Engineering Entrance Sample Papers

Manipal Entrance Test Maths Model Question Paper

Manipal Entrance Test Maths sample practice questions

Ques. If the distance of any point (x, y) from origin is defined as d(x, y) = max {|x|, |y|}, then the locus of the point (x, y), where d (x, y) = 1 is
(a) circle
(b) a square
(c) a triangle
(d) none of these
Ans. (b)

Ques. How many nine digit numbers can be formed by using the digits 2, 2, 3, 3, 5, 5, 8, 8, 8 so that  the odd digits occupy even positions ?
(a) 7560
(b) 180
(c) 16
(d) 60
Ans. (d)

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Ques. The angle between two equal forces acting on a particle when the square of their resultant is three times their product is
(a) 90º
(b) 60º
(c) 120º
(d) none of these
Ans. (b)

Ques. If (1 + x – 2x2)6 = 1 + a1x + a2x2 + a3x3  . . .  . .  then the value of a2 + a4 + a6 +  . . .  .+ a12 will be
(a) 32
(b) 31
(c) 64
(d) 1024
Ans. (b)

Ques. Number  of  G.P.’s  having   5, 9 and  11 as  it’s  three  terms  is  equal  to;
(a) exactly two
(b) atmost two
(c) at least one
(d) none of these
Ans. (d)

Ques. If f’(x) = g(x) and g’(x) = –f(x) for all x and f(2) = 4 = f’(2), then f2 (24) + g2 (24) is
(a) 32
(b) 24
(c) 64
(d) 48
Ans. (a)

Ques. If  nP3 + nCn–2 = 14n, then n =
(a) 5
(b) 6
(c) 8
(d) 10
Ans. (a)

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Ques. cot x – tan x =
(a) cot 2x
(b) 2 cot2 x
(c) 2 cot 2x
(d) cot2 2x
Ans: (c)

Ques. The coefficient of x4 in the expansion of (1 + x + x2 + x3)11 is
(a) 900
(b) 909
(c) 990
(d) 999
Ans. (c)

Ques. The product of lengths of perpendiculars from any point of the hyperbola x2 – y2 = 8 to its asymptotes is
(a) 2
(b) 3
(c) 4
(d) 8
Ans. (c)

Ques. The roots of the equation 32x – 10.3x + 9 = 0 are
(a) 1, 2
(b) 0, 2
(c) 0, 1
(d) 1, 3
Ans. (b)

Ques. Total number of ways in which four boys and four girls can be seated around a round table, so that no two girls together, is equal to
(a) 7 !
(b) (3 !) (4 !)
(c) (4 !) (4 !)
(d) (3 !) (3 !)
Ans. (b)

Ques. In a triangle ABC, the tangent of half difference of two angles is one third the tangent of half the sum of the two angles. The ratio of the sides opposite the angles in
(a) 2 : 3
(b) 1 : 3
(c) 2 : 1
(d) 3 : 4
Ans. (c)

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Ques. From an urn containing 3 white and 5 black balls, 4 balls are transferred into an empty urn. From this urn a ball is drawn and found to be white. The probability that out of four balls transferred, 3 are white and 1 is black, is
(a) 1/3
(b) 1/7
(c) 2/3
(d) none of these
Ans. (b)

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Ques. The curve y – exy + x = 0 has a vertical tangent at the point
(a) (1, 1)
(b) at no point
(c) (0, 1)
(d) (1, 0)
Ans. (d)

Ques. If  are in A.P. 10ax + 10 , 10bx + 10 , 10cx + 10 are in
(a) A.P.
(b) G.P. when x > 0
(c) G.P. for all x
(d) G.P. when x < 0
Ans. (c)

Ques. A man has 7 friends. In how many ways he can invite one or more of them for a tea party
(a) 128
(b) 256
(c) 127
(d) 130
Ans. (c)

Ques. If log 2, log (2n – 1) and log (2n + 3) are in A.P., then  n =
(a) 5/2
(b) log2 5
(c) log3 5
(d) 3/2
Ans:
 (b)

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Ques. The sum of all positive divisors of 960 is
(a) 3048
(b) 3087
(c) 3047
(d) 2180
Ans. (a)

Ques. The area of the triangle formed by the line x + y = 3 and the angle bisectors of the pair of straight lines x2 – y2 + 2y = 1 is
(a) 2
(b) 4
(c) 6
(d) 8
Ans. (a)

Ques. The normal chord of a parabola y2 = 4ax at (x1,x1) subtends a right angle at the
(a) Focus
(b) Vertex
(c) (–a, 0)
(d) None of these
Ans. (a)

Ques. If iz3 + z2 – z + i = 0 then the value of |z| is
(a) 1
(b) 2
(c) < 1
(d) > 1
Ans. (a)

Ques. Number of three digit numbers of the form xyz with x > 1 and digits are not repeated, is
(a) 640
(b) 576
(c) 800
(d) none of these
Ans. (b)

Ques. The graph of the function y = f(x) is symmetrical about x = 2, then
(a) f(x + 2) = f(x – 2)
(b) f(2 + x) = f(2 – x)
(c) f(x) = f(–x)
(d) none of these
Ans. (b)

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Ques. The number of distinct terms in the expansion of (x + 2y – 3z + 5w – 7u)n is
(a) n + 1
(b) n+4C4
(c) n+4Cn+2
(d) none of these
Ans. (b)

Ques. In an election the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, then the number of candidates is
(a) 7
(b) 10
(c) 8
(d) 6
Ans. (c)

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