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2001.

Prove that : (Using identify "cosec"^2A =1 + cot^2 A) (cosA - sinA + 1)/(cos A + sin A - 1) = "cosec"A + cot A.

Answer»


ANSWER :`4(3 + SQRT(3))m`
Discussion
2002.

If alphaand beta be the roots of the equation x^(2)+px+q=0, then find the values of the quantities given below : (alpha+p)^(-3)+(beta+p)^(-3)

Answer»

<P>

ANSWER :`(p(p^(2)-3Q))/Q^(2)`
Discussion
2003.

Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.

Answer»


ANSWER :8.7 CM
Discussion
2004.

If in a certain code language ABCD is written as ZYXW, then how is the word DANCE written in that code?

Answer»

WZMXV
MXZWV
VMZXM
ZMWXV

Solution :The role of coding is `T_(+N)` is CODED as `T_(-n)`. A is the first letter from the START which is coded as first letter from the end i.e., Z and so on.
`:.` DANCE is coded as WZMXV.
Discussion
2005.

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the adjoining figure. Find the area of the shaded region.

Answer»

Solution :Required AREA = (area of large semicircle with radius 4.5 CM)
`-` (area of two smaller semicircle with radius of each `(3)/(2) cm` and a circle with radius `(4.5)/(2) cm`) `+` (area of smaller semicircle with radius `(3)/(2) cm`)
`= (1)/(2) pi (4.5)^(2) - [2 xx (1)/(2) pi ((3)/(2))^(2) + pi ((4.5)/(2))^(2)] + [(1)/(2)pi ((3)/(2))^(2)]`
`= (1)/(2) pi (4.5)^(2) - pi ((3)/(2))^(2) - pi ((4.5)/(2))^(2) + (1)/(2) pi ((3)/(2))^(2)`
`= (1)/(4) pi [2 xx (4.5)^(2) - 9 - (4.5)^(2) + (9)/(2)] = (1)/(4) pi xx 4.5 [2 xx 4.5 - 2 - 4.5 + 1]`
`= (1)/(4) pi xx 4.5 (3.5) = (1)/(4) xx (22)/(7) xx 4.5 xx 3.5 = 12.375 cm^(2)`
Discussion
2006.

A sum of 700 is to be paid to give sevencash prizes to the students of a school for their overall academic performance. If the cost of each prize is 20 less than its preceding prize, find the value of each of the prizes.

Answer»


ANSWER :160, 140, 120, 100, 80, 60, 40
Discussion
2007.

Solvethe following pair of linear equations by cross multiplication method : 8x+5y=9 3x+2y=4.

Answer»


ANSWER :`X = -2, y= 5`
Discussion
2008.

In which of the following situations, does the list of numbers involved in the form a G.P.? (i) Salary of Sharmila, when her salaryis Rs. 5,00,000 for the first year and expected to receive yearly increase of 10%.

Answer»


ANSWER :(i) NO, (II) No, (III) YES
Discussion
2009.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actualcalculation.

Answer»


ANSWER :`2sqrt(5)CM`
Discussion
2010.

For a trader, marked price of a refigerator = Rs. 15,680 exclusive GST, (GST is 12%). Gagan, a customer for this refrigerator, asks the trader to reduce the price of the refrigerater to such an extent that its reduced price plus GST equal to the marked price of the refrigerator. Find the required reduction.

Answer»


ANSWER :RS. 1,680
Discussion
2011.

Draw the graphs of the pair of linear equations : x+2y=5 and 2x-3y=-4 Also find the points where the lines meet the x -axis.

Answer»


ANSWER :(5, 0) and (-2, 0)
Discussion
2012.

Three metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted together to form a single solid sphere. Find the radius ofthe resulting sphere.

Answer»


ANSWER :12 CM
Discussion
2013.

find the equation of cicle in each of the following cases )(d) touches both the coordinate axes in fouth quadrant and having rasius

Answer»


ANSWER :d `(x-4)^(2)+(y+4)^(2)=16`
Discussion
2014.

Choose the best alternative as the answer- A window always has

Answer»

Curtain
Panes
Grill
Bolt

Answer :D
Discussion
2015.

On which day of the week did Hitesh visit the zoo? I. Hitesh did not visit zoo either on Tuesday or on Thursday. II. Hitesh visited zoo two days before his mother reached his house which was day after Monday.

Answer»

if the data in STATEMENT I ALONE are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question,
if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question,
if the data either in statement I alone or in statement II alone are sufficient to answer the question,
if the data given in both statements I and II TOGETHER are not sufficient to answer the question,

Solution :According to I, Hitesh visited the zoo on any of the week DAYS except Tuesday and Thursday.
According to II, Hitesh.s mother reached his house day after MONDAY i.e. on Tuesday. Thus, Hitesh visited zoo two days before Tuesday i.e. on Sunday.
Discussion
2016.

Simplify : sinA[(sinA,-cosA),(cosA, sinA)]+cosA[(cosA,sinA),(-sinA, cosA)].

Answer»


ANSWER :`[(1,0),(0,1)]`
Discussion
2017.

If (2)/(3) and -(1)/(2) are solution of quadratic equation 6x^(2)+ax-b=0, find the values of a and b.

Answer»


ANSWER :`a=-1 "and" b=2`
Discussion
2018.

A toy is made in the form of hemisphere sumounted by a right cone whose circular base is joined with the plane surface of the hemisphere . The radius of the base of the cone is 7 cm and its volume is 3/2 of the hemisphere . Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal (Take pi= 3 1/7)

Answer»


Answer :SLANT Height of CONE (l) = 22.14 cm, SURFACE AREA of TOY = `795.08 cm^2`
Discussion
2019.

Statements: 1. All fans are watches. 2. Some watches are black. Conclusions: 1. All watches are fans. 2. Some fans are black.

Answer»

If only conclusion I follows,
If only conclusion 2 follows,
If either conclusion 1 or 2 follows,
If NEITHER conclusion 1 nor 2 follows,

Solution :`F implies` fan
` W implies`watches
`B implies `black
Discussion
2020.

(a) Draw the graph of y=x^(2) and hence solve x^(2)-4x-5=0.(b)Draw the graph of y=x^(2)-5x-6 and hence solve x^(2)-5x-14=0

Answer»


ANSWER :(a) `{-1,5}`
(B)`-2` and 7
Discussion
2021.

A flower vase is in the form of a frusturn of a cone. The perimeters of its bases are 44 cm and 8.4 pi cm, if the depth is 14cm, then find how much soil it can hold. OR A toy is in the form of a cone mounted on a hemisphere both are of same radius. The diameter of the conical portion is 6cm and its height is 4cm. Determine the surface area of the solid. (taken pi =3.14)

Answer»


ANSWER :`1408.572`CC
OR
`204.2857cm^(2)`
Discussion
2022.

A cone of radius 4 cm is divided into twoparts by drawing a plane through the mid-point of its axis and parallel to its base. Compare the volumesof the two parts.

Answer»


ANSWER :` (1)/(7)`
Discussion
2023.

The point P(3, 4) is reflected to P' in the x-axis, and O' is the image of O (the origin) when reflected in the line PP'. Write : the length of the segments PP' and OO'

Answer»


ANSWER :PP' = 8 units; OO' = 6units
Discussion
2024.

The point P(3, 4) is reflected to P' in the x-axis, and O' is the image of O (the origin) when reflected in the line PP'. Write : the co-ordinates of P' and O',

Answer»

<P>

ANSWER :P'= (3,-4) and O' = (6,0)
Discussion
2025.

Complete thetable : {:("Point","Transformation ","Image"),((6,-6), .....................,(-6,6)):}

Answer»


ANSWER :REFLECTION in ORIGIN
Discussion
2026.

Find three numbers in A.P. whose sum is 24 and whose product is 440.

Answer»


ANSWER :5, 8 and 11 or 11,8 and 5
Discussion
2027.

Fill in the blanks A tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q so that OQ=13cm. Find length of PQ.

Answer»


ANSWER :`PQ=`12`CM`
Discussion
2028.

Rajan is the brother of Sachin and Manik is the father of Rajan.Jagat is the brother of Priya and Priya is the daughter of Sachin.Who is uncle of jagat?

Answer»

RAJAN
SACHIN
Manik
Can't be determined

Solution :JAGAT is the brother of Priya who is the daughter of Sachin ,so ,jagat is the SON of sachin.Now,Rajan is the brother of sachin,so Rajan is the uncle of jagat.
Discussion
2029.

What number should be subtracted from 2x^3 - 5x^2 + 5x + 8so that the resulting polynomial has a factor 2x - 3?

Answer»


ANSWER :11
Discussion
2030.

Find the mean of the following frequency distribution: {:("Class", 0-5,5-10,10-15,15-20,20-25,25-30),("Frequency",1,2,2,6,7,2):}

Answer»


ANSWER :MEAN = 18
Discussion
2031.

The point P(3, 4) is reflected to P' in the x-axis, and O' is the image of O (the origin) when reflected in the line PP'. Write : the perimeter of the quadrilateral POP'O'

Answer»


ANSWER :20 UNITS
Discussion
2032.

The point P(3, 4) is reflected to P' in the x-axis, and O' is the image of O (the origin) when reflected in the line PP'. Write : the geometrical name of the figure POP'O'

Answer»


ANSWER :RHOMBUS
Discussion
2033.

If alpha = 5+2 sqrt2 " and " beta = 5 -2 sqrt(2) are the roots of the equation x^2-10x+k thenfind the value of k .

Answer»
Discussion
2034.

If the first five elements of the set x_(i) +5, i = 1, 2, 3 ..... 5and the next five elements are replaced by x_(j) -5,j= 6..... 10then the mean will change by

Answer»

0
5
10
25

Answer :A
Discussion
2035.

Among T, V, B, E and C, who is the third from the top when arranged in the descending order of their weights? I. Bis heavier than T and C and is less heavier than V who is not the heaviest. II. C is heavier than only T.

Answer»

if the DATA in statement I alone are SUFFICIENT to answer the question, while the data in statement II alone are not sufficient to answer the question,
if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question,
if the data either in statement I alone or in statement II alone are sufficient to answer the question,
if the data given in both statements I and II together are not sufficient to answer the question,

Solution :From I, we have: `BgtT,BgtC,VgtB`. Thus, V is heavier than each one of B, T and C. But V is not the heaviest. So, E is the heaviest. Thus, we have the order:
`EgtVgtBgtTgtCorEgtVgtBgtCgtT`.
Clearly, B is third from the TOP.
Discussion
2036.

Market value of a share is 150. If the brokerage rate is 0.2% then find for the investment of 10,000.

Answer»


ANSWER :150.3
Discussion
2037.

Using ruler and a compass only, construct a semi-circle with diameterBC = 7 cm. Locate a point A on the circumference of the semi-circle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. MeasureangleADCand write it down.

Answer»


ANSWER :`angleADC=135^(@)`
Discussion
2038.

A clown'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.

Answer»


ANSWER :`5500 cm^2`
Discussion
2039.

Determine a point which divides a line segment 6cm long externally in the ratio 5:3

Answer»

Solution :Steps of Construction
1. Draw a LINE segement AB=6cm.
2. Draw any ray making an acute `angleBAX` with AB.
3. ALONG AX, MARK off ( larger among the ratios ) 5 points `A_(1),A_(2),A_(3),A_(4),A_(5)` such that `A A_(1)=A_(1)A_(2)=A_(2)A_(3)=A_(3)A_(4)=A_(4)A_(5)`.
4. Join the point `A_(2)(5-3)` with end point B.
5. Draw a line parallel to `A_(2)B` from `A_(5)` ( larger among the ratios ) which MEETS AB produced at P.
Point P, so obtained is the required point such that AP:BO=5:3.
Justification: In`DELTAA A_(5)P`,
Since `A_(2)B||A_(5)P` ( construction )
`:. (AP)/(BP)=(A A_(5))/(A_(2)A_(5))` ( By B.P. theorem )
`implies (AP)/(BP)=(5)/(3)` (construction )
Discussion
2040.

Draw a pair of tangents to a circle of radius 3 cm inclined to each other at an angle of 45°.

Answer»


ANSWER :`AOB - 135^@`.
Discussion
2041.

Solve the following systems of inequalities for all xinR|2x-3|le11,|x-2|ge3

Answer»


Answer :`[44, -1]CUP[5, 7]`
Discussion
2042.

P is point on x -axis at a distance of 3 unit from y-axis to its left . The co-ordinates of Pare :

Answer»

(3, 0)
(0,3)
(-3,0)
(0, -3)

ANSWER :C
Discussion
2043.

If x+y=2z, what is the value of (x)/( x-z) + (z)/(y-z)?

Answer»


ANSWER :`1`
Discussion
2044.

Define point of contact.

Answer»


Answer :The common point of TANGENT and the circle is called the point of CONTACT
Discussion
2045.

Find the median for the following frequency distribution:

Answer»

Solution : First we will convert the givendata in EXCLUSIVE from :

Here,
N=400
`rArr"" (N)/(2)=(400)/(2)=200`
`rArr` Median class is 165.5-168.5
Now, `l_(1)=165.5l_(2),=168.5,i=168.5-165.5=3,f=136,C=132`
and median `:. M=l_(1)+(((N)/(2)-C))/(f)xxi`
`=165.5+((200-132))/(136)xx3`
`=165.5+(3xx68)/(136)=167`
Discussion
2046.

At the foot of the mountain the elevation of its summit is 45^(@), after ascending 1000 m towards the mountain up a slope of 30 degree inclination, the elevation found to be 60^(@). Find the height of the mountain.

Answer»


ANSWER :1.366 KM
Discussion
2047.

Rewrite p(x) and h(x) in theirstandard form .

Answer»

<P>

Answer :STANDARD form of p(x) : `= 2X^(3) + x^(2) - sqrt(3) x - 18`
Standard form of h(x) is `x^(5) + 5X^(3) - 6x^(2) - 2x + 8`
Discussion
2048.

Market value of shares and dividend declared by the two companies is given below. Face value of same and it is 100 for both the shares. Investment in which company is more profitable? (i) Company A- 131, 12% (ii) Company B -144.16%

Answer»


Answer :`therefore` INVESTMENT in COMPANY B is more PROFITABLE.
Discussion
2049.

Find the sum of 10 terms of the series : 96-48+24 . . . . . . . . . . .

Answer»


ANSWER :`63(15)/(16)`
Discussion
2050.

Find the median for the following frequency distribution:

Answer»


ANSWER :36
Discussion