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501.

A teacher analyses the performance of two sections of students in a mathematics test of 100 marks given in the following table : :Find the probability that a student obtained less than 20 marks in the mathematics test.

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ANSWER :`7/90`
502.

Expand : (a + 2b - 3c)^(2)

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ANSWER :`a^(2) + 4b^(2) + 9C^(2) + 4ab - 12BC - 6ca`
503.

Draw a flowchart to determine whether a given number is even or odd

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504.

Find the value of x in the following figures.

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ANSWER :(a) `42^(@)` (B) `110^(@)`
505.

Use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases : p(x) + x^(3) + 3x^(2) + 3x +1, g(x) = x+2

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ANSWER :is not a FACTOR
506.

Use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases : p(x) = x^(3) - 4x^(2) + x + 6, g(x) = x -3

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ANSWER :is a FACTOR
507.

Find the area of the given trapezium.

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ANSWER : `259.48 CM^(2)`
508.

AFLATOUN social and financial educational program intiated savings program among the high school children in Hyderabad district. Mandal wise savings in a month are given in the following table Find arithmetic mean of school wise savings in each mandal. Also find the arithmetic mean of saving of all schools.

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ANSWER :(i) ₹359, ₹413, ₹195, ₹228, ₹200, ₹837
(II) ₹444 SAVING PER SCHOOL.
509.

What type of numberwill beresultedwhen the sum,subtraction , product and division (divisor is not zero)of two rational numbers are taken ?

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ANSWER :Divisoris not ZERO
510.

The ratio of the base radius and height of a cone is 3 : 4. Its volume is 301.44 cm^(3). Find its curved surface area. Given that pi = 3.14.

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ANSWER :`188.4 CM^(2)`
511.

If a + b = 15 and a + b + c = 15 + c which axiom of Euclid does the statement illustrate ?

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ANSWER :SECOND AXIOM
512.

Draw the straight lines x-y+2=0 and 3x-8y=12 on the same graph pap[er (i) Find the point where the two lines meet each other. (ii) Find the area of traingle foprmed by these lines and x-axis.

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Solution :We have
x-y+2=0
x=y-2
When y =0 `rArr` x=-2
when y=1 `rArr` x=-1
When y =2 `rArr` x=0
when y=3 `rArr` x=1
Table for these values :

Plot the points A(-2),B(-I,1), c(0,2),D(1,3) on the GRAPH paper and join them
3x-8y = 12
3x=8y+12
x=8y+12
3
When , y=0 `rArr` x=4
Wheny =-1.5 `rArr` x=0
Tables for these values

plot the points p(4,0) and Q(0,-1.5) on the graph paper and joint them.

(i) From the graph we see that the two lines intersect each other at R-(-5.6,-3.6).
(ii) Area of triangle formed by these lines and x axis is
`ar(triangle PAR) =(1)/(2)XX"base" xx "corresponding ALTITUDE"`
`=(1)/(2)APxxMR=(1)/(2)xx(a+2)xx3.6 sq` units
=10.8 sq units.
513.

E and F are respec­tively the midpoints of equal sides AB and AC of triangle ABC (see the given figure). Show that BF = CE.

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ANSWER :CE
514.

Factorise : b^(2)c^(2)(b^(2)-c^(2))+c^(2)a^(2)(c^(2)-a^(2))+a^(2)b^(2)(a^(2)-b^(2))

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ANSWER :`-(a-b)(b-c)(c-a)(a+b)(b+c)(c+a)`
515.

If A={:[(-1,3),(4,1)]:}andB={:[(-2,3),(1,-4)]:}, then verify whether (A+B)(A-B)=A^(2)-B^(2).

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516.

Ashok invested in three types of shares, P, Q and R, of a company. He invested Rs.5000 and Rs.7500 in P and Q, respectively. He obtained rates of returns of 10%, 8% and 15% from P, Q and R, respectively. His annual income from the three types was a total of Rs.1550. How much did he invest in R? (in Rs.)

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2500
2000
3500
3000

Solution :(i) Let dthe investment of ASHOK be Rs.x in R and equate the total dividend to Rs.1550.
(ii) Let the investment on SHARE R be Rs.x.
(iii) `10%` of `5000+8%` of `7500+15%` of `x=1550`.
517.

Find the zero of each of the following polynomials : p(t) = pi t + 7

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ANSWER :`-(7)/(PI)`
518.

Find acute angles A and B, if sin(A+B)=cos(A-B)=sqrt(3)/2.

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ANSWER :`A=45^(@)" and "B=15^(@)`
519.

Insert 2 rationaland 2 irrational numbers in between each pair of numbers givenbelow : (i) 3/7 and 4/7 (ii) 1/13 and 1/11

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ANSWER :(i) RATIONAL(II)Rational
520.

Represent sqrt(3.8) on the number line.

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Solution :Step 1 : Mark 3.8 on a number LINE (say AB).
Step 2 : Make 1 more than 3.8 i.e., (3.8+1) on number line (say point C).
Step 3 : Take `(4.8)/(2)` i.e., 2.4 as centre and draw a semi-circle.
Step 4 : Draw perpendicular at B INTERSECTING the semi-circle at D.
Step 5 : Using COMPASS measure BD and mark it on number line.

521.

find the mean of the following data.

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ANSWER :15.1
522.

If x-3 is a factor of k^(2)x^(3) - kx^(2) + 3kx - k, find the value of k. (k ne 0).

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ANSWER :`K = (1)/(27)`
523.

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys the number of girls.

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ANSWER :`2:1`
524.

Solve the following equations for A, if : sin3A=sqrt(3)/2

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ANSWER :`20^(@)`
525.

Details of Mahan 's saving bank account are given below Calculate the sum for which he earns interest from august 1999 to november 1999

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ANSWER :RS 11800
526.

On what sum of money will the compound interest for 2 years at 5 per cent per annum amount to Rs768*75 ?

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ANSWER :RS 7,500
527.

Verify whether the following are zeroes of the polynomial, indicated against them : p(x) = l x + m, x = -(m)/(l)

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ANSWER :`-(m)/(L)` is a ZERO
528.

Evaluate : (i) (98)^(3) "" (ii) (598)^(3) "" (iii) (1003)^(3)

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ANSWER :(i) 941192 (II) 213847192 (III) 1009027027
529.

Expand each of the following using suitable identities : (3a-7b-c)^(2)

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Answer :`9A^(2) + 49B^(2) + C^(2) - 42ab + 14 BC - 6ca`
530.

If the bank pays interest at different rates for different periods as follows (i) 4% per annum up to the date 1-9-2006 (ii) 3% annum form 2-9-2006 to 31-12-2006 ltbnrgt Then the total interestis _______

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RS 285
Rs 310
Rs 290
Rs 303

Solution :Find the MINIMUM balance TILL 1-9-06 SIMILARLY find the minimum balance from 2-9-06 to 31-12-06
531.

Into how m any chapters did Euclid divide his compilation ‘Elements’ ?

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ANSWER :13
532.

Check whether the value of x given against each polynomial is a zero of that polynomial or not : p(x) = x^(2) - 5x + 4, x = 1, 4

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<P>

ANSWER :p(1) = 0, p(4) = 0
533.

Check whether the value of x given against each polynomial is a zero of that polynomial or not : p(x) = x^(2)- 8x + 15, x = 3, 5

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<P>

ANSWER :p(3) = 0, p(5) = 0
534.

Check whether the value of x given against each polynomial is a zero of that polynomial or not : p(x) = x^(2) + 7x + 6, x = -1, -6

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<P>

ANSWER :p(-1) = 0, p(-6) = 0
535.

If 4sin^(2)theta-1=0 and angle theta is less than 90^(@), find the value of theta and hence the value of cos^(2)theta+tan^(2)theta.

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ANSWER :`theta=30^(@); 13/12`
536.

Factorise the following . ( I )2a^(2) +9a+10(ii)5x^(2) -29xy -42y^(2)(iii)9-18x+8x^(2) (iv)6x^(2) +16xy +8y^(2)(v)12x^(2) +36x^(2) y +27y^(2) x^(2)(vi)(a+b) ^(2)+9( a+b) +18

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ANSWER :` (a+b)^(2) +9( a+b) +18= (a+b+6) (a+b+3) `
537.

A triangular park ABC has sides 120m, 80m and 50m. Agardener Dhania has to put a fence all around it and also plant grassinside. How much area does she need to plant? Find the cost of fencing itwith barbed wire at the rate of Rs 20 per metre l

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(i) RS 12250, (II) `374sqrt(15)m^(2)`
(i) Rs 12250, (ii) `375sqrt(15)m^(2)`
(i) Rs 12240, (ii) `375sqrt(15)m^(2)`
(i) Rs 12240, (ii) `374sqrt(15)m^(2)`

ANSWER :B
538.

Find the mean of 5,6,17,8,9,15,23,18,10 and 24.

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ANSWER :`13*5`
539.

Select the correct answer (MCQ) : If log_(x) 1/3 = 1/3 then x =

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27
9
3
`1/27`

ANSWER :A
540.

Number of villages with respect to their population as per India census 2011 are given below. Find the average population in each village.

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ANSWER :`BAR x=17.7`
541.

Simplify the following expressions : (sqrt5+sqrt3)^(2)

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ANSWER :`8+2sqrt(15)`
542.

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

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ANSWER :173.25 `CM^(2)`
543.

The sides of a triangle measure 12 cm, 17 cm and 25 cm. Then, the area of the triangle is …………….cm^(2).

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54
90
180
135

Answer :B
544.

A metal pipe is 77 cm long. The inner diameter of across section is 4 cm, the outer diameter being 4.4 cm. Find its(i) inner curved surface area,(ii) outer curved surface area,(iii) total surface area

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Answer :(i) 968 `CM^(2)`
(II) 1064.8 `cm^(2)`
(iii) 2038.08 `cm^(2)`
545.

Construct an isosceles triangle whose base is 6 cm and altitude is 4 cm.

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Solution :Steps of construction :
1.Draw `BC = 6 cm`.
2. Draw the PERPENDICULAR bisector `EF` of `BC` which intersects `BC` at point `D`.
3. With centre `D` and radius `4 cm`, draw an arc which cuts `DE` at `A`.
4. Join `AB` and `AC`.
`therefore DeltaABC` is the REQUIRED triangle.
546.

When a balanced die is thrown, the porbability of receiving an even number is ..........

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`1/6`
`5/6`
`1/2`
`1/4`

ANSWER :C
547.

Equilateral Delta ABC is inscribed in a circle with centre P. Then, angleBPC = ..........

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`60^(@)`
`90^(@)`
`120^(@)`
`75^(@)`

Answer :C
548.

Out of the group of employees, twice the square root of the number of the employees, twice the square root of the number of the employes are on a trip to attend a conferenceheld by the company , halfthe number are in the the office and the remainingsix employees are on leave. What is the number of employees in the group ?

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49
64
36
100

Solution :(i) FORM the QUADRATIC equation and solve for x.
(II)Assume NUMBER of employesin the group as x. Then write the quadratic equation in x according to the data and solve it.
549.

Sameena has a saving bank account with a state bank branch .The entries in her pass book for the month of may are as follows As on 1-5-2006 balance is Rs 22200 On 5-5-2006 amount deposited is Rs 8800 On 9-5-2006 amountdeposited is Rs 1000 On10-5-2006 amount deposited is Rs 5000 On 16-5-2006 amount deposited is Rs 40000 Calulate the interest she earns for the month of may at the rate of 4% per annum

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RS 100
Rs 223.30
Rs 90
Rs 256.60

Answer :C
550.

Ifa point C lies between two points A and B such that AC =BC then prove that AC=1/2 AB

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Solution :Let US consider three POINTS A,C and B on a line such that AC=BC .then AC=CB
By EUCLID 's Axiom 2 we know that if EQUALS be added to equals then the wholes are equal

`therefore AC=CB rarr AC+AC=AC+CB`
`rarr 2AC=AB`
`rarr AC=1/2 AB`
Hence `AC=1/2 AB`