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Test: Numeric Entry- 5


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*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 1

Find (r-x), if 2P(5,3) = P(r,4) and P(9,5) + 5P(9,4) = P(10,x)


Detailed Solution for Test: Numeric Entry- 5 - Question 1

2P(5,3) = P(r,4) 2*5!/(5-3)!
= r!/(r-4)! 2*5!/2!
= r(r-1)(r-2)(r-3)(r-4)!/(r-4)! 5!
= r(r-1)(r-2)(r-3) r = 5 P(9,5) + 5P(9,4)
= P(10,x) 9!/(9-5)! + 5*9!/(9-4)!
= 10!/(10-x)! 9!/4! + 5*9!/5!
= 10!/(10-x)! 2*9!/4!
= 10*9!/(10x)! 1/4!
= 5/(10-x)! 5! = (10-x)! 5
= 10-x x = 5 (r-x)
= 5-5 = 0

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 2

The average of 6 observations is 12. When the seventh observation is added the average decreases by 1. Find the seventh observation.


Detailed Solution for Test: Numeric Entry- 5 - Question 2

Let the seventh observation be x. Average = sum of observations/number of observations Sum of observations
= 12*6 = 72
The new average is 12-1 = 11
Sum of observations = 72 + x
Number of obervations
= 6+1 = 7 11 = (72+x)/7 77
= 72+x x = 77 - 72 = 5
The seventh observation is 5

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 3

How many sides does a polygon with 44 diagonals have?


Detailed Solution for Test: Numeric Entry- 5 - Question 3

Let the number of sides be x.
The number of diagonals is given by
x(x-3)/2 x(x-3)/2
= 44 x^2-3x-88=0
x^2 -11x+8x-88=0
x(x-11)+8(x-11)=0
x=-8,
11 Since x cannot be negative,
x = 11
The polygon has 11 sides.

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 4

Pam bought some apples for Rs.110. Had the shopkeeper given him one extra apple, each apple would have cost him Re.1 lesser. How many apples did he buy?


Detailed Solution for Test: Numeric Entry- 5 - Question 4

Let the number of apples bought be x.
Price per apple = 110/x
Had he bought 1 more, the number of apples would have been x+1 Price per apple would have been 110/(x+1)
The apples would have costed Re.1 lesser.
Hence, we have
110/(x+1) = 110/x-1
110/(x+1) = (110-x)/x
110x = (110-x)(x+1)
110x = 110x -x^2+110-x
x^2+x-110=0
x^2+11x-10x-110=0
x(x+11)-10(x+11)=0
(x-10)(x+11)=0
x=10,-11
Rejecting negative value,
we get x = 10
The number of apples bought was 10.

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 5

Find the length of the longest stick that can be filled in a cuboid of length 12 cm, breadth 5 cm and height 84 cm.


Detailed Solution for Test: Numeric Entry- 5 - Question 5

The longest possible stick that can be fitted shall be along the diagonal of the cuboid.
Diagonal of a cuboid with length, breadth and height as l, b and h is given by
sqrt(l2+b2+h2)
= sqrt(122+52+842)
= sqrt(144+25+7056)
= sqrt(7225) = 85
The length of the stick should be 85 cm.
[l2=l*l]

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 6

The length of the square is increased by 30%. The breadth of the square is increased by 20%. By what percent does the area of the rectangle exceed the area of the square?


Detailed Solution for Test: Numeric Entry- 5 - Question 6

Let the original side of the square be x units.
Area of square = side*side = x2 sq.units
Length of the rectangle formed = x + 30% of x = x + 30x/100 = 130x/100
Breadth of the rectangle formed = y + 20% of y = y + 20y/100 = 120y/100
Area of the rectangle
= length*breadth
= 130x/100*120x/100
= 156x2/100
Percentage increasse in area
= (area of rectangle-area of square)/ area of square *100
= (156x2/100 - x2)/x2*100
= (156-100)/100*100
= 56% [x2=x*x]

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 7

The sum of the squares of the numbers is 37/6 times their product. The sum of the numbers is 35. Find the difference of the two numbers.


Detailed Solution for Test: Numeric Entry- 5 - Question 7

Let the two numbers be x and y such that
x>y x2+y2 = (37/6)xy...(1)
x + y = 35...(2)
We know that
(x+y)2 = x2+y2+2xy
Substituting from (1) and (2),
we get 352 = (37/6)xy + 2xy
1225 = (37xy+12xy)/6
49xy = 1225*6 xy = 1225*6/49 xy = 150 Putting x = 150/y in (2),
we get
150/y + y = 35
150 + y2 = 35y y2 - 35y +150=0 y2 - 30y - 5y +150=0 y(y-30) -5(y-30) = 0 (y-5)(y-30) = 0 y = 30,5
The two numbers are 30 and 5 x - y = 30 - 5 = 25 [x2=x*x]

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 8

The item was listed at Rs 65 and sold at Rs. 56.16. Two successive discounts were given on the item and the first discount was 10%. Find the second discount percent.


Detailed Solution for Test: Numeric Entry- 5 - Question 8

Let the SP be the selling price and CP be the cost price of the item.
Let MP be the marked price.
For the first discount, the MP was Rs.65 SP = (100-discount%)*MP/100
= (100-10)*65/100
= 90*65/100
= 58.50
For the second discount, the SP will be Rs. 56.16 and the MP will be Rs.58.50 56.16 = (100-discount%)*58.50/100 100-Discount%= 96 Discount% = 4%

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 9

 

A man rows 12 km upsteram and 22 km downstream. He takes 5 hours to complete each part of his journey. What is the speed of the water in the stream?


Detailed Solution for Test: Numeric Entry- 5 - Question 9

Let the speed of the water in the stream be x km/hr.
Let the speed of the man in still water be y km/hr When he goes upstream, the relative speed is (y-x) km/hr
When he goes downstream, the relative speed is (y+x) km/hr
According to the given conditions, Distance = Speed * Time
12 = (y-x)*5...(1)
22 = (y+x)*5...(2)
Subtracting (1) from (2),
we get
22 - 12 = 5y + 5x -5y +5x 10 = 10x x = 1km/hr
Speed of the water is 1 km/hr

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 10

Two numbers are in ratio 6:13. The least common multiple of the two numbers is 312. Find the sum of the two numbers.


Detailed Solution for Test: Numeric Entry- 5 - Question 10

Let the two numbers be 6x and 13x.
LCM of 6x and 13x = 6*13*x = 78x
78x = 312
x = 312/78 = 4
The two numbers are 6*4 and 13*4 i.e.
24 and 52 The sum of the numbers is
24+52 = 76

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 11

 

Find the value of x3/y3+y3/x3 if x/y+y/x=6 [x2=x*x]


Detailed Solution for Test: Numeric Entry- 5 - Question 11

198 Explanation:
(x/y+y/x) = 6 (x/y+y/x)3
= 63 (x/y)3 + (y/x)3 +3(x/y*y/x)(x/y+y/x)
= 216 (x/y)3+(y/x)3
= 216 - 3*6
= 216 - 18
= 198

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 12

Find a3/b3+b3/a3 if a2+b2=5ab. [x2=x*x]


Detailed Solution for Test: Numeric Entry- 5 - Question 12

a2+b2
=5ab a2/ab+b2/ab
=5ab/ab a/b+b/a
=5 (a/b+b/a)3
=53 (a/b)3+(b/a)3+3(a/b*b/a)(a/b+b/a)
= 125 (a/b)3+(b/a)3
=125-3*5 a3/b3+b3/a3
=125-15
=110

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 13

ABC is an isosceles triangle with AC=CB. A square whose one side is the altitude of the triangle from the vertex to the non-equal side has perimeter 140 cm. The area of the triangle is equal to 420 sq.cm. Find the length of the equal sides of the triangle.


Detailed Solution for Test: Numeric Entry- 5 - Question 13

Let CD be the altitude of the triangle with D lying on AB, which is the base.
Side of square = perimeter/4
The altitude of the triangle will be = 140/4 = 35cm.
Area of triangle = 1/2*base*altitude 1/2*base*35 = 420
base = 2*420/35 = 24cm
In triangle ADC, AD will be perpendicular to CD AD = 24/2=12 and CD = 35 AC = sqrt(AD2+DC2)
= sqrt(122+352)
= sqrt(144+1225)
= sqrt(1369)
= 37 cm
Each of the equal sides in 37 cm long.
[x2=x*x]

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 14

 

The lengths of the two diagonals of a rhombus are 72 cm and 30 cm. Find the length of each side.


Detailed Solution for Test: Numeric Entry- 5 - Question 14

The diagonals of a rhombus bisect each other at right angles.
Hence, we get four right angled triangles with two sides 72/2 and 30/2 cm long Hypotenuse of the triangle
= sqrt(362+152)
= sqrt(1296+225)
= sqrt(1521)
= 39 cm
Each side of the rhombus is 39 cm long.
[x2=x*x]

*Answer can only contain numeric values
Test: Numeric Entry- 5 - Question 15

In a groups of hens and cows, the number of heads is 48 and the number of feet is 140. How many cows are there in the group?


Detailed Solution for Test: Numeric Entry- 5 - Question 15

Let the number of hens be x and the number of cows be y.
Accordng to the conditions
x+y=48...(1)
2x+4y=140...(2)
Multiply (2) by 2 and subtract from
(2) 2x+4y-2x-2y=140-96
2y=44
y = 44/2=22
There are 22 cows in the group.

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