Engineering Entrance Sample Papers

AUEET Maths Sample Paper Andhra University Engineering Entrance Test Mathematics Practice Sample Paper:

Ques. If the portion of the line lx + my = 1 falling inside the circle x2 + y2 = a2 subtends an angle of 45o at the origin, then
(a) 4[a2 (l2 + m2) – 1] = a2 (l2 + m2)
(b) 4[a2 (l2 + m2) – 1] = a2 (l2 + m2) – 2
(c) 4[a2 (l2 + m2) – 1] = [a2 (l2 + m2) – 2]2
(d) None of these
Ans. (c)

Ques. To expand (1 + 2x)–1/2 as an infinite series, the range of x should be
(a) [–1/2, 1/2]
(b) (–1/2, 1/2)
(c) [–2, 2]
(d) (–2, 2)
Ans. (b)

Ques. The vector b = 3j + 4k is to be written as the sum of a vector b1 parallel to a = i + j and a vector b2 perpendicular to a. Then b1 =
(a) 3/2(i + j)
(b) 2/3(i + j)
(c) 1/2(i + j)
(d) 1/3 (i + j)
Ans. (a)

Ques. The quartile deviation of daily wages (in Rs.) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is
(a) 14.5
(b) 5
(c) 9
(d) 4.5
Ans. (d)

Ques. If value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be
(a) 11
(b) 121
(c) 1331
(d) 14641
Ans. (d)

Ques. If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
(a) 120
(b) 30
(c) 31
(d) 32
Ans. (c)

Ques. If the equation y3 – 3x2 y + m (x3 – 3xy2) = 0 represents the three lines passing through origin, then
(a) Lines are equally inclined to each other
(b) Two lines makes equal angle with x-axis
(c) All three lines makes equal angle with x-axis
(d) None of these
Ans. (a)

Ques. If |a x b| = 4 and |a . b| = 2, then | a |2 | b |2 =
(a) 2
(b) 6
(c) 8
(d) 20
Ans. (d)

Ques. A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table

 x : 0 10 20 30 40 50 60 70 80 d : 0 4 7 9 12 15 14 8 3

Then approximate area of cross-section of river by Trapezoidal rule, is
(a) 710 sq. m
(b) 730 sq. m
(c) 705 sq. m
(d) 750 sq. m
Ans. (c)

Ques. The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are
(a) 2 and 9
(b) 3 and 8
(c) 4 and 7
(d) 5 and 6
Ans. (c)

Ques. The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals
(a) |m + n| / (m – n)2
(b) 2 / | m + n |
(c) 1 / | m + n|
(d) 1 / |m – n|
Ans. (d)

Ques. If the sum of the roots of the equation ax2 + bx + c = 0 be equal to the sum of the reciprocals of their squares, then bc2, ca2, ab2 will be in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Ans. (a)

Ques. The value of xo (the initial value of x) to get the solution in interval (0.5, 0.75) of the equation x3 – 5x + 3 = 0 by Newton-Raphson method, is
(a) 0.5
(b) 0.75
(c) 0.625
(d) None of these
Ans. (b)

Ques. 49n + 16n – 1 is divisible by
(a) 3
(b) 19
(c) 64
(d) 29
Ans. (c)

Ques. If a, b and c are the three non-coplanar vectors, then (a + b + c) . [(a + b)  x (a + c)] is equal to
(a) [a b c]
(b) 2 [a b c]
(c) – [a b c]
(d) 0
Ans. (c)

Ques. From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x = 7.47, x = 7.52, is

 x :    : 7.47 7.48 7.49 7.5 7.51 7.52 f(x) : 1.93 1.95 1.98 2.01 2.03 2.06

(a) 0.0996
(b) 0.0896
(c) 0.6977
(d) 0.0776
Ans. (a)

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

Ques. If cosh–1 (p + iq) = u + iv, then the equation with roots cos2 u and cosh2 v
(a) x2 – x (p2 + q2) + p2 = 0
(b) x2 – x(p2 + q2 + 1) + 1 = 0
(c)    x2 + x(p2 + q2 + 1) + 1 = 0
(d)    x2 – x (p2 + q2 + 1) = 0
Ans. (d)

Ques. In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The no. of newspaper is
(a) At least 30
(b) At most 20
(c) Exactly 25
(d) None of these
Ans. (c)

Ques. If the circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points P (x1, y1), Q (x2, y2), R (x3, y3), S (x4, y4), then
(a) x1 + x2 + x3 + x4 = 0
(b) y1 + y2 + y3 + y4 = 0
(c) x1 x2 x3 x4 = c4
(d) y1 y2 y3 y4 = c4
Ans. (a,b,c,d)

Ques. Let p a non singular matrix 1 + p + p2 + … + pn = O (O denotes the null matrix), then p–1 =
(a) pn
(b) –pn
(c) – (1 + p + … + pn)
(d) None of these
Ans. (a)

Ques. The real root of the equation x3 – 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is
(a) 1.909
(b) 1.904
(c) 1.921
(d) 1.940
Ans. (a)

Ques. If the length of the tangents drawn from the point (1,2) to the circles x2 + y2 + x + y – 4 = 0 and 3x2 + 3y2 – x – y + k = 0 be in the ratio 4 : 3, then k =
(a) 7/2
(b) 21/ 2
(c) – 21/ 4
(d) 7/ 4
Ans. (c)

Ques. The lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are perpendicular to each other,  if
(a) aa’ + cc’ = 1
(b) aa’ + cc’ = –1
(c) ac + a’c’ = 1
(d) ac + a’c’ = –1
Ans. (b)

Ques. If the equation x2 + y2 + 2gx + 2fy + 1 = 0 represents a pair of lines, then
(a)    g2 – f2 = 1
(b) f2 – g2 = 1
(c) g2 + f2 = 1
(d) f2 + g2 = ½
Ans. (c)

Ques. The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
(a) 11
(b) 7
(c) 5.5
(d) 6
Ans. (b)

Ques. The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is
(a) 1/5
(b) 15/4
(c) 4
(d) 8
Ans. (b)

Ques. If  a matrix A is such that 4A3 + 2A2 + 7A + I = O,  then A–1 equals
(a) (4A2 + 2A + 7I)
(b)    –(4A2 + 2A + 7I)
(c)    –(4A2 – 2A + 7I)
(d)    (4A2 + 2A – 7I)
Ans. (b)

Ques. If for positive integers r > 1, n > 2 the coefficient of the (3r)th and (r + 2)th powers of x  in the expansion of (1 + x)2n are equal, then
(a)    n = 2r
(b)    n = 3r
(c) n = 2r + 1
(d) None of these
Ans. (c)

Ques. The value of the nearest root of the equation x3 + x – 1 = 0 after third iteration by Newton-Raphson method near x = 1 is
(a) 0.51
(b) 0.42
(c) 0.67
(d) 0.55
Ans. (c)

Ques. x + y + z + 2 = 0 together with x + y + z + 3 = 0 represents in space
(a) A line
(b) A point
(c) A plane
(d) None of these
Ans. (d)

Ques. Two tangents PQ and PR drawn to the circle x2 + y2 – 2x – 4y – 20 = 0 from point P (16, 7). If the centre of the circle is C, then the area of quadrilateral PQCR will be
(a) 75 sq. units
(b) 150 sq. units
(c) 15 sq. units
(d) None of these
Ans. (a)

Ques. If the expression (mx – 1 + 1/x) is always non-negative, then the minimum value of m must be
(a)    –½
(b)    0
(c)    ¼
(d)    ½
Ans. (c)

Ques. Let a and b be roots of x2 – 3x + p = 0 and let c and d be the roots of x2 – 12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to
(a) 8 : 7
(b) 11 : 10
(c) 17 : 15
(d) None of these
Ans. (c)

Ques. If the equations of opposite sides of a parallelogram are x2 – 7x + 6 = 0 and y2 – 14y + 40 = 0, then the equation of its one diagonal is
(a) 6x + 5y + 14 = 0
(b) 6x – 5y + 14 = 0
(c) 5x + 6y + 14 = 0
(d) 5x – 6y + 14 = 0
Ans. (b)

Ques. Locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse x2/a2 + y2/b2 = 1, is
(a) (x2 + y2)2 = b2x2 + a2y2
(b) (x2 + y2)2 = b2x2 – a2y2
(c) (x2 + y2)2 = a2 x2 – b2 y2
(d) (x2 + y2)2 = a2x2 + b2y2
Ans. (d)

Ques. Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random from urn A, the probability that it is found to be red, is
(a) 32/55
(b) 21/55
(c) 19/55
(d) None of these
Ans. (a)

Ques. sin (2 sin–1 0.8) =
(a) 0.96
(b) 0.48
(c) 0.64
(d) None of these
Ans. (a)

Ques. The length of subtangent to the curve x2 y2 = a4 at the point (–a, aa) is
(a) 3a
(b) 2a
(c) a
(d) 4a
Ans. (c)

Ques. A root of the equation x3 – x – 4 = 0 lies between 1 and 2. Its approximate value, as obtained by applying bisection method 3 times, is
(a) 1.375
(b) 1.750
(c) 1.975
(d) 1.875
Ans. (d)

Ques. The total expenditure incurred by an industry under different heads is best presented as a
(a) Bar diagram
(b) Pie diagram
(c) Histogram
(d)  Frequency polygon
Ans. (b)

Ques. If (sec A + tan A) (sec B + tan B) (sec C + tan C) = (sec A – tan A) (sec B – tan B) (sec C – tan C) then each side is equal to
(a) 1
(b) – 1
(c) 0
(d) None of these
Ans. (a, b)

Ques. A root of the equation x3 – 18=0 lies between 2 and 3. The value of the root by the method of false position is
(a) 2.526
(b) 2.536
(c) 2.546
(d) 2.556
Ans. (a)

Ques. If x1, x2, x3 as well as y1, y­2, y3­ are in G.P. with the same common ratio, then the points (x1, y1), (x2, y2) and (x3, y3)
(a)    Lie on a straight line
(b)    Lie on an ellipse
(c)    Lie on a circle
(d)    Are vertices of a triangle

Ans. (a)

Ques. For a normal distribution if the mean is M, mode is Mo and median is Md, then
(a) M > Md > M0
(b) M < Md < M0
(c) M = Md M0
(d) M = Md = M0
Ans. (d)

Ques. A ball is thrown vertically upwards from the ground with velocity 15 m/s and rebounds from the ground with one-third of its striking velocity. The ratio of its greatest heights before and after striking the ground is equal to
(a) 4 : 1
(b) 9 : 1
(c) 5 : 1
(d) 3 : 1
Ans. (b)

Ques. Let E = {1, 2, 3, 4} and F = {1, 2}.Then the number of onto functions from E to F is
(a) 14
(b) 16
(c) 12
(d) 8
Ans. (a)

Ques. One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are (–3, 1) and (1, 1). Then the equations of other two sides are
(a) 7x – 4y + 25 = 0, 4x + 7y = 11 and 7x – 4y – 3 = 0
(b) 7x + 4y + 25 = 0, 7y + 4x – 11 = 0 and 7x – 4y – 3 = 0
(c) 4x – 7y + 25 = 0, 7x + 4y – 11 = 0 and 4x – 7y – 3 = 0
(d) None of these
Ans. (a)

Ques. Two tangents are drawn from a  point P on radical axis to the two circles touching at Q and R respectively then triangle formed by joining PQR is
(a) Isosceles
(b) Equilateral
(c) Right angled
(d) None of these
Ans. (a)

Ques. The domain of the function f(x) = 16 – x C2x – 1 + 20 – 3x P4x – 5, where the symbols have their usual meanings, is the set
(a) {2, 3}
(b) {2, 3, 4}
(c) {1, 2, 3, 4}
(d) {1, 2, 3, 4, 5}
Ans. (a)

Ques. If cosh y = sec x, then the value of tanh2 (y/2) is
(a) tan2 (x/2)
(b) cot2 (x/2)
(c) sin2 (x/2)
(d) tan2 x/2
Ans. (a)

Ques. The area of the triangle formed by the line 4x2 – 9xy – 9y2 = 0 and x = 2 is
(a) 2
(b) 3
(c) 10/3
(d) 20/3
Ans. (c)

Ques. The mean deviation from the median is
(a) Greater than that measured from any other value
(b) Less than that measured from any other value
(c) Equal to that measured from any other value
(d)  Maximum if all observations are positive
Ans. (b)

Ques. The sum of three consecutive terms in a geometric progression is 14. If 1 is added to the first and the second terms and 1 is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is
(a) 1
(b) 2
(c) 4
(d) 8
Ans. (b)