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551.

Find A, if : 2cos3A=1

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ANSWER :`A=20^(@)`
552.

Solve for theta(0^(@) lt theta lt 90^(@)) : 2sin^(2)theta-2costheta=1/2

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ANSWER :`theta=60^(@)`
553.

In trianglePQR, angleQ=90^@, PQ=5 cm and PR=13 cm. Then ar(PQR)=____ cm^2

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15
30
45
60

Answer :C
554.

In triangleABC the bisectorsof angleB and angleCintersect at I if angleA=70^(@) then angle BIC=…………..

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`35^(@)`
`75^(@)`
`100^(@)`
`125^(@)`

ANSWER :A::B
555.

The ratio of the measures of three sides of a triangle is 4 : 2 : 3 and its perimeter is 36 cm. Find the area of this triangle.

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ANSWER :`12 sqrt(15) cm^(2)`
556.

Find the value of the polynomial 5x - 4x^(2) + 3 at x = -1.

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ANSWER :`-6`
557.

Find the remainder when 2x ^(2) - 3x + 5 is divided 2x-3. Does it exactly divided the polynomial ? State reason.

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ANSWER :Not a FACTOR, as REMAINDER is 5
558.

Let the heights of a group of students are more than 4 feet and less than 6 feet. Now if E be the random experiment of measuring the heights of the students and if S be the sample space then.

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Answer :There will have INFINITELY MANY number of uncountable event POINTS.
559.

Rahul opened a saving bank account with a bank on 1-1-2006 with a deposit of rs 1000 .Hedeposited Rs 100 on 9-1-2006 .The amount on which he would received interest for the month of february 2006

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Rs 1000
Rs 100
Rs 1100
0

Solution :Find the minimum BALANCE between the 10th DAY and the LAST day of the month
560.

Compute the division : (x^3-y^2)+(x^(1/2)-y^(1/3)).

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ANSWER :`X^(5/2)+x^2y^(1/3)+x^(3/2)y^(2/3)+xy+x^(1/2)y^(4/3)+y^(5/3)`
561.

Boundaries of surface are

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lines
curves
polygons
NONE of these

SOLUTION :BOUNDARIES of surface are cuves
562.

What is the total amount for which the bank will pay interest ?

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RS 500000
Rs 100000
Rs 110700
Rs 120900

Solution :FIND the MINIMUM BALANCE for differetn MONTHS
563.

State True or False, if 'false' write correct statement. The point (2,-3) lies in the third quadrant.

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ANSWER :FALSE
564.

Calculate the value of A, if : (tanA-1)(cosec3A-1)=0

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ANSWER :`45^(@) and 30^(@)`
565.

Expand :(4t + 5)(4t-5)

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ANSWER :`16T^(2) - 25`
566.

State the coefficient of x^(2) in each of the following polynomials : x^(3) + 3x^(2) + 3x +1

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ANSWER :3
567.

The weights (in kg) of 30 girls of Primestreet Society are as below: Prepare a frequency distribution with classes 30-35, 35-40 ....

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ANSWER :`(##NVT_MAT_IX_C14_E06_002_A01##)`
568.

Find the minimum value of the quadratic expression 4x^(2) -3x + 4.

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`(-55)/(16)`
`(55)/(16)`
`(16)/(15)`
`(161)/(22)`

Solution :Use the FORMULA of tfind the minimum value.
569.

A man borrowed 16,000 for 3 years under the following terms: 20% simple interest for the first 2 years. 20% C.I. for the remaining one year on the amount due after 2 years, the interest being compounded half-yearly. Find the total amount to be paid at the end of three years.

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ANSWER :RS 27,104
570.

Find the zero of the polynomial in each of the following cases : p(x) = c x + d, c ne 0, x, d are real numbers.

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ANSWER :`-(d)/(C)`
571.

Evaluate: ((sin 77^(@))/(cos 13^(@)))^(2)+((cos 77^(@))/(sin 13^(@)))^(2)-2cos^(2)45^(@)

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ANSWER :1
572.

Simplify each of the following by rationalising the denominator: (sqrt7-sqrt5)/(sqrt7+sqrt5)

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ANSWER :`6-sqrt(35)`
573.

If x = 2, y = 3, u = - 2 and v = - 3, in which quadrant does the point (x + y, u + v) lie ?

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ANSWER :in FOURTH QUADRANT
574.

From the adjoining figure, find : cosx^(@)

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ANSWER :`COSX^(@)=1/2`
575.

Expand :(5a-4b)(5a+4b)

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ANSWER :`25A^(2) - 16B^(2)`
576.

Evaluate the following using suitable identites.(102) ^(3)

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ANSWER :`10,61,208` `
577.

Try to construct a triangle with 5 cm, 8 cm and 1 cm. Is it possible or not ? Why ? Give your justification?

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ANSWER :No.
578.

If sinx=cosy, write the relation between x and y, if both the angles x and y are acute.

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ANSWER :`x+y=90^(@)`
579.

State True or False, if 'false' write correct statement. In the Cartesian plane the vertical line is called Y-axis.

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ANSWER :TRUE
580.

If a, b, c are all non-zero and a+b+c=0, then (a^(2))/(bc)+(b^(2))/(ca)+(c^(2))/(ab)= ?.

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1
2
3
4

Solution :We have, a,B,C are all non-zero and a+b+c=0, THEREFORE
`a^(3)+b^(3)+c^(3)=3abc`
Now, `(a^(2))/(bc)+(b^(2))/(ca)+(c^(2))/(ab)=(a^(3)+b^(3)+c^(3))/(ABC)=(3abc)/(abc)=3`
581.

A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m times 15 m times 6 m. For how many days will the water of this tank last ?

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ANSWER :3 DAYS
582.

Find the square root of (a^(2))/(4) + (1)/(a^(2)) - (1)/(a) + (a)/(2) - (3)/(4)

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`(a)/(2) - (1)/(a) + (1)/(2)`
`(a)/(2) + (2)/(a) -1`
`(a)/(2) + (1)/(a) - (1)/(2)`
`(a)/(2) - (2)/(a) - (1)/(2)`

SOLUTION :
`:.` The SQURE root of the given expression is `(a)/(2) - (1)/(a) + (1)/(2)`
583.

Express the following rational numbers in decimal form. (354)/(500)

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ANSWER :0.708
584.

Draw an angle of 110^(@) with the help of a protractor and bisect it. Measure each of these angles. Justify your answer.

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Solution :STEPS OF CONSTRUCTION
(i) Draw `angleAOB=110^(@)` with the help of a protractor.
(ii) With `O` as centre and a convenient radius, draw an arc CUTTING `OA` at `P` and `OB` at `Q.`
(iii) With `P` as centre and a convenient radius, draw an arc.
(iv) With `Q` as centre and with the same radius, draw another arc, cutting the PREVIOUS arc at a point `C.`
(v) Join `OC` and produce it beyond `C`.
Then, `OC` is the required bisector of `angleAOB`

Verification :
On measuring `angleAOC` and `angleBOC` you will find that
`angleAOC=55^(@)` and `angleBOC=55^(@)`.
Thus, `angleAOC=angleBOC=55^(@)` and therefore, OC is the bisector of `angleAOB`.
Justification :
Join CP and CQ.
In `Delta OPC` and `Delta OQC`, we have
`OP=OQ` (RADII of the same arc)
`PC=QC` (arcs of equal radii)
`OC=OC` (common)
`:. Delta OPC cong Delta OQC`.
Hence, `anglePOC=angleQOC` (c.p.c.t.).
CONSEQUENTLY, OC is the bisector of `angleAOB`.
585.

Factorise : 3x^(3) + 14x^(2) - 7x - 10

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ANSWER :`(x-1)(x+5)(3x+2)`
586.

If sin3A=1 and 0 le A le 90^(@), find : cos 2A

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ANSWER :`1/2`
587.

The mean of 100 observations was found to be 30. If two observations were wrongly taken as 32 and 12 instead of 23 and 11, find the correct mean.

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ANSWER :`29*9`
588.

Write each of the following equationsin the form ax + by + c = 0and indicate the values of a , b and c in each case : x-4=sqrt3y

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Answer :`a =1, B = sqrt3 and C =-4`
589.

Write each of the following equationsin the form ax + by + c = 0and indicate the values of a , b and c in each case : 2x + 3y = 4.37

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ANSWER :`a = 2, B = 3 and C = -4.37`
590.

Write each of the following equationsin the form ax + by + c = 0and indicate the values of a , b and c in each case : 4 = 5x -3y

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ANSWER :`a=5 , B = 3 and C = 4`
591.

Write each of the following equationsin the form ax + by + c = 0and indicate the values of a , b and c in each case : 2x = y

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Answer :`a = 2, B = -1AND C = 0 `
592.

Rationalise the denominators of the following: (1)/(3+sqrt2)

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ANSWER :`(3-sqrt2)/(7)`
593.

It is required to make a closed cylindrical tank of height 1m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ?

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ANSWER :7.48 `m^(2)` sheet is required to make the CLOSED cyclindrical tank
594.

Evaluate the following products without actual multiplication. (i) 101 xx 99 (ii) 999 xx99 (iii) 50 (1)/(2) xx 49 (1)/(2) (iii) 501 xx 501 (iv) 30.5 xx 29.5

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Answer :`(i) 9999`
(II) 998011
(III) `(9999)/(4)= 2499 (3)/(4)`
(IV) 251001
(V) `899.875`
595.

Use the given figure to find : tantheta^(@)

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ANSWER :1
596.

Expand : ((1)/(2)a-(1)/(4)b)^(3)

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Answer :`(1)/(8)a^(3) - (1)/(64)b^(3) - (3)/(16)a^(2)b + (3)/(32)AB^(2)`
597.

A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length of length 15 cm and diameter 49 cm to cover its volume surface. Find the length and volume of wire. If the specific gravity of copper be 9g per cubic cm. Find the weigth of the wire.

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ANSWER :38.5 m, 1089 CUBIC CM, 9.801 KG
598.

Find the total surface area of a right circular cone whose slant height is 25 cm and area of base is 154 cm^(2).

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ANSWER :`704 CM^(2)`
599.

Find: 64^((1)/(6))

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ANSWER :2
600.

Find the median of : 34,47,41,52,53,56,35,49,55 and 42.

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ANSWER :48