The area of a rhombus is 216 cm2 and the length of its one diagonal is 24 cm. The perimeter ( in cm) of the rhombus
52
60
120
100
Answer : Option B.
Area of rhombus = 1/2 × d1 × d2 where d1 and d2 are lengths of diagonal 1 and 2
So, 216 = 1/2 × 24 × d2
=> d2 = 18cm
In ▲DOC, a2 + ( 18/2 )2 = 144 + 81 = 225
Therefore, a = √225 = 15cm
So, perimeter = 4a = 4 × 15 = 60cm
So, Ans. is option B
The perimeter of an isosceles triangle is 544 cm and each of the equal sides is 5/6 times the base. What is the area (in cm2) of the triangle?
38172
18372
31872
13872
Answer : Option C.
Perimeter = 544
x + 5x/6 + 5x/6 = 544
Therefore x = 204
Let. AB = AC = a = 5x/6
=> a = 5/6 × 204, A = 170
Now, in ▲APC, 1702 = h2 + 1022
h2 = 1702 - 1022
=> h = √18496 = 136
=> area of ▲ABC = 1/2 × 204 × 136 = 13872 cm2
A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. The number of cones thus formed is
140
132
112
126
Answer : Option D.
If the ratio of the diameters of two right circular cones of equal height be 3: 4, then the ratio of their volumes will be
3:4
9:16
16:9
27:64
Answer : Option B.
The sum of two numbers is equal to 15 and their arithmetic mean is 25 per cent greater than their geometric mean. Find the numbers.
5 & 10
3 & 12
1 & 14
6 & 9
None of these
Answer : Option B.
AM of 2 numbers is a+b/2.GM of 2 numbers is √a+b.When sum of 2
numbers is 15, their AM is 7.5. AM = 1.25 (GM)
=> GM =7.5/1.25 = 6. Hence 36 = ab. So product of 2 numbers is 36. Try by
options.2nd is the correct answer.
The product of the digits of a two-digit number is twice as large as the sum of its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.
36
27
63
88
None of these
Answer : Option C.
Go by options. 3rd option is the answer because 63 => product of digits = 6*3 = 18.
Sum of digits = 6 + 3 = 9. Hence product of digits is twice as the sum of the digits. Also 63 – 27 = 36.
So digits are reversed.
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What will be the weight of the new person?
76
76.5
85
80
90
Answer : Option C.
Increased wt. of 8 persons = 8 × 2.5 = 20 kg
wt. of new person = 65 + 20 = 85 kg
50% of a number is 18 less than two-third of that number. Find the number.
123
115
119
108
101
Answer : Option D.
Let the no. be x
Given : 50x/100 = 2x/3 – 18
½ x – 2/3 x = - 18
=> x = 108
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
648
1800
2700
2000
3080
Answer : Option B.
Let the no. of bottles be ‘B’. Using chain rule:
(6×1)/270 = (10×4)/B => B = 1800
At 60% of its usual speed, a train of length L meters crosses platform 240 meters long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in meters)?
140
225
220
480
240
Answer : Option D.
Let usual speed = S m/s.
According to the question,
60% of S=
9S= L+240………… (i)
Also given that, S = L/6
L = 6S …. (ii)
From (i) & (ii)
=> 9S= 6S+240
=> 3S= 240
S=80 m/s
From (ii)
L= 6×80 =480 m
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