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AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that CD = 4 cm, then find the length of AB.

Length of tangent drawn from any point of circle $x^2+y^2+2gx+2fy+c=0$ to the circle $x^2+y^2+2gx+2fy+d=0$, (d > c) is

If the sum of the first $n$ terms of an AP is $5n-n^2$, the common difference is ______

A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal is

If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is:

Question 1 (iii)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^4-5x+6,g\left(x\right)=2-x^2$

If tanθ + sinθ = m; tanθ - sinθ = n show that m²-n² = 4(mn)^1/2

A paper is rectangular in shape with negligible thickness. A stack of papers is arranged one above the other.

S1 : The resulting figure is three dimensional.

S2 : The figure is called a cuboid.

Find the value of k, if the line represented by the equation 3x – ky = 12 passes through the point (4,2). [2 MARKS]

Determine the ratio in which the line $2x+y-4=0$ divides the line segment joining the points A(2, -2) and B (3, 7).

Radhika bought a new mobile phone and saved ₹ 1000 when a discount of 10$\%$ was given. What was the price of the mobile phone before the discount? What was the selling price of the phone?
[4 MARKS]

Which of the following graphs represent the solution of the inequation written below:

$2x-5\le 5x+4<11,xϵR$

Which among the following is a polynomial in one variable?

What is the angle between two planes having normal vectors as
$\overrightarrow{n_1}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{n_2}=4\hat{i}-4\hat{j}+2\hat{k}$ ?

In a right angled triangle, If cot x = 4, what is the value of tan x ?

The given figure shows a trapezium in which AB is parallel to DC and diagonals AC and BD intersect at point P, If AP : CP = 2 : 3.

Find -

(i) $\Delta APB:\Delta CPB$

(ii) $\Delta DPC:\Delta APB$

(iii) $\Delta ADP:\Delta APB$

The number of terms of an A.P. is even; the sum of odd term is 24, of the even terms is 30, and the last term exceeds the first by $10\frac{1}{2}$, find the number of terms and the series.

ABC is a right triangle, right angled at B. A circle is inscribed in it. The lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the incircle. [4 MARKS]

Which among the following is irrational?

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.

If you are asked to construct APQ ~ ABC in the scale factor $\frac{3}{5}$. In $△ABC$, AB = 4 cm, BC = 3 cm and $\angle ABC$ = ${90}^{\circ }$.

A Technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. What should be the length of the ramp that she should use which, when inclined at an angle of ${30}^{\circ }$ to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ramp? (You may take $\sqrt{3}$ = 1.73)

Find the area of a circle whose circumference is 8$\pi$.

A man invests some money in his shares. He invests $60\%$ of his money at $10\%$. Rs 100 shares at Rs 110 and the rest in $20\%$. Rs 50 shares at Rs 60. If his total annual income from both the investments is Rs 2000, then his total investment is ____

If the median of the data $4,7,x-1,x-3,16,25$,written in ascending order,is 13 then x is equal to

(a) 13 (b) 14 (c) 15 (d) 16

ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places. (Take $\pi =3.142$ and $\sqrt{3}=1.732$)

The probability of drawing an even prime from cards marked 1 to 20, is?

Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.

Find the LCM of all the numbers from 1 to 10 (both inclusive)

The sum of first n terms fo an AP is $(5n-n^2)$ the nth term of the AP is
(a) (5-2n) (b) (6-2n) (c) (2n-5) (d) (2n-6)

In a right circular cone, the cross section made by a plane parallel to the base is a

(a) sphere (b) hemisphere (c) circle (d) a semicircle

Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of the third is atmost $20.$

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Prove that, Tan theta upon sec theta - 1=Tan theta + sec theta +1 upon Tan theta + sec theta - 1.

In a G.P. if the ${(m+n)}^{th}$ term is p and ${(m-n)}^{th}$ term is q , then its $m^{th}$ term is:

Kapil purchased goods for Rs. 21,000 from Gaurav on 1st February, 2016 and accepted the bills of exchange drawn by Gaurav for the same amount. The bill was payable after a month. On 25th February, 2016, Gaurav sent the bill to his bank for collection. The bill was duly presented by the bank. Kapil dishonoured the bill and the bank paid Rs. 100 as noting charges.

Record the necessary journal entries for the above transactions in the books of Kapil and Gaurav.

Correct meaning, definition , and differences between rational and irrational which I can understand clearly

In the adjoining figure, O is the centre of the circle and AB is a tangent to it at point B. $\angle BDC={65}^o$. Find $\angle$ BAO.

Consider a circle of diameter 7 cm which is confined in a square of the side 7cm. A point is chosen at random in the plane of the square. What is the probability that the chosen point lies in the circle?

The probability of getting 53 Fridays in a leap year is .

Which of the following is an empty set