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751.

Prakash, Rohit and Sameer cam complete a job in 1 days, 20 days, adn 10 days, respectively. They sarted the job but Prakash was unwell on the first day, he couldnot work at his full capacity and Prakash left after a day. Theother two completed the job. Rohit was pair Rs. 17,000 out of the totalof Rs. 60,000 paid to them. At what percentage of his full capicity, did Prakash work on the first day ?

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ANSWER :`15%`
752.

If a= (sqrt5 +1 )/( sqrt5 -1)and b = (sqrt5 -1)/(sqrt5 +1) the find the value of(4a^(2) -3ab + 4b^(2))

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Answer :(a)= 32
(B) =289
© = ` 22 SQRT2`
753.

For parallelogram ABCD, ar(ABCD)=48 cm^2 . Then ar(ABC)=___ cm^2

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96
48
24
12

Answer :B::D
754.

The mean of 10 numbers is 24. If one more number is included, the new mean is 25. Find the included number.

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ANSWER :35
755.

The mid-points of the sides AB, BC and CA of the equilateral DeltaABC are D, E and F respectively, AE intersects DF at O. If angleOBD=15^@ , then angleAOB=

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`45^@`
`105^@`
`120^@`
`135^@`

ANSWER :d
756.

Verify whether 2 and 1 are zeros of the polynomial x ^(2) - 3x + 2 or not ?

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ANSWER :` X ^(2) - 2X + 2`
757.

Which of the following is an appropriate algorithm to add two numberA and B

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(i) Read the two NUMBER A and B
(II) Display the sum of the numbers
(iii) Add the two numbers
(i) Read the two number A and B
(ii) Add the two number A and B
(iii) Display the sum
(i) Display the sum of the number
(ii) Read the two number A and B
(iii) Add the number A and B
(i) Add the two number A and B
(ii) Read the two number A and B
(iii) Display the sum

Solution :Read the option carefully and DECIDE the correct output for p =6
758.

Write four solutions for each of the following equations : pix + y = 9

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ANSWER :`(0,9),(1,9,-PI) ,(-1,9+pi) and (1/(pi),8)`
759.

Expand each of the following using suitable identities : (-2x+3y+2z)^(2)

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Answer :`4X^(2) + 9y^(2) + 4z^(2) - 12XY + 12YZ - 8zx`
760.

Find the value of (sqrt(10)-sqrt5)/(2sqrt2) upto three decimal places. (take sqrt2=1.414 and sqrt5=2.236)

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ANSWER :0.3273
761.

Goutham invested Rs.4000 to buy Rs.125 shares of type from a company and invested Rs.4800 to buy Rs.120 shares of type B from it. He obtains 8% dividend from A and 10% dividend from B. Find the total annual dividend he carried if the market value of each equals its face value. (in Rs.)

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600
750
800
1000

Solution :(i) Find the dividend RECEIVED per SHARE each case.
(II) Total dividend from share A is `8%` of Rs.4000.
(III) Total dividend from share B is `10%` of Rs.4800.
762.

On the occasion of New year's day a sweet stall prepared sweet packets. Number of sweet packets and cost of each packet are given as follows. Find the mean, median and mode of the data.

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Answer :`bar x=80`; MEDIAN = 75; MODE = 50
763.

A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

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ANSWER :`550 CM^(2)`
764.

Faactorise (i) 27a ^(3) + 64 b ^(3)

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Answer :(i) `(3A + 4b) (9a^(2) -12ab+ 16 B ^(2)) `
765.

From a circle of radius 15cm . A sector with angle 216 ^(@)is cut out and its bounding radius are bent so as to form a cone . Find its volume.

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ANSWER :` 1018.3 CM ^(3) `
766.

Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.

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ANSWER :44
767.

In the given figure ‘O’ is the centre of the circle andAB, CD are equalchords.If angleAOB = 70^@ . Find the angles of the DeltaOCD

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ANSWER :`70^@ , 55^@, 55^2`
768.

Find p (0) p, (1) and p (2) forthe following polynomials. p (x) = x ^(2) - x +1

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ANSWER :`1,1,3`
769.

Boundaries of solid are

Answer»

LINES
curves
surfaces
none of these

SOLUTION :BOUNDARIES of soliders are CALLED surface
770.

Classify the following numbers as rational or irrational. sqrt(27)

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ANSWER :IRRATIONAL
771.

Rohit invested Rs.39,600 in buying shares of nominal value of Rs.100 at a 20% premium. The dividend paid to him was at 6% per annum. Find his annual income. (in Rs.)

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1950
1980
1920
2010

Solution :FACE value/share=RS.100
Premium/share `=20%` of Rs.100 = Rs.20
Market value/share (in Rs.) = `100+20=120`
Total market value = Rs.39,600
`"NUMBER of shares bought"=(39,600)/(12)=330`
Dividend rate `=6%` per annum
`"Anuual INCOME/share"=(6)/(100)("Rs. 100")`
= Rs.6
Total annual income (in Rs.) = (330)(6)
= Rs.1982.
772.

A tank measures 2 m in length, 1.6 m in width and 1 m in depth. Water is there upto 0.4 m heigth. Bricks measuring 25 cm xx 14 cm xx 10 cm are put into tank so that the water may come up to the top.Each brick absorbs water equal to(1)/(7)th of its own volume. How many bricks will be needed ?

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ANSWER :640
773.

In the previous question, if Rohit bought all shares at par, then find the rate at which the dividend was paid to him.

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`4.5%`
`4%`
`5.5%`
`5%`

SOLUTION :Whenever a person BUYS all SHARES at par, the rate at which the dividend is paid to him is the rate of return that he receives.
`therefore" Rohit would be paid a dividend at "5%`.
774.

A sum of Rs 100,000 amounts to Rs 171,600 in 3 years under compound interest, interest being compounded annually. It is lent at 10% per annum for the first year, 20% per annum for thesecond year and x% per annum for the third year. Find x.

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SOLUTION :RS 304.50
775.

The mean of 6 numbers is 42. If one number is excluded, the mean of remaining numbers is 45. Find the excluded number.

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ANSWER :27
776.

Rationalise the denominators of the following: (1)/(sqrt7-sqrt6)

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ANSWER :`sqrt7+sqrt6`
777.

Find two solutions for each of the following equations : 2x +5y=0

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ANSWER :`(0,0) and (1,-(2)/5)`
778.

For any angle theta, state the value of : ""sin^(2)theta+cos^(2)theta.

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ANSWER :1
779.

Simple interest on a sum of money for 2 years at 4% growth rate is Rs 450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half yearly.

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ANSWER :RS 227,25
780.

Write the mark wise frequencies in the following frequency distribution table.

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ANSWER :`(##NCERT_BEN_MAT_IX_C09_E01_001_A01##)`
781.

ABC is a right angled triangle in which angle A = 90^(@) and AB = AC. Find angle B and angle C.

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ANSWER :`angleB=angleC=45^(@)`
782.

Factorise : 4x^(2) + 9y^(2) + 16z^(2) +12xy - 24yz - 16xz

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ANSWER :`(2x+3y-4z)(2x+3y-4z)`
783.

The marks scored by 40 students in a Mathematics test are given below:Prepare the frequency distribution with classes 0-4, 5-9.....

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ANSWER :`(##NVT_MAT_IX_C14_E06_001_A01##)`
784.

Solve for x : 3tan^(2)(2x-20^(@))=1

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ANSWER :`25^(@)`
785.

Solve the following equations for A, if : 2sin3A=1

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ANSWER :`10^(@)`
786.

Consider the frequency distribution table (Table14.3, Example 4, Chapter 14), which gives the weights of 38 students of aclass.(i) Find the probability that the weight of astudent in the class lies in the interval 46-50 kg.(ii) Give two eve

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ANSWER :1
787.

The mean of 10 observations is 28. If 2 is added to each observation and then each result is divided by 3, find the mean of new observations so obtained.

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ANSWER :10
788.

Find zero of the polynomial 2x -1.

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ANSWER :`((1)/(2))`
789.

To find the antilog of 1.301 .

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Solution :Step1: in the anilog we find the number 30 in the left HAND column. In that row in the column under 1, we find 2000.
Step 2: As the charcteristic is 1, we place the decimal after two DIGITS from the left. That is , antilog 1.301 = 20.00.
if the chaacteristic was 2, we would place the decimal after three digits from the left. that is, antilog 2.301 = 200.0
if the characteristic was 3, we would place the decimal after four digits from the left . that is, antilog 3.301 = 2000.
790.

Simplify : root4(81)-8root3(343)+15 root5(32)+sqrt(225)

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ANSWER :`-8`
791.

Find the median of : 18, 30, 39, 36, 28, 27, 31, 40, 33, 25 and 37.

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ANSWER :31
792.

If the rate of return and dividend from a share are r% and d% respectively, find the premium/discount %, given d gt r.

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`((r-d))/(r)%" PREMIUM"`
`((r-d))/(d)%" discount"`
`((d-r))/(r)%" premium"`
`((d-r))/(d)%" discount"`

Solution :(i) `"Anuual DIVIDEND "=(d)/(100)xx"Share value"=(r)/(100)xx"market value"`.
(ii) As `lgtr`, shares are BROUGHT at permium.
(ii) LET the income from each share be
`d=(i)/(FV)xx100 and r=(i)/(MV)xx100`
(iii) `"Premium"=MV-FV."Percentage of premium"`
`=(MV-FV)/(FV)xx100`
793.

In Delta PQR, PQ = 3and QR =7 Then ……….holds good.

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`PR=4`
`PR=10`
`10gt PR gt4`
`7gtPRgt3`

794.

The perimeter of right-angled isosceles triangle is (sqrt(2)+1)m. Find the length of the hypotenuse.

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ANSWER :`SQRT(2)" m "`,(1)/(2)sq.m`
795.

Find the amount of water displaced by a solid spherical ball of diameter (i) 28 cm (ii) 0.21 m

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ANSWER :(i) `11498""2/3cm^(3)`
(II) 0.004851 `m^(3)`
796.

A match boxmeasure 4\ c m\ x\ 2. 5\ c m\ x\ 1. 5\ c m. What willbe the volume of a packet containing 12 such boxes?

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ANSWER :180 `CM^(3)`
797.

A is the centre of the circle and ABCD is a square. IfBD = 4cm then findthe radius of the circle

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ANSWER :4 CM
798.

The ratio of the base radius and height of a cone is 5 : 12. Find its slant height and radius if its volume is 800 pi m^(3).

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ANSWER :26 m, 10 m
799.

The point corresponding to ordered pair (5, - 3) lies in the .......... quadrant

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ANSWER :FOURTH
800.

State the degree of each the following polynomials : 81 - 16x^(2)

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ANSWER :2