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2301.

Find the possible pairs of co-ordinates of the fourth vertex D of the parallelogram if three of its verices are A (5,6) , B (1,-2) and C (3,-2) .

Answer»


ANSWER :`THEREFORE` The POSSIBLE pairs of co-ordinates of the fourth VERTEX D of the PARALLELOGRAM are (3,6),(-1,-10) and (7,6) .
Discussion
2302.

Verify whether 3, -1 and -(1)/(3) are the zeroes of the cubic polynomial p(x)=3x^(3)-5x^(2)-11x-3, and then verify the relationship between the zeroes and the coefficients.

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ANSWER :`(-d)/(a)`.
Discussion
2303.

Find the number zeroes of the given polynomials. And also find their values. q(y)=y^(2)-1

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ANSWER :1
Discussion
2304.

(#KPL_SAT_MAT_PRP_PS_10_E01_003_Q01.png" width="80%"> A system of three equation and their graphs are shown above. How many solutions does the system of equations have?

Answer»

None
One
Two
Three

SOLUTION :Difficult: Easy
CATEGORY: Passport to ADVANCED Math/ Quadratics
Strategy ADVICE: Graphically speaking, the solution to a system of equations is the point or points where ALL the graphs intersect.
Getting to the Answer: There is only one point on the graph where all three equations intersect (1, 4). Therefore, (B) is the correct answer.
Discussion
2305.

A bag contains5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

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ANSWER :NUMBER of BLUE BALLS = 10
Discussion
2306.

A conical tent is required to accommodate 157 persons each person must have 2 mm^(2) of space on the ground and 15 m^(3) of air to breath .Find the height of the tent , also calculate the slant height.

Answer»

Solution :1 person NEEDS 2 `m^(2)` of space
157 persons needs `2xx157 m^(2)` space on the GROUND.
`pi^(2)=2xx157`
`r^(2)=(2xx157)/(3.14)=100 RARR r=10 m`
Also 1 person needs 15`m^(3)` of air.
157 persons need `15xx157 m^(3)`of air.
`(1)/(3) pir^(2)h =15xx157`
`h=(15xx157xx3)/(3.14xx100)=22.5 m`
`(l^(2))=(h^(2)+r^(2)=(22.5)^(2)+10^(2))=606.25`
`l=sqrt(606.25)=24.62 m`
Discussion
2307.

The values of x and y in the equations sqrt2x+sqrt3y=0 and sqrt3x-sqrt8y=0 are sqrt3x-sqrt8y=0 are :

Answer»

`x=1,y=2`
`x=0, y=2`
`x=0, y=0`
`x=1, y=0`.

ANSWER :C
Discussion
2308.

Three numbers which are in AP together make a 39 and their product is a 325. Find the AP.

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Answer :AP I: 13, 25, 27, ...... .
AP II: 1, - 11, -23, ..... ..
Discussion
2309.

Find the mode of following frequency distribution :

Answer»


ANSWER :1847.83
Discussion
2310.

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

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ANSWER :`616 cm^3`
Discussion
2311.

A group of students decided to buy an. F.M. Radio (transistor) from 256 to 300 rupees. But at the last moment two students backed out of the decision so that the remaining students had to pay one rupee each more than they had planned. What was the price of F.M. Radio, if the students paid equal shares?

Answer»

Solution :Let the cost of F.M. Radio =RS.x
and the TOTAL number of students =n
`because` Share of each STUDENT `=RS.(x)/(n)`
But, if 2 students backed out of the decision, then share of each student `=RS.(x)/(n-2)`
`because` But the given condition,
`(x)/(n-2)-(x)/(n)=1impliesx((1)/(n-2)-(1)/(n))=1`
`=x((n-n+2)/(n(n-2)))=1impliesx=(n^(2)-2n)/(2)""......(1)`
But, `265lexle300""("given")`
`implies265le(n^(2)-2n)/(2)le300""["from"(1)]`
`implies530len^(2)-2n+1le601""("multiplying both SIDES by 2")`
`implies531len^(2)-2n+1le601""("adding 1 to each side")`
`implies531le(n-1)^(2)le601`
`impliessqrt531len-1lesqrt601`
`implies1+sqrt531lenle1+sqrt601`
If `nle1+sqrt531impliesnle1+23.04....impliesnle24.04""......(2)`
If `nle1+sqrt601impliesnle1+24.515.....impliesnle25.52......(3)`
From (2) and (3), we get
`n=25""(because"number of students cannot be in fraction")`
`because` From (1), we get
`x=((25)^(2)-2xx25)/(2)=(625-50)/(2)=(575)/(2)=RS.287.500`
Discussion
2312.

Show that 5-sqrt3 is irrational.

Answer»


ANSWER :`5-sqrt3.`
Discussion
2313.

Express cos85^(@)+cos75^(@) in terms of trigonometric ratio of angles between 0^(@) and 1.7^(@).

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ANSWER :`SIN5^(@)+SIN15^(@)`.
Discussion
2314.

If the sum of the first n terms of an AP is 4n - n^2, what is the first term (that is S_1 ) ? What is the sum of first two terms ? What is the second term ? Similarly . Find the 3rd, the 10th and the nth terms .

Answer»


Answer :`S_(1) =3, S_(2) =4; a_(2)=1; a_(3)=-1, a_(10)= -15`
`a_(N) \ 5-2n`
Discussion
2315.

At the rate of 4% compound interest per annum the difference between compound and simple interest of a sum of money is Rs. 20 .Find the sum of money.

Answer»


ANSWER :RS. 12500
Discussion
2316.

Find two consecutive positive odd integers, sum of whose squares is 290.

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ANSWER :11 and 13
Discussion
2317.

Diameter of a right circular cylinder is 10cm and hight is 14cm,find its lateral surface.

Answer»
Discussion
2318.

There is sign (s) of ? mark in the blank space in which only one of the five alternatives satisfy the same relationship. Find the correct one. CDF : DEG : EFH : ?

Answer»

FGH
GHF
FGI
FHG

Answer :B
Discussion
2319.

There is sign (s) of ? mark in the blank space in which only one of the five alternatives satisfy the same relationship. Find the correct one. CAT : ECV : PEN : ?

Answer»

RGP
QFO
QGP
NCL

Answer :A
Discussion
2320.

There is sign (s) of ? mark in the blank space in which only one of the five alternatives satisfy the same relationship. Find the correct one. ACE : KIG : M?Q : WU ?

Answer»

OZ
NS
OS
PT

Answer :C
Discussion
2321.

A boat is rowed away from a cliff 150 m high. At the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2.5 minutes. The speed of the boat (in m/sec) is

Answer»

`1+1/SQRT(3)`
`1-1/sqrt(3)`
`sqrt(3) + 3`
`2sqrt(3)-3`

ANSWER :B
Discussion
2322.

Which one of the following is not correct?

Answer»

statistics is liable to be misused
the data collected by the INVESTIGATOR to beused by himself are called primary data
statistical laws are EXACT
statistics do not take into ACCOUNT of INDIVIDUAL cases

Answer :C
Discussion
2323.

Write the following expressions as log N and find their values. 3 log_(64) 4

Answer»


ANSWER :`log_(64)64,1`
Discussion
2324.

Find the distance between each of the following pairs of points . (i) A (2,3),B(4,1)

Answer»


ANSWER :`THEREFORE` The distance between the points A and B is 2`sqrt(2)` units.
Discussion
2325.

Find the sum given below: 34 + 32 + 30 +….. + 10

Answer»


ANSWER :`286`
Discussion
2326.

As given in Q.1, suppose a person has paid 15,075 for buying 100 shares. In that 75. Find the amount of GST he paid to the broker and prepare the contract note.

Answer»


ANSWER :GST=13.50
Discussion
2327.

(1,-1),(-(1)/(2),(1)/(2)) and (1, 2) are the vertices of a/an ______________ triangle.

Answer»

EQUILATERAL
isosceles
right angled
scalene

ANSWER :B
Discussion
2328.

Rahul and Ram hold a pair of die in their hands. Rahul has a pair of an 8-sided dice and Ram has a pair of tetrahedral dice in hand. What is the probability of each of them throwing a pair of numbers whose sum is 8 ?

Answer»


ANSWER :`1/(16)`
Discussion
2329.

Find a point on the line through A(5, -4)and B(-3, 2),that is, twice as far from A as from B.

Answer»

SOLUTION :Let `P(x, y)` be a point on AB such that
`""PA=2PB`

`rArr""(PA)/(PB)=(2)/(1)""rArr" "PA:PB=2:1`
So, by using SECTION formula for internal division,
`""x=(mx_(2)+nx_(1))/(m+n), y= (my_(2)+ny_(1))/(m+n)`
`rArr""x=(2(-3)+1(5))/(2+1)rArr" "x=-(1)/(3)`
and `""y=(2(2)+1(-4))/(2+1)rArr""y=0`
`rArr" "` Required point `-=(-(1)/(3), 0)`
`"""BUT"""`
This is not the END of this question.
Think : Is it not POSSIBLE that `P(x,y)` divides AB externally in the ratio 2 : 1.

So, by using section formula for external division,
`therefore""x=(2(-3)-1(5))/(2-1)rArr" "x=-(11)/(1)rArr" "x=-11`
and `""y=(2(2)-1(-4))/(2-1)rArr" "y=(8)/(1)rArr" "y=8`
So, co-ordinates of `p` are (-11, 8) also.
Hence, required POINTS are `(-(1)/(3),0) and (-11, 8)`.
Discussion
2330.

The model of a building is constructed with the scale factor 1:30. (i) If the height of the model is 80 cm, findthe actual height of the building in metres.

Answer»


ANSWER :24 m
Discussion
2331.

Prove that the points (-7, -3), (5, 10), (15, 8) and (3, -5) taken in order are the corners of a parallelogram.

Answer»


Answer :AB = CD = `sqrt(313)` , BC = AD = `sqrt(104)` , AC `NE` BD (vertices of parallogram)
Discussion
2332.

Evaluate cos 12^(@) -sin 78^(@)

Answer»


ANSWER :`0`
Discussion
2333.

Find the slope of the line passing through the given two point A (-3 (1)/(2) ,3), B (-7,2 (1)/(2))

Answer»


ANSWER :`(1)/(7)`
Discussion
2334.

Find the ratio in which the line2x+ 3y -5=0divides the line segment joining the points (8,-9)and (2,1)Also. Find the co-ordinates of the point of divisions

Answer»


ANSWER :` 8 :1 ((8)/(3),(1)/(9)) `
Discussion
2335.

Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs56 per sq m. Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

Answer»


ANSWER :28 CM and RS 15.68;
Discussion
2336.

Find the roots of the following quadratic equations(1)/(x+4) - (1)/( x- 7 )= (11)/(30 ), x ne -4,7

Answer»


ANSWER :1, 2
Discussion
2337.

Construct a triangle similar to a given triangle PQR with its sides equal to (7)/(3) of the corresponding sides of the triangle PQR (scale factor (7)/(3)).

Answer»


ANSWER :`(7)/(3)`
Discussion
2338.

Find the annual income derived from 125, 120rs shares paying 5% dividend.

Answer»


ANSWER :`750RS`
Discussion
2339.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations ). If the average speed of the express train is 11km/h more than that of the passenger train , find the average speed of the two trains.

Answer»


Answer :Speed of the passenger train = 33 KMPH
Speed of the EXPRESS train = 44 kmph
Discussion
2340.

Area of the largest triangle that can be inscribed in a semicircle of radius a is

Answer»

`1/2 a^2 SQ. UNITS B]`
`2a^2 sq. units`
`a^2 sq.units`
`3/2 a^2 sq.units`

ANSWER :C
Discussion
2341.

Show that 2x+7 is a factor of 2x^(3)+5x^(2)-11x-14. Hence factorise the given expression completely, using the factor theorem.

Answer»


ANSWER :(2x+7) (x-2) (x+1)
Discussion
2342.

To draw a figure as per the given information. (Use a graph paper)

Answer»

SOLUTION :
The coordinates of the point of INTERSECTION of the LINES `AB` and `CD` are `(2,2)`.
Discussion
2343.

Draw a circle with radiuys 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle

Answer»

SOLUTION :
Discussion
2344.

Two APs have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th terms?

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ANSWER :100
Discussion
2345.

A(-2, 4) and B(-4, 2) are reflected in the y-axis. If A and B' are images of A and B respectively. Find the co-ordinates of A' and B'

Answer»


ANSWER :` A ' = (2,4) ; B ' = (4,2)`
Discussion
2346.

Find the class limits corresponding to each frequency if the mean of thefollowing distribution is 33 and assumed mean 35 :

Answer»

SOLUTION : Here, we are given `barx` =33 and a=35
WIDTH="80%">
Now, ` "mean"barx=a+(sumf_(i)u_(i))/(sumf_(i))xxh`
`33=35+(-20)/(100)xxh`
`rArr -200=-20h "" rArr =10`
No w, `"if" u_(i)=-3rArr(x_(i)-35)/(10)=-3x_(i)-35=-30rArrx_(i)=5` and width i.e., 10 So, class limits of first group is 0-10 (substract and add `(H)/(2)` from lower and upper boundaries) if `u_(i)=-rArr(x_(i)-35)/(10)=-2rArr-35=-20x_(i)=15` and width i.e., h=10 So, class limits of second group is 10-20 (subtract and add `(h)/(2)` from lower and upper boundaries). Simliarly. class limits of other groups are 20-30,30-40,40-50, and 50-60
Discussion
2347.

which of the following rational numbers is esxpressible as a terminating decimal ?

Answer»

`124/165`
`131/30`
`2075/625`
`1625/462`

Solution :`2027/625 = 2075/((5^(4)xx 2^(0)))`
So , it is EXPRESSIBLE as a terminating decmial.
Discussion
2348.

Prove that sqrt(3) is irrational.

Answer»
Discussion
2349.

3080 cm^(3)of water is required to fill a cylindrical vessel completely and 2310 cm ^(3) of water is required to fill it upto 5 cm below the top. Find :height of the vessel.

Answer»


ANSWER :20 CM
Discussion
2350.

3080 cm^(3)of water is required to fill a cylindrical vessel completely and 2310 cm ^(3) of water is required to fill it upto 5 cm below the top. Find :radius of the vessel.

Answer»


ANSWER :7 CM
Discussion