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901.

Find for solutions of each of the following equation : y = 3x

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ANSWER :`(0,0),(1,3),(2,6),(3,9)`
902.

Write four solutions for each of the following equations : x = 4y

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ANSWER :`(0,0),(4,1),(-4,-1) and (8,2)`
903.

Construct a Delta ABC whose perimeter is 12 cm and the base angles are 60^(@) and 70^(@). Justify the construction.

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Solution :STEPS OF CONSTRUCTION
(i) Draw a line segment `PQ=12` CM.
(II) Make `angleQPR=60^(@)` and `anglePQS=70^(@)`.
(iii) Draw the bisectors of `angleQPR` and `anglePQS` to meet at`A`.
(iv) Draw the perpendicular bisectors of `PA` and `QA` to meet `PQ` at `B` and `C` respectively.
(v) JOIN `AB` and `AC`.
Then, `Delta ABC` is the required triangle.

Justification :
Since `B` lies on the perpendicular bisector of `AP`, we have `BA=BP`. Since `C` lies on the perpendicular bisector of `AQ`, we have `CA=CQ`. Thus, `AB=PB` and `AC=CQ`.
`:. AB+BC+AC=PB+BC+CQ=PQ=12` cm.
Now, `BA=BP implies angleBPA=angleBAP`
`implies angleABC=angleBPA+angleBAP=2 angleBPA`
`=2xx1/2xx60^(@)=60^(@)`.And, `CA=CQ implies angleCQA=angle CAQ`
`implies angleACB=angleCQA+angleCAQ=2angleCQA`
`=2xx1/2xx70^(@)=70^(@)`.
Verification :
On measurement, we find that
`AB+BC+CA=(4.4+3.5+4.1) cm =12` cm.
`angleB=60^(@)` and `angleC=70^(@)`.
904.

angleA and angleB are complementary angles. If angleA=x+20^(@) and angleB=x-10^(@), find angleA and angleB.

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ANSWER :`angleA=60^(@),angleB=30^(@)`
905.

Expand : (5x + 3y)(5x-3y)

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ANSWER :`25X^(2) - 9Y^(2)`
906.

Divide the polynomial 2x ^(4) - 4x ^(3) - 3x -1 by (x-1)

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ANSWER :`=-6`
907.

Factorise : 4x^(2) + 9y^(2) + z^(2) + 12xy - 6yz - 4zx

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ANSWER :`(2x+3y-z)(2x+3y-z)`
908.

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see the given figure). Show that the line PQ is the perpendicular bisector of AB.

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ANSWER :`45^(@)`
909.

Determine which of the following polynomials has (x+1) a factor : x^(4) + 3x^(3) + 3x^(2) + x +1

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ANSWER :is a FACTOR
910.

Which the quadrant in which following points lie? (i) (-2,3) (ii) (5,-3) (iii) (4,2) (iv) (-7,-6) (v) (0,8) (vi) (3,0) (vii) (-4,0) (viii) (0,-6)

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ANSWER :(i) `Q_2` (ii) `Q_4` (III) `Q_(1)` (V) `Q_(3)`
(v) Y-axis (vi) X-axis (vii) X-axis (viii) Y-axis
911.

Write the following cubes in expanded form : [(3)/(2)x+1]^(3)

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Answer :`(27)/(8)x^(3) +1+(27)/(4)x^(2) + (9)/(2)x`
912.

Classify the following numbers as rational or irrational. 7.484848…

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ANSWER :RATIONAL
913.

A closed cylindrical tank of height 1.4 m. and radius of the base is 56 cm. is made up of a thick metal sheet. How much metal sheet is required (Express in square meters)

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ANSWER :`6.90 m^(2) `
914.

When Polynomial (2x^(3)+ax^(2)+3x-5) and (x^(3)+x^(2)-4x-a) are divisible by x-1leaves the same remainder find the value of a.

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ANSWER :`(-13)/(3)`
915.

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family . The information gathered is listed in the table below Suppose a family is chosen, Find probability that the family chosen is earning Rs 10000 - Rs 13000 per month and owning exactly 2 vehicles.

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ANSWER :`(29)/2400`
916.

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family . The information gathered is listed in the table below Suppose a family is chosen, Find probability that the family chosen is earning Rs 16000or more per month and owning exactly 1 vehicle.

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ANSWER :`(193)/800`
917.

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family . The information gathered is listed in the table below: Suppose a family is chosen . Find the probability that the family chosen is earning less than Rs 7000 per month and does not own any vehicle.

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ANSWER :`1/(240)`
918.

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family . The information gathered is listed in the table below Suppose a family is chosen, Find probability that the family chosen is earning Rs 13000 - Rs 16000 per month and owning more than 2 vehicles.

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ANSWER :`1/96`
919.

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family . The information gathered is listed in the table below Suppose a family is chosen, Find probability that the family chosen is owning not more than 1 vehicle.

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ANSWER :`1031/1200`
920.

Find the degree of each of the polynomials given below (i) x ^(5) - x ^(4) +3 (ii) x ^(2) + x -5 (iii) 5 (iv) 3x ^(6) + 6y ^(3) -7 (v) 4- y ^(2) (vi) 5t - sqrt3

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ANSWER :(i) 5 (ii) 2 (iii) 0 (iv) 6 (V) 2 (vi) 1
921.

Factorise : 5x^(2) - 18x -8

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ANSWER :`(5x+2)(x-4)`
922.

If he closes the account on august 31 when what is the total paid by the bank ?(including interest)

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Rs 21159
Rs 21000
Rs 21400
Rs 21304

Solution :FIND the minimum BALANCE till august
923.

Visualise 2.364 on the number line using successive magnification.

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SOLUTION :N/a
924.

Draw a histogram to represent the following:

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Solution :Scale:
Let 1 CM = 6 units on X-axis
1 cm = 5 units on Y-axis
Here, the CLASS intervals starts from 30, a zig-zag CURVE is shown from 0 to 30
925.

If a + b = sqrt10 and a - b = sqrt8, then the value of a^2 + b^2 is

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Answer :(i) ` 32sqrt3`
(ii) `6 +3sqrt2 + 2SQRT3 + sqrt6`
(III) ` 7 + 2sqrt10`
(IV)
(v) `sqrt6/3`
(VI) 0
(vii) `4sqrt6`
viii (x)
926.

A metallic cylinder of diameter 5cm. And height3(1)/(3) cmis melted and cast into a sphere. What is its diameter.

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ANSWER :5 CM
927.

Find the mean of the following data : 30,32,24,34, 26,28, 30, 35, 33, 25 Show that the sum of the deviations of all the given observations from the mean is zero.

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ANSWER :`29*7`
928.

A plane has three dimensions.

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ANSWER :FASE
929.

Express the following in terms of angles between 0^(@) and 45^(@) cosec 68^(@)+cot 72^(@)

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ANSWER :`sec22^(@)+tan18^(@)`
930.

Are the positions of (5,-8) and (-8,-5) is same? Justify your answer.

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Answer :No. (5,-8) lies in `Q_(4)` and (-8,5) lies in `Q_(2)`
931.

If A.M and G.M of two positive real numbers are 100 and 5 respectively, then find their H.M.

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ANSWER :x=0
932.

Calculate the area of quadrilateral ABCD in whichangle = 90^(@), triangle BCD is an equilateraltriangle of side 24 cm and AD = 26 cm.

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ANSWER :`369.41 CM^(2)`
933.

On a graph paper draw a straight line represented by the equation 2x-3y+132=0. Use the graph drawn to find the values of m and n so that the points (m,-2) and (3,n) lie on the given straight line.

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Solution :GIVEN equation is 2x-3y+12=0
`rArr` , 2x=3y-12
`rArr , x=(3y-12)/(2)`
Let y = 0 `rArr x=(3xx0-12)/(2)=-6`
Let y =2 `rArr x=(3xx2-12)/(2)=-3`
Let y = 4 `rArr x=(3xx4-12)/(2)=0`
Table for values :

Point the points (-6,0), (-3, 2), (0, 4) on the same graph PAPER.

Since point (m,-2) LIES on the straight line drawn through y = -2 draw a straight line which meets line AB at point A. draw a vertical line through A WHIHC meets x axis at point x= -9
`therefore` m=-9
Also (3,n) lies onthe straight line drawn through x= 3 .Draw a vertical line which meets the straight line at point B. Through point B draw a horizontal line which meets y axis at the point y =6
934.

Classify the following numbers as rational or irrational. 4pi

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ANSWER :IRRATIONAL
935.

Name the following parts from the adjacent figure where ‘O’ is the centre of the circle (i) bar(AO) (ii) bar(AB) (iii) frown(BC) (iv) bar(AC) (v) frown(DCB) (vi) frown (ACB) (vi) bar(AD) (viii) shadedregion

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ANSWER :(i) Radius
(II) Diameter
(III) Minor arc
(iv) Chord
(v) Major acr
(VI) Semi-circle
(vii) Chord
(VIII) Minor segment
936.

Factorise each of the following : 27-125a^(3)-135a + 225a^(2)

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ANSWER :`(3-5a)(3-5a)(3-5a)`
937.

Kira invests in the shares of a company. If he buys 48 shares more, he will invest Rs.1200 more. If he buys 40 shares less, the total face value of his shares will be Rs.800 less. He must buy each share ________.

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at par
below par
above par
Cannot be determined

Solution :Market value of each SHARE (in Rs.)`=(1200)/(48)=25`
`thereforem=25`
`"FACE value of each share (in Rs.)"=(800)/(40)=20`
`thereforef=20`
`thereforem gt 25`
`therefore " KIRAN bought each share above par"`.
938.

Find the area of the given figure Given AB = 18 cm, BC = 7 cm, CD = 20 cm, DE = 8 cm, EA = 17 cm, AF = 30 cm, BF = 24 cm, CF = 25 cm, FD = 15 cm, EF = 17 cm.

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`610 SQ. CM.`
`640 sq. cm.`
`630 sq. cm.`
`650 sq. cm.`

ANSWER :C
939.

Find the remainder when x ^(3) + 3x ^(2) + 3x +1 is divided by the following Linear polynomials: (i) x +1 (ii) x - 1/2 (iii) x (iv)x + pi (v)5 + 2x

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Answer :(i) 0 (II) `(27)/(8) (iii)1 (iv) -pi ^(3) + 3pi^(2) -3pi+1 (v) (-27)/(8)`
940.

In the quadrilateral ABCD, AB=BC and AD=DC Measure of angleBCD is . . . . . . .

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`150^(@)`
`30^(@)`
`105^(@)`
`72^(@)`

ANSWER :C
941.

The statement that the lines are parallel if they do not intersect is in the form of

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a definition
an AXIOM
a POSTULATE
a THEOREM

Solution :Lines are parallel if they do not intersect is STATED as a " definition "
942.

Evaluate each of the following using proper identity : (79)^(3)

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ANSWER :4,93,039
943.

Find the degree of each of the polynomials given below : 2 - y^(3) + 2y^(8)

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ANSWER :8
944.

Factorise : 2x^(2) - 9x - 35

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ANSWER :`(2x+5)(x-7)`
945.

Angle in a minor segment is. . . . . . .

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an acute ANGLE
an OBTUSE angle
a RIGHT angle
a REFLEX angle

Answer :B
946.

Plotthe following pointsin thecoordinateplaneand join the m . Whatis yourconclusionaboutthe resultingfigure ? (i) (5-,3) (-1,3) (0,3) (5,3) (ii) (0,-4) (0,-2)(0,4) (0,5)

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ANSWER :
947.

The population of a town decreased by 12% during 1998 and then increased by 8% during 1999. Find the population of the town, at the beginning of 1998, if at the end of 1999 its population was 2,85,120.

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ANSWER :3,00,000
948.

Evaluate: ((cos 47^(@))/(sin 43^(@)))^(2)+((sin72^(2))/(cos 18^(@)))^(2)-2cos^(2)45^(@)

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ANSWER :1
949.

Write an algorithm for finding the length of the side of a rhombus when the length of its diagonals is given

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950.

Evaluate : ((0.35)^(3)+(0.41)^(3)-(0.76)^(3))/(9(0.35)(0.41)(0.76))

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ANSWER :`-(1)/(3)`