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Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

Find an A.P in which the sum of any number of terms is always three times the squared number of these terms.

Find the value of k, if x - 1 is a factor p(x) in each of the following cases:
(i) $p\left(x\right)=x^2+x+k$
(ii) $p\left(x\right)=2x^2+kx+\sqrt{2}$
(iii) $p\left(x\right)=k{x}^2-\sqrt{2}x+1$
(iv) $p\left(x\right)=k{x}^2-3x+k$

If the Cartesian product A $\times$ A has 16 elements among which a few elements are found to be (-1, 0), (0, 1), (1, 2). Find set A.

Show that the right circular cone of
least curved surface and given volume has an altitude equal to

time the radius of the base.

Which of the following list of numbers forms an AP?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

In a certian A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.

Find the coordinates of a point on y-axis which are at a distance of $5\sqrt{2}$ from the point $P(3,-2,5).$

Which of the following debts is comparatively greater than the other debt as a percentage of the Gross Domestic Product of India?

Question 13

The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is



(A) $4950c{m}^2$

(B) $4951c{m}^2$

(C) $4952c{m}^2$

(D) $4953m^2$

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.

$(Use\pi =\frac{22}{7})$

Fig shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and $\Delta CEF$ is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.

Coffee is draining from a conical filter with height and diameter both $15$ cm, into a cylindrical coffee pot with diameter $15$ cm. The rate at which coffee drains from the filter into the pot is $100$ cc/min. The rate in cm/min at which the level in the pot is rising at the instant when the coffee in the pot is $10$ cm, is

Consider the following pattern.





Choose the option that comes next in the pattern.

The cost of 2kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

If A and B invest some amount for the same time and after one year share their profit in the ratio of 3: 4 respectively. If the total investment is ₹ 7000, what is the investment of A?

If the zeros of the polynomial $f\left(x\right)=x^3-3x^2+x+1$ are (a-b), a and (a+b), find a and b.

If ($x^5$-9$x^2$+12x-14) is divided by (x – 3), the remainder is

If a cuboidal carton has length 80 cm, breadth 40 cm and height 60 cm, then the volume of the carton is .

If the probability of an event happening is x, then the probability of event not happening is___

What is the sum of the first 30 odd numbers?

Cost of production of each unit of electricity is 3 less than twice the total number of units produced. If the total cost of production is ₹ 20, find the number of units of electricity produced.

A car travels at a speed of 60 km/hr. Write the distance – time formula and draw the graph of it. Also, find the distance travelled by the car in 5 hours.

A hundred rupee note was changed to ten rupee notes and twenty rupee notes, eight notes in all. How many tens and how many twenties?

If $x+4y=14$ is a normal to the curve $y^2=\alpha x^3-\beta$ at point $(2,3),$ then value of $\alpha +\beta$ is

One angle of a triangle is 110° and the side opposite to it is 4 centimetres long. What is its circumradius?

The equation of the line given in the following graph is:

Condition satisfied by the pair of equation $2x+3y=-5$ and $4x+6y-10=0$ is

$cosx+secx=2,(0<x<{90}^{\circ })$
What is the value of $se{c}^{n}x+co{s}^{n}x$ equal to if n is an integer?

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 45 cm, find the area in $c{m}^2$ between the two consecutive ribs of the umbrella.

The area of the parallelogram constructed on the Vectors $\overrightarrow{a}=\overrightarrow{p}+2\overrightarrow{q}$​ and$\overrightarrow{b}=2\overrightarrow{p}+\overrightarrow{q}$ ​ as sides, where $\overrightarrow{p},\overrightarrow{q}$​ are unit Vectors forming an angle of ${60}^0$ in square units is

From the alphbet of English, pick out one alphbat which has (i) one-3 node (ii) two-3 node (ii) one 4-node.