 3)

Question 6

Shaina pays Rs 7500 as rent for 3 months. How much does she have to pay for a whole year, if the rent per month remains same?

Solve each of the following systems of equations by the method of cross-multiplication:

$\frac{ax}{b}-\frac{by}{a}=a+b$

$ax-by=2ab$

$5$ pencils and $7$ pens together cost $Rs.50,$ whereas $7$ pencils and $5$ pens together cost $Rs.46.$ Find the costs of one pencil and one pen.

Question 73

In the given figure, O is the centre of the circle,

a) Name all chords of the circle.

b) Name all radii of the circle.

c) Name a chord, which is not the diameter of the circle.

d) Shade sectors OAC and OPB.

e) Shade smaller segment of the circle formed by CP.

Which of the following rational number have a terminating decimal expansion?

$△ABC$ is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.$△DEF$ is similar to $△ABC$. If EF = 4 cm, then the perimeter of $△DEF$ is -

Q8. Consider the following statements about Equity Markets:

1. An equity market is different from a share market.

2. Equity market is the aggregation of buyers and sellers of stocks.

Select the correct answer using the codes given:

Which of the following are the graphs of even functions?

In a right $△$ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of $△$ABD and $△$ACB?

To draw a pair of tangents to a circle which are inclined to each other at an angle of ${120}^{\circ }$, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

The sum of 'r' terms of an AP is $2r^2+3r$. The $n^{th}$​ term of the AP is :

Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.

From the foot and the top of a building of height $230m$, a person observes the top of a tower with angles of elevation of $\beta$ and $\alpha$ respectively. What is the distance between the top of the building and the top of the tower if $\tan \alpha =\frac{5}{12}$ and $\tan \beta =\frac{4}{5}$?

What is the smallest number that when divided by 35 , 36 and 91 leaves remainder 7 in each case?

If a line is making ${60}^o$ with the positive X direction. The slope of the line is:

Find the values of k for which th efollowing equations have real roots.
$\left(i\right)2x^2+kx+3=0\left(ii\right)kx(x-2)+6=0\left(iii\right)x^2-4kx+k=0\left(iv\right)kx(x-2\sqrt{5})+10=0\left(v\right)kx(x-3)+9=0\left(vi\right)4x^2+kx+3=0$

A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

1. 368

The length of a room exceeds its breadth by 3 metres.If the lengths increased by 3 metres and the breadth is decreased by 2 metres,the area remains the same.Find the length and the breadth of the room.

A (4, 2), B(6, 5) and C (1, 4) are the vertices of ΔABC.



(i) The median from A meets BC in D. Find the coordinates of the point D.



(ii) Find the coordinates of point P and AD such that AP : PD = 2 : 1.



(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1



(iv) What do you observe?

Prove that the areas of similar triangles have the same ratio as the squares of the radii of their circum circles.

In the following figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Question 11 (ii)

State whether the following are true or false. Justify your answer.

(ii) sec A = $\frac{12}{5}$ for some value of angle A.

A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.

All goods are classified by giving numerical code called ___ code.

What number added to 3x³ − 2x² + 5x given a polynomial for which x − 1 is a factor?

If -4 is a zero of the polynomial $x^2-x-(2k+2)$ then find the value of k.