WorksheetsEngineering Mathematics#1
Total questions: 20
Worksheet time: 40mins
Evaluate the limit of (x^2 – x – 6)/(x^2 – 4x + 3) as x approaches 3.
3/2
3/5
0
5/2
The derivative with respect to x of 2cos^2 (x^2 + 2).
4 sin (x^2 + 2) cos (x^2 + 2)
-4 sin (x^2 + 2) cos (x^2 + 2)
8x sin (x^2 + 2) cos (x^2 + 2)
-8x sin (x^2 + 2) cos (x^2 + 2)
Find the radius of curvature of the curve y = 2x^3 + 3x^2 at (1,5).
97
90
101
87
A rectangular corral is to be built with a required area. If an existing fence is to be used as one of the sides, determine the relation of the width and the length which would cost the least.
width=twice the length
width=1/2 length
width=length
width=3 times the length
The sum of two numbers is 12. Find the minimum value of the sum of their cubes.
432
644
346
244
A printed page must contain 60 sq m of printed material. There are to be margins of 5 cm on either side and margins of 3 cm on top and bottom. How long should the printed lines be in order to minimize the amount of paper used?
10
18
12
15
Find two numbers whose sum is 36 if the product of one by the square of the other is a maximum.
12 , 24
13, 23
20, 16
11, 25
If the hypotenuse of a right triangle is known, what is the ratio of the base and the altitude of the right triangle when its are is maximum?
1:1
1:2
1:3
1:4
The profit function for a product is P(x) = 5601x + 85x^2 – x^3 – x – 200000. How many items will produce a maximum profit?
80
70
60
40
The edges of a rectangular box are to be reinforced with a narrow metal strips. If the box will have a volume of 8 cu m, what would its dimensions be to require the least total length of strips?
2 x 2 x 2
4 x 4 x 4
3 x 3 x 3
2 x 2 x 4
If x - y = 1, then x3 - y3 - 3xy equals
0
1
2
x2 - y2
If a and b are prime numbers, which of the following is true?
I. a2 has three positive integer factors.
II. ab has four positive integer factors.
III. a3 has four positive integer factors.
I and II only
II and III only
All of these
None of these
If x = b + c, y = c a, z = a b, then
x2 + y2 + z2 - 2xy - 2xz + 2yz is equal to
a + b + c
4b2
abc
a2 + b2
An Egyptian fraction has a numerator equal to 1, and its denominator is a positive integer. What is the maximum number of different Egyptian fraction such that their sum is equal to 1, and their denominators are equal to 10 or less?
3
5
7
9
What is the harmonic mean of two numbers whose geometric mean and arithmetic mean is 8 and 5 respectively?
12.8
12
13.5
14.6
Anil wants to divide Rs.100 into a number of bags so that one can ask for any amount between Rs.1 and Rs.100, he can give the proper amount by giving certain number of these bags without taking out the amount from them. What is the minimum number of bags he will require if each bag has whole number of rupees?
5
6
7
8
When x + y + z = 9 and xy + yz + zx = 11, then x3 - y3 - z3 - 3xyz equals
384
192
432
48
HCF and LCM of two numbers is given. It is possible to ind out the two numbers uniquely if
I. either sum or difference between the two numbers is known.
II. HCF of two numbers = LCM of two numbers.
III. (LCM/HCF)= Prime number.
I and II only
II only
II and III only
I, II and III
A number when divided by sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is
1220
1250
22030
220030
A ball is dropped from a height of 12 m and it rebounds 1/2 of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?
36 m
30 m
48 m
60 m
