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Which of the following equations represents a circle with centre $(g,-2f)$ and radius $\sqrt{2g^2+4f^2-c}$ ?

(a) In a G.P of 6 terms the first and last terms are 5 and 160, find the remaining terms.

(b) Ganga marked a dot in the first square, 2 dots in the second, 4 in the third square and so on. How many dots should she mark in the 8^th square?

(c) Sahil purchased certain number of laddus and distributed five of his friends. He gave half of them to the first friend, half of the remaining to the second and so on. He and his fifth friend are remaining 33 laddus. How many laddus did Sahil purchase?

A man sold two goats at 900 rupees each. There was 10% profit on the first sale and 10% loss on the second sale. Was there a profit or a loss on the whole transaction? What percent?

There are 50 mangoes in a basket, 20 of which are unripe. Another basket contains 40 mangoes, with 15 unripe. If we take one mango from each basket, what is the probability of both being ripe?

In the given fig. $\theta$ ABC is an equilateral triangle inscribed in a circle of radius 4 cm and centre O. Show that the area of the shaded region is $\frac{4}{3}(4\pi -3\sqrt{3})c{m}^2$. [4 MARKS]

In fig. XP and XQ are tangents from X to the circle with center O. R is a point on the circle. Prove that, XA + AR = XB + BR. [2 MARKS]

Write the following in increasing order:

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For the equation y = 3x - 7, if y = 0, then what is the value of x?

Circles centred at A and B cut at P. Prove that if AP is a tangent to the circle centred at B, then BP is tangent to the circle centred at A.

From the figure, given below, calculate the length of CD.

If the straight lines $\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar, then the plane(s) containing these two lines is/are

Solve the following inequalities graphically in two dimensional plane: x+y < 5

While drawing a histogram for the discontinuous grouped data, if in case, the class intervals are given in the inclusive form, then in order to convert them into exclusive form, we must,

$\frac{sinA-2si{n}^{3}A}{2co{s}^{3}A-cosA}$

If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y =0.

The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

(a) 3 : 2 (b) 4 : 9 (c) 2 : 3 (d) 81 : 16

If the zeroes of $x^2+ax+b$ have opposite signs but equal magnitude, then

Draw two tangents to a circle of radus 3.5 cm from a point P at a distance of 6.2 cm from its centre.

Which of the following statement is true for the given triangles?

Solve ax²-9(a+b)x+(2a²+5ab+2b²)=0

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$, then $A^4$=__________________

The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge $4.2cm$ is

(a) $2.1cm$ (b) $4.2cm$ (c) $8.4cm$ (d) $1.05cm$

Which of the following represents an empirical relationship between Median, Mode and Mean?

Which of the following statements are true?

(i) All cubes are cuboids.

(ii) All cuboids are cubes.

(iii) A cube has 6 faces, 8 corners, 12 edges.

(iv) A cube has 8 faces, 12 corners and 6 edges.

Find the point on the y-axis which is equidistant from A (3, - 4) and B (- 5, 9).

1. 7

$\frac{4}{co{t}^2{30}^{\circ }}+\frac{1}{si{n}^2{30}^{\circ }}-2co{s}^2{45}^{\circ }-si{n}^2{0}^{\circ }$

Find the coordinates of points of trisection of the line segment joining the points A(-2, 8) and B(4,12)

Three dices are painted with 3 different colours such that the opposite faces of the dice have the same colour. If they are thrown simultaneously, then what is the probability of getting different colours on all the three dices?

Ogives can be used to find _____.

Rakesh bought a Shirt for ₹ 1035 including a sales tax of 15 % and a pant for ₹ 1100 including a sales tax of 10 % . The printed price ( without sales tax ) of Shirt and Pant together is ₹ _____________