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1551.

Expression sin75^(@) +cos 65^(@)in terms of trigonometric ratios of angles between 0^(@) and 45^(@)

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ANSWER :` COS 15^(@) +SIN 25^(@) `
Discussion
1552.

Seg XY is a diameter of a circle . Point Y lies in its interior . Howmany of the following statements are true ?(i)It is not possible thatangleXYZis an acute angle.(ii) angleXYZ can't be a right angle.(iii) angleXYZis an obtuse angle.(iv)Can't make a difinite statement for measure of angleXYZ

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Only ONE
Only TWO
Only THREE
All
Discussion
1553.

Find the distance between the pair of points (2, 3) and (4, 1)

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ANSWER :`2 SQRT(2)`
Discussion
1554.

For an A.P. if the 11th term is 38 and 16th term is 73, then find the 31th term of the progression.

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ANSWER :178
Discussion
1555.

For the box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. If it must have a volume of 18 unit, what must be its length ?

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6 unit
3 unit
4 unit
2 unit

Solution :We have
`V(x)=x^(3)+x^(2)-6`
`18=x^(3)+x^(2) -6X`
`x^(3) +x^(2) -6x -18=0`
`x^(3) -3X^(2) +4x^(2) -12x +6x -18=0`
`x^(2)(x-3) +4x(x-3) +6(x-3) =0`
`(x-3) (x^(2) +4x +6)=0`
Thus WIDTH is 3 unit.
Length `=x+3=6m`
Thus (a) is CORRECT option.
Discussion
1556.

For the box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. Which of the following polynomial represent the area of paper sheet used to make box ?

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`X^(2)-5x-6`
`6x^(2)+4x-12`
`x^(3) -6x^(2) -6x`
`6x^(2)+3x-4 `

Solution :`S(x)=2(LW+WH+HL)`
`=2[x(x+3) +(x+3)(x-2) +x(x-2)]`
`=2[x^(2) +3x+x^(2)+x-6+x^(2)-2x]`
`=2(3x^(2)+2x-6) =6x^(2) +4x-12`
THUS (b) is CORRECT OPTION.
Discussion
1557.

For the box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. If width is taken as x , which of the following polynomial represent volume of box ?

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`x^(2)-5x-6`
`x^(3)+x^(2)-6x`
`x^(3)-6x^(2) -6x`
`x^(2)+x-6`

Solution :`V(x)=x(x+3)(x-2) = x(x^(2)+x-6) =x^(3) +x^(2) -6x`
Thus (d) is CORRECT OPTION.
Discussion
1558.

For the box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. If box is made of a paper sheet which cost is 100 rs per square unit, what is the cost of paper?

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Rs 5400
Rs 10800
Rs 2700
Rs 3400

Solution :`S(x) = 6x^(2) +4x -12 = 6xx 3 xx 3 +4 xx 3 - 12 = 54 `
`S= 2(LW +WH + HL)`
`= 2(6xx3 + 3XX 1 + 1xx 6)`
`= 2xx (18 + 3 +6 ) = 2xx 27 = 54 m^(2)`
`C = 100xx 54 = 5400 Rs `
THUS (a) is correctoption.
Discussion
1559.

For the box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. At a volume of 18 cubic unit, what must be its height ?

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1 unit
3 unit
2 unit
4 unit

Solution :Height `= x − 2 = 3 − 2 = 1m`
Thus (a) is correct option.
Discussion
1560.

Which one of the following Venn diagrams correcltly illustrates the relationship among the classes:Carrot,Food ,Vegetable?

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SOLUTION :All CARROTS are VEGETABLES.All vegetables are FOOD.
Discussion
1561.

The volume of acone is 90cm^(3). The volume of a cylinder whose height and radius is same as that of the coneis :

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`30 cm^(3)`
`45 cm^(3)`
`90 cm^(3)`
`270CM^(3)`

Answer :d
Discussion
1562.

Find the mean of the following distribution :

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ANSWER :83.25
Discussion
1563.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Girl, Singer, Athlete

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ANSWER :C
Discussion
1564.

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub. ""("Take "pi=22/7)

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ANSWER :`616 CM^(3)`
Discussion
1565.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Copper, Paper, Wire

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SOLUTION :Some WIRES are made of COPPER, but PAPER is entirely DIFFERENT.
Discussion
1566.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: State, Country, City

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SOLUTION : A CITY LIES WITHIN a STATE, which lies within a country.
Discussion
1567.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Man, Worker, Garden

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ANSWER :D
Discussion
1568.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Teacher, Graduate, Player

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SOLUTION :All the THREE are PARTLY RELATED to each other
Discussion
1569.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Ear, Body, Mouth

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ANSWER :B
Discussion
1570.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Painler, table, Scholar

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ANSWER :D
Discussion
1571.

Directions (Questions 1 to 10). Choose the Venn diagram which best illustrates the three given classes in each question: Swimmer, carpenter, Singer

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ANSWER :C
Discussion
1572.

Find the value of ‘K’ for which the points are collinear (7, -2) (5, 1) (3, K)

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ANSWER :K=4
Discussion
1573.

Find the number of straight lines in the following figure.

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11
14
16
15

Answer :C
Discussion
1574.

If the two roots of the equation are 1 and 2, then find the equation.

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Discussion
1575.

Find the ratio in which x - y - 2 = 0 divides the line segment joining (8, -1) and (8, 9).

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ANSWER :2
Discussion
1576.

Solve each of the following pairs of equations by reducing them to a pair of linear equations. (1)/(3x+y)+(1)/(3x-y)=(3)/(4) and (1)/(2(3x+y))-(1)/(2(3x-y))=(-1)/(8).

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ANSWER :(1,1)
Discussion
1577.

A survey was conducted in Aadarsh Vidyalaya to know the inclination of students towards different subjects. The data obtained is presented by the adjacent pie diagram. If the total number of students was 500 , answer the following questions : (i) How many students show inclination towards mathematics ? (ii) How many students are inclined towards social sciences? (iii) How many more students are inclined towards Inaguages than science?

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ANSWER :(1) 175 (ii) 75 (iii) 100.
Discussion
1578.

Without solving, examine the nature of the roots of the equations : (i) 5x^(2)-6x+7=0 (ii) x^(2)+6x+9=0 (iii) 2x^(2)+6x+3=0

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Answer :(i) The roots are not REAL i.e. the roots are IMAGINARY.
(ii) The root are real and EQUAL.
(III) The roots are real and unequal.
Discussion
1579.

If tan theta=(20)/(21),show that (("cosec"^(2)theta -sec^(2) theta))/(("cosec"^(2)theta+cos ^(2)theta ))=(3)/(4).

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Solution :`tan theta =(1)/(7)= (BC)/(AB).`
`therefore AC^(2)=AB^(2)+BC^(2)=(sqrt(7))^(2)+(1)^(2)=(7+1)=8impliesAC=sqrt(8)=2sqrt(2).`
` therefore "cosec" theta=(AC)/(AB)=(2sqrt(2))/(sqrt(7))IMPLIES sec^(2)thetatheta =(8)/(7).`
Discussion
1580.

Find the distances between the following points:R(-3a,a),S(a,-2a)

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Solution :`R(-3a,a)` and `S(a,-2A)`
Let `R(x_(1),y_(1))` and `S(x_(2),y_(2))`
Here `x_(1)=-3a,y_(1)=a,x_(2)=a` and `y_(2)=-2a`
By distance formula,
`d(R,S)=sqrt([a-(-3a)]^(2)+[-2a-a]^(2))`
`=sqrt((a+3a)^(2)+(-3a)^(2))`
`sqrt((4a)^(2)+(-3a)^(2))`
`=sqrt(16A^(2)+9a^(2))`
`=sqrt(25a^(2))=5a`
`d(R,S)=5a`
Discussion
1581.

X-coordinate of intersecting point of two ogives, represents ......

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MEAN
Median
Range
Mode

Answer :B
Discussion
1582.

Find the coordinates of points which divide the line segment joining A(-4, 0) and B(0, 6) into four equal parts.

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ANSWER :`(-3,(3)/(2)), (-2,3) , (-1,(9)/(2))`
Discussion
1583.

In a certain code, FORGE is written as FPTJI. How is CULPRIT wirtten in that code?

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CSJNPGR
CVMQSTU
CVNSVNZ
CXOSULW

Solution :First letter remains the same and other letters move ONE, two, THREE and FOUR steps forward to obtain the corresponding letters of the CODE
Discussion
1584.

Find the sixth term of the series : 2,2^(2),2^(3),2^(4), . . . . . . . . . . . .

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ANSWER :128
Discussion
1585.

Using ruler and compasses only, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.

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ANSWER :1.4CM
Discussion
1586.

How many two-digit numbers are divisible by 3?

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ANSWER :30
Discussion
1587.

How many triangles are contained in the following lowing figure ?

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11
12
16
16

Answer :D
Discussion
1588.

Identify and write the "common property" of the following collectons. 2,4,6,8

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Answer :(i) Finite (ii) INFINITE (III)Infinite (IV) Infinite
Discussion
1589.

If the total surface of a cube is 486 square meters , calculateone of its side.

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Discussion
1590.

The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r is given by

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`(4)/(3) PI R^(3)`
`(2)/(3) pi r^(3)`
`4PI r^(3)`
`(1)/(3) pi r^(3)`

Answer :A::C
Discussion
1591.

Draw a DeltaABCwith side BC=6 cm,angleB=45^(@)" and "angleA=100^(@), then construct a triangle whose sides are ( 4)/(7) times the corresponding sides of DeltaABC.

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Answer :`DeltaPBQ` is the required TRIANGLE SIMILAR to the GIVEN `DeltaABC.`
Discussion
1592.

17: 120 :: 19:?

Answer»

381
164
134
132

Solution :`X : (7^(2) + 1)`
Discussion
1593.

A class teacher has the following attendence record of 40 students of a class for the whole term. Find the mean number of days a student was present out of 56 days in the term.

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ANSWER :49 DAYS
Discussion
1594.

3 angles to traingle are x^@,3x^@,5x^@. Find measures of each angle.

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ANSWER :`100^@`
Discussion
1595.

If in a certain language CARROM is coded as BZQQNL, which word will be coded as HOUSE?

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IPVTF
GNTRD
INVRF
GPTID

Solution :Each LETTER of the WORD is ONE STEP ahead of the CORRESPONDING letter of the code
Discussion
1596.

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

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ANSWER :37
Discussion
1597.

Solve for x by fractorisation 2x^(2)-ax+a^(2)=0-

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ANSWER :`X = -SQRT3, x = (-7 sqrt3)/(3)`
Discussion
1598.

Construct Caley's table for Z_(8) under addition modulo 8.

Answer»
Discussion
1599.

A flagstaff 10 m high stands at the centre of a equilateral triangle, which is horizontal. At the top of the flagstaff each side subtends at an angle of 60°. The length of each side of the triangle is

Answer»

`6sqrt(3)`
`4sqrt(6)`
`5sqrt(6)`
`6sqrt(5)`

ANSWER :C
Discussion
1600.

Find the relation between x and y such that the points (x, y) is equidistant from the point (3, 6) and (-3, 4).

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ANSWER :`3X + y - 5 = 0`
Discussion