Engineering Entrance Sample Papers

# Amrita Entrance Exam Maths Questions

### Amrita Engineering Entrance Exam Maths Sample Papers:

Ques: The number of reflexive relations of a set with four elements is equal to
(a) 216
(b) 212
(c) 28
(d) 24
Ans:- (d)

Ques: The ratio of the greatest value of 2 – cos x + sin2 x is to its least value is
(a) 7/4
(b) 11/4
(c) 13/4
(d) none of these
Ans:- (c)

Ques: The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
(a) 6! x 5!
(b) 30
(c) 5! x 4!
(d) 7! x 5!
Ans:- (a)

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Ques: Two masses are projected with equal velocity u at angle 30° and 60° respectively. If the ranges covered by the masses be R1 and R2 then
(a)  R1 > R2
(b)  R1 = R2
(c)  R1 = 4R2
(d) R2 > R1
Ans:- (b)

Ques: The two lines of regression are given by  3x + 2y = 26 and 6x + y = 31. The coefficient of correlation between x and y is
(a) – 1/3
(b) 1/3
(c) – ½
(d) ½
Ans:- (c)

Ques: If one root of the equation x3 + x2 – 1 = 0 is near to 1.0, then by Newton-Raphson method the first calculated approximate value of this root is
(a) 0.9
(b) 0.6
(c) 1.2
(d) 0.8
Ans:- (d)

Ques: If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in
(a) arithmetic progression
(b) geometric progression
(c) harmonic progression
(d) arithmetic-geometric-progression
Ans:- (c)

Ques: The octal equivalent of the decimal number (0.225)10 is
(a) (0.163146)8
(b) (0.164136)8
(c) (0.2641)8
(d) (0.1646)8
Ans:- (a)

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Ques: We are to form different words with the letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then m1/m2  is equal to
(a) 30
(b) 60
(c) 90
(d) 180
Ans:- (a)

Ques: The locus of the middle points of the chords of hyperbola 3×2 – 2y2 + 4x – 6y = 0 parallel to y = 2x is
(a) 3x – 4y = 4
(b) 3y – 4x + 4 = 0
(c) 4x – 4y = 3
(d) 3x – 4y = 2
Ans:- (a)

Ques: Which one is True?
(a) sin 1 > sin 2 > sin 3
(b) sin 1 < sin 2 < sin 3
(c) sin 1 < sin 3 < sin 2
(d) sin 3 < sin 1 < sin 2
Ans:- (d)

Ques: Solution of the equation ydx – xdy + log xdx = 0 is
(a) y = cx – (1 + log x)
(b) y =cx + (1 + log x)
(c) y + cx + (1 + log x) = 0
(d) None of these
Ans:- (a)

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Ques: A body of mass 10 kg is suspended by two strings 7 cm and 24 cm long, their other ends being fastened to the extremities of a rod of length 25 cm. If the rod be so held that the body hangs immediately below its middle point, then the tension of the strings in kg-wt are
(a) 7/5, 24/5
(b) 14/5, 48/5
(c) 3/5, 7/5
(d) None of these
Ans:- (b)

Ques: In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is
(a) 4
(b) 5
(c) 6
(d) 7
Ans:- (b)

Ques: Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex. Further, assume that the origin, z1 and z2 form an equilateral triangle, then
(a) a2 = b
(b) a2 = 2b
(c) a2 = 3b
(d) a2 = 4b
Ans:- (c)

Ques: Zn = {0, 1, 2, …, (n – 1)} fails to be a group under multiplication modulo n because
(a) Closure property fails
(b) Closure holds but not associativity
(c) There is no identity
(d) There is no inverse for an element of the set
Ans:- (d)

Ques: In Boolean Algebra, the unit element ‘1’
(a) Has two values
(b) Is unique
(c) Has atleast two values
(d) None of these
Ans:- (b)

Ques. If a set A has n elements, then the total number of subsets of A is
(a) n
(b) n2
(c) 2n
(d) 2n
Ans: (c)

Ques. The number log2 7 is
(a) An integer
(b) A rational number
(c) An irrational number
(d) A prime number
Ans: (c)

Ques: If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr-1 + 2 ´ nCr equals
(a) n+2Cr
(b) n+2Cr+1
(c) n+1Cr
(d) n+1Cr+1
Ans:- (b)

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Ques. 150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is
(a) 15
(b) 20
(c) 25
(d) 30
Ans: (c)

Ques. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then men select the chairs from amongst the remaining. The number of possible arrangements is
(a) 6C3 x 4C2
(b) 4C2­ x 4P3
(c) 4P2­ x 4P3
(d) None of these
Ans: (d)

Ques. For the straight lines given by the equation (2 + k)x + (1 + k)y = 5 + 7k, for different values of k which of the following statements is true
(a) Lines are parallel
(b) Lines pass through the point (– 2, 9)
(c) Lines pass through the point (2, – 9)
(d) None of these
Ans: (b)

Ques. If the pair of straight lines xy – x – y + 1 = 0 and the line ax + 2y – 3 = 0 are concurrent, then a =
(a)  – 1
(b) 0
(c) 3
(d) 1
Ans: (d)

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Ques. A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is
(a) (y – q)2 = 4px
(b) (x – q)2 = 4py
(c) (y – p)2 = 4qx
(d) (x – p)2 = 4qy
Ans: (d)

Ques. The number of values of c such that the straight line y = 4x + c touches the curve x2/4 + y2 = 1 is
(a) 0
(b) 1
(c) 2
(d) Infinite
Ans: (c)

Ques: The real number x when added to its inverse gives the minimum value of the sum at x equal to
(a) 2
(b) 1
(c) – 1
(d) – 2
Ans:- (b)

Ques. The triangle formed by the tangent to the curve f(x) = x2 + bx – b at the point (1, 1) and the co-ordinate axes, lies in the first quadrant. If its area is 2 then the value of b is
(a) –1
(b) 3
(c) –3
(d) 1
Ans: (c)

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Ques. The solution of the differential equation sec2 x tan ydx + sec2 y tan xdy = 0 is
(a) tan x = c tan y
(b) tan x = c tan (x + y)
(c) tan x = c cot y
(d) tan x sec y = c
Ans: (c)

Ques. Two uniform solid spheres composed of the same material and having their radii 6 cm and 3 cm respectively are firmly united. The distance of the centre of gravity of the whole body from the centre of the larger sphere is
(a) 1 cm
(b) 3 cm
(c) 2 cm
(d) 4 cm
Ans: (a)

Ques. A man falls vertically under gravity with a box of mass ‘m’ on his head. Then the reaction force between his head and the box is
(a) mg
(b) 2 mg
(c) 0
(d) 1.5 mg
Ans: (c)