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The sequence of numbers 5, - 2, -9, -16 ... is

There is a circle on the co -ordinate plane with two tangent lines x - y = 3 and x - y = 0. The meeting points of the circle with the 2 lines are ($\frac{3}{2}$,$\frac{3}{2}$) and (0,- 3). Find the radius and the centre of the circle.

Vijay inherited a large amount of wealth from his father and by establishing a soft drinks company, he squared his wealth. He then started a company which manufactured airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at a debt of 4 crore. Comment on the value of k.

If an A.P. consists of n terms with first term a and nth term l show that the sum of the mth term from the beginning and the mth term from the end is(a+l).

If tan  + sin  = m and tan  - sin  = n , Show that (m^2 – n^2 )^2 = 16 mn .

Find the values of k for which the quadratic equation $(k+4)x^2+(k+1)x+1=0$ has equal roots.

Select all that apply.

If the first term of an AP is 4 and the common difference is -4, find the second term.

The angle A of the triangle ABC is a right angle. The circle with AC as diameter cuts BC at point D. If BD = 6 cm & DC = 18 cm , calculate the length of AB.

Complete the following procedure of finding HCF of 1650 and 847

Solution :1650=__*1+803

______=___*1+44

803=___*___+11

44=__*1+____

HCF of 1650 and 847 is _______

Find the solution set for the following inequation:
$x+\frac{5}{2}<-\frac{5}{2}+5x$; $xϵR$

If fifth term of a G.P. is 4, then product of first nine terms is

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$, $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$,then the values of k, a, b respectively are ______ .

If the zeroes of the polynomial $P\left(x\right)=a{x}^2+bx+c$ are 1 and 2 , then find the value of a, b and c.

A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground.
The height of the pole is ___ if the angle made by the rope with the ground level is ${30}^{\circ }$.

If the value of $sin\theta =\frac{12}{13},$ then what is the value of $cosec\theta ?$

If $pcot\theta$ = $\sqrt{q^2-p^2}$ where θ is an acute angle , then the value of $sin\theta$ is___.

A tangent PA is drawn from an external point P to a circle of radius 3√2 cm such that the distance of the point P from O is 6 cm as shown figure. The value of ∠APO is

Which of the following about $x^2+12$ is true?

Find the roots of the quadratic equation $\sqrt{2}$$x^2$ + 7x + 5$\sqrt{2}$ = 0 using factorization method.

In Fig.6, OABC is a square of side 7 cm. IF OAPC is a quadrant of a circle with centre O, then find the area of the shaded regions. [Use =$\frac{22}{7}$]

Which of the following is an example of a direct tax?

Number of tangents can be drawn from a point which lies outside the circle is ___ .

A Pythagorean triplet is 7, 24, X. What is the value of X?

Step 4. Now, change the radius to R. Draw an arc such that it intersects line XY at E and line OD at F. Draw arcs with radius R and centres at E and F respectively such that they intersect at G. The $\angle GOE$ is __.
Note: Answer in degrees.

Question 12 (i)
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) quadrant OACB

There vertices of square are given in the figure below. If the fourth vertex is (2,P), find the value of P and the area of the square.

$(3,0)$ is a point on the line joining the points $(3x^2,6x)$ and $(3y^2,6y)$. Then,

Find the value of $\sqrt{20}$ using geometric method.

The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 (including 100) by _____.

If the sum of first 10 natural numbers is $S_1$ and that of first 10 whole numbers is $S_2$ . Then $S_1-S_2$ is ___

(i) A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35 m wide. If the area of the path is 420$m^2$, find the width of the path.

(ii) A carpet is laid on the floor of a room 8 m by 5m. There is a border of constant width all around the carpet. If the area of the border is 12 $m^2$, find its width.

If $(cosec\theta +cot\theta )=m$ and $(cosec\theta -cot\theta )=n$, show that mn = 1.

In the given figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5 cm and DE $\perp$ DF then the radius fo the circle is

(a) 3 cm (b) 4 cm

(c) 5 cm (d) 6 cm

The degree of a linear equation is

Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square .

The angle of elevation of an aeroplane from a point on the ground is ${45}^{\circ }$. After a flight of 15 seconds, the elevation changes to ${30}^{\circ }$. If the aeroplane is flying at a height of 3000 meters, find the speed of the aeroplane.

Solve each of the following quadratic equations:
$\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1},x\ne -1,\frac{1}{3}$

The sum of the digits of a two-digit number is 15.The number obtained by interchanging the digits exceeds the given number by 9.Find the number.

A hut has cylindrical base with radius 7 m and conical top of height 3 m. The total height of the hut is 7 m. Then the Curved surface area of the hut is ____

I have 6 terms in order a, b, c, d, e, f. What is/are the middle term/s?

The maximum number of common tangents that can be drawn to two given circles is

Find the common difference (d) in the following APs respectively.

(i) 20, 40, 60, 80, 100,..

(ii) 5, 0, -5, -10, -15, ...

(iii) 2, 2, 2, 2, 2..

For a matrix A, if $A^2=I$ where I is a unit matrix of same order, then (I - A)(I + A) is

If A = {x: $x^2$ - 5x + 6 = 0}, B = {2,4} , C = {4,5}, then

A×(B $\cap$ C) is