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How many terms of the AP: 9, 17, 25, ... must be added to get a sum of 636?___

Overdraft shown by the pass book of Mr Murli is Rs. 20,000. Prepare bank reconciliation statement on dated December 31, 2010.

(i) Bank charges debited as per pass book, Rs. 500,

(ii) Cheques recorded in the cash book but not sent to the bank for collection, Rs. 2,500.

(iii) Received a payment directly from a customer, Rs. 4,600.

(iv) Cheque issued but not presented for payment, Rs. 6,980.

(v) Interest credited by the bank, Rs. 100.

(vi) LIC paid by the bank, Rs. 2,500.

(vii) Cheques deposited with the bank but not collected, Rs. 3,500.

The sum of n terms of an AP is given by

Take a one-meter rod and mark $4$ points on it such that each segment is of equal length.

If we take OA to be X units, then X units is equal to:

A square pyramid covers an area of $400m^2$ on the ground.
If the height of the pyramid is 10 m, then the total surface area of the pyramid is .

Solve the equation $x^2–2x–3=0$ using quadratic formula.

r Two Isosceles triangles have equal vertical angles and their areas are in the ratio 36:25 find then ratio of their corresponding height.

Find the general term $\left(n^{th}term\right)$ and ${23}^{rd}term$ of the sequence 3, 1, -1, -3, ......... .

What will be the angle of elevation of top of a 15 m high tower at a point 15 m away from the base of the tower?

A point lies inside the circle. So it can have __ tangents. (Fill in the blanks with 0,1,2 or 3)

Degree of any constant polynomial is ______________

Which of the following should be the LAST sentence after rearrangement?

If the squared difference of the zeroes of the quadratic polynomial f(x)=x^{​​​​​​2}+px+45 is equal to 144 find the value of p.

The photograph of a house occupies an area of 1.75cm^2 on a 35mm slide. The slide is projected on to a screen and the area of the house on the screen is 1.55m^2.what is the linear magnification of the projector-screen arrangement?

Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data :

AB = 3.5 cm, BC = 6 cm and $\angle ABC={120}^{\circ }$

(ii) In the same diagram draw a cricle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure $\angle BCP.$

Prove that

Cot^{​​​​2} ​​​​​​A × cosec^​​2​A - cot^{​​​​2}​​​B × cosec^​​2 B = cot^{​​​​2}​​​A - cot^{​​​​2} B

If the equation 9x² – 6x + c = 0 has equal roots then, the value of c is

The ratio between the sum of n terms of two A.Ps is 3n + 8 : 7 n + 15. Then the ratio between their ${12}^{th}$ terms is :

If a, b, c are in AP as well as GP, then which one of the following is correct?

If the mean and the median are 25.41 and 26.5 respectively. then the mode is

One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son's age. Find their present ages.

Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.

If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

The value of p when x³ + 9x² + px - 10 is exactly divisible by (x+ 2 ) is ____

Household income of 31 houses has been given in the table.

Calculate the median income.

$\begin{array}{cc}\text{Monthly income (Rs)}& \text{No. of households}\\ 40000& 3\\ 50000& 7\\ 60000& 8\\ 70000& 5\\ 80000& 5\\ 90000& 3\end{array}$

If two zeros of the polynomial f(x) = $x^4-6x^3-26x^2+138x-35$ are $2\pm \sqrt{3},$ find other zeros.

In the figure, PT touches a circle with center O at R. Diameter SQ when produced meets RT at P. ∠SPR = ^o, ∠QRP = y^o, find the value of ^o + 2y^o.

If $A=\left[\begin{array}{cc}cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{array}\right]$, then $A^2=$

In the figure, O is the centre of a circle of radius 9 cm. Semicircle with Diameter OA cuts the circle at D and BC is a tangent through B.

If OA = 25 cm , then BC = ____.

If A = ${115}^{\circ }$ and B = ${110}^{\circ }$, then the value of

$\frac{1+cotA}{cotA}.\frac{1+cotB}{cotB}$ is __ .

Find the value of the following expression:
$\frac{cos{38}^{o}cosec{52}^o}{tan{18}^{o}tan{35}^{o}tan{60}^{o}tan{72}^{o}tan{55}^o}$ .

Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of her other diagonal.

In the figure, $AC=10cm,PC=15cm,PQ=12cm,$ find PB.

If in an A.P., $S_n=n^{2}p$ and $S_m=m^{2}p$, where $S_r$ denotes the sum of r terms of the A.P., then $S_p$ is equal to

Quadratic equation consists a polynomial of degree:

Find the median of the following data.

$\begin{array}{ccccccccc}\text{MARKS OBTAINED}& 20& 29& 28& 33& 42& 38& 43& 25\\ \text{NUMBER OF STUDENTS}& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$

The angle of elevation of a cloud from a point 'h' m above a lake is $\theta$. The angle of depression of its reflection in the lake is ${45}^{\circ }$. Find the height of the cloud.

Find the additive inverse of the matrix$\left[\begin{array}{ccc}2& 0& -1\\ -2& 34& -13\\ 45& 12& 78\end{array}\right]$

The graph of the polynomial p(x) intersects the x-axis three times in distinct points, then which of the following could be an expression for p(x):

If a - 14, a - 2, a + 34 are in G.P, find the value of a.

___

If 1 is a zero of the polynomial $a{x}^2-3(a-1)x-1$ then find the value of a.

Prove the following trigonometric identities:

$se{c}^6\theta =ta{n}^6\theta +3ta{n}^2\theta se{c}^2\theta +1$

For a certain distribution,mode and median were found to be 1000 and 1250 repsectively.Find mean for this distribution using an empirical relation.

Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this AP is ______.

What is the 5th term from the end of the AP 2, 7, 12, ..., 47?