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Question 2 (iii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^3-3x+1,x^5-4x^3+x^2+3x+1$

From the following Receipts and Payments Account of Golden Cricket Club, New Delhi, prepare the Income and Expenditure Account for the year ended March 31, 2017:

$\begin{array}{cccc}\text{Receipts}& \text{Rs}& \text{Payments}& \text{Rs}\\ \text{Cash in hand as on}& & \text{Printing and Stationery}& 38,750\\ \text{April 1, 2016}& 20,000& \text{Lighting}& 26,250\\ \text{Cash at Bank as on}& & \text{Rates and Taxes}& 17,000\\ \text{April 1, 2016}& 35,000& \text{Telephone charges}& 2,600\\ \text{Subscriptions}& & \text{Postage and Courier}& 2,000\\ 2015-1630,000& & \text{Wages and Salaries}& 88,000\\ 2016-172,25,000& & \text{Insurance Premium}& 15,000\\ 2017-18\underset{–}{10,000}& 2,65,000& \text{Purchase of Funiture}& 2,00,000\\ \text{Donation for building}& 60,000& \text{Cash in hand as on}& \\ \text{Entrance fees}& 23,000& \text{March 31, 2017}& 23,400\\ \text{Life membership fee}& 20,000& \text{Cash at Bank as on}& \\ \text{Interest}& 18,000& \text{March 31, 2017}& 70,000\\ \text{Locker's rent}& 42,000& & \\ & \underset{–}{\overline{4,83,000}}& & \underset{–}{\overline{4,83,000}}\end{array}$

What are the roots of the quadratic equation $(x+2{)}^2$-16 = 0?

There is a circular swimming pool with centre O. There are 2 points on the wall named A and B. A rope is attached between A and B. This rope separates the shallow section of pool from deep section of pool. The shallow section is the smaller section. Which of following statements are true?

$\frac{x}{a}cos\theta$ + $\frac{y}{b}sin\theta$ = 1

$\frac{x}{a}sin\theta$ - $\frac{y}{b}cos\theta$ = 1

Which of the following options is correct ?

The characters in the phrase "THE END" are randomly rearranged. (This includes the six letters and the space.) What is the probability that
(i) The Es will appear together. (ii) The new phrase will also have two 3 letter words. (iii) There will be one 6 letter word. [4 MARKS]

From the top of a tower $50m$ high angles of depression of the top and bottom of a pole are observed to be ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the height of the pole.

2 triangles are similar if their corresponding angles are porportional.true or false and justification.

Solve the following inequation;
$9x+7\le 2x+84;xϵR$.

The sum of the radius of the base & height of a solid cylinder is 37 m. If the total surface area of solid cylinder is 1628 m², find the circumference of its base & volume of cylinder

$If\frac{si{n}^4\theta }{a}+\frac{co{s}^4\theta }{b}=\frac{1}{a+b^{\prime }},provethat\frac{si{n}^8\theta }{a^8}+\frac{co{s}^8\theta }{b^8}=\frac{1}{a+b^8}$

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. What is the surface area of the cylinder?

Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46,find the integers.

The sum to n terms of the series 1 + 3 + 7 + 15 + . . . . . .

Five times a number exceed 60 by 5. Find the number.

If Pand Q are the points of trisection of the segment AB,what is the ratio of AQ:QB ?

What is the reflection of the point $A(1,2)$ in the line $x=1$?

In triangle ABC, DE is parallel to BC; where D and E are the points on AB and AC respectively. Also, if AD = 12 cm, BD = 24 cm and BC = 8 cm, the length of DE is

Two dice are thrown. The probability that the sum of numbers coming up on them is 9, if it is known that the number 5 always occurs on the first die, is

Find the area of the dotted portion if the dimensions are as specified in the figure. r = $\frac{l}{4}$.

Saraswati Ltd. issued 10,000 $6\%$ Debentures of Rs 100 each at a premium of $5\%$ on 1st April, 2013 redeemable on March 31,2018. The issue was fully subscribed. It was decided to invest $15\%$ of the face value of debenture to be redeemed towards Debenture Redemption Investment on 30th April 2017. Investments were encashed and Debentures were redeemed on due date. Record necessary entries for issue and redemption of deberature.

If the equation px² – 6x – 2 = 0 has real roots then, ________

Which method of purification is represented by the following equations?

$Ni+4CO$ $\stackrel{{70}^{\circ }C}{\to }$ $Ni(CO{)}_4$ $\stackrel{{180}^{\circ }C}{\to }$ $Ni+4CO$

A rhombus whose side measures 20 cm has one of the angles as ${60}^{\circ }.$. The area of the rhombus will be equal to

If an isosceles right - angled triangle has area $200c{m}^2$, then the measure of its hypotenuse is _______________ cm.

The value of the expression $16x^2+24x+9$ for $x=0$ is _____.

There are 2 questions titled A and B and there are 6 answers numbered from 1 to 6. In each of the answer options, each question is matched with an answer. Pick the correct match from the answer options.

A - What is the shortest distance between center of a circle and tangent?

B - What is the shortest distance between a point and a line?

A line segment can be divided in any given ratio.What property of similar triangles justify this construction? [1 MARK]

The prime factorisation of 272 is .

Water running in a cylindrical pipe of inner diameter $7cm$, is collected in a container at the rate of $192.5$ litres per minute. Find the rate of flow of water in the pipe in $km/hr$.

A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be Rs. 2640 at the rate of Rs. 12 per metre. Then, the field is to be thoroughly ploughed at the cost of Rs. 0.50 per $m^2$. What is the amount required to plough the field? [Take $\pi =\frac{22}{7}$]

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).

1. 32

Rs. 9800 are invested partly in $9\%$ stock at 75 and $10\%$ stock at 80 to have equal amount of incomes. The investment in $9\%$ stock is:

If the points A(1,2) ,O(0,0), C(a,b) are collinear then find ratio a is to b.

Please give the answer based on those three methods of co-ordinate geometry and not on slope and alll

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs Rs. 8,000. If it breaks into two pieces whose weights are in the ratio 3:2, then the loss incurred (in rupees) is

The circumference of a circle is 123.2 cm. Calculate

TanA÷1-cotA+ cot A÷1-tanA=1+ sec A *cosec A

A box contains 10 red flowers, 6 white flowers, 4 pink flowers, and 8 yellow flowers. When Swetha picks a flower at random, what is the probability that the flower is Pink?

The following graphs give annual data of Assets, Sales (as fraction of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 - 2009.

What was the maximum value of spending on CSR activities in the period 2004-2009 (approximately)?

___________ = $\sqrt{\left(\frac{1+sinA}{1-sinA}\right)}$

Find the value of x³+1/x³,if x²+1/x²=14

AB = $\sqrt{{}^{\prime }\_\_{\_}^{\prime }}units$

__

Find the equation of a straight line passing through (1,2) and perpendicular to the line y=7.