Engineering Entrance Sample Papers

UPSEE Maths Practice Paper Uttar Pradesh State Entrance Exam (UPSEE) Maths Practice Paper with Answers [PDF]:

Ques: Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
(a) Reflexive
(b) Transitive
(c) Not symmetric
(d) A function
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: n – 1C3 + n – 1C4 > nC3 then the value of n is
(a) 7
(b) < 7
(c) > 7
(d) None of these
Ans:- (c)

Ques: Three forces P, Q and R act along the sides BC, AC and BA of an equilateral triangle ABC. If their resultant is a force parallel to BC through the centroid of the triangle ABC,  then
(a) P = Q = R
(b) P = 2Q = 2R
(c) 2P = Q + 2R
(d)  2P = 2Q = R
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)

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Ques: A particle possess two velocities simultaneously at an angle of tan–1 12/5 to each other. Their resultant is 15 m/s. If one velocity is 13m/s, then the other will be
(a) 5 m/s
(b) 4 m/s
(c) 12 m/s
(d) 13m/s
Ans:- (b)

Ques: If sin x + sin2 x = 1, then the value of expression cos12 x + 3 cos10 x + 3 cos8 x + cos6 x – 1 is equal to
(a) 0
(b) 1
(c) –1
(d) 2
Ans:- (a)

Ques: A box contains 100 tickets numbered 1, 2 …… 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability
(a) 1/8
(b) 13/15
(c) 1/7
(d) None of these
Ans:- (b)

Ques: If y = 2x is a chord of the circle x2 + y2 – 10x = 0, then the equation of the circle of which this chord is a diameter, is
(a) x2 + y2 – 2x + 4y = 0
(b) x2 + y2 + 2x + 4y = 0
(c) x2 + y2 – 2x + 4y = 0
(c) x2 + y2 – 2x – 4y = 0
Ans:- (d)

Ques: If there are n harmonic means between 1 and 1/31 and the ratio of 7th and (n – 1)th harmonic means is 9 : 5
then the and value of n will be
(a) 12
(b) 13
(c) 14
(d) 15
Ans:- (c)

Ques: If mean = (3 median – mode) k, then the value of k is
(a) 1
(b) 2
(c) 1/2
(d)  3/2
Ans:- (c)

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)

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Ques: If the lines of regression are 3x + 12y = 19 and 3y + 9x = 46 then rxy will be
(a) 0.289
(b) – 0.289
(c) 0.209
(d) None of these
Ans:- (b)

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: Let G denote the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication
(a) G is a subgroup
(b) G is a finite abelian group
(c) G is an infinite, non-abelian group
(d) G is infinite, abelian
Ans:- (c)

Ques: In Boolean Algebra, the zero element ‘0’
(a) Has two values
(b) Is unique
(c) As atleast two values
(d) None of these
Ans:- (b)

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Ques: What is the decimal equivalent of the octal number 1217
(a) 640
(b) 620
(c) 650
(d) 655
Ans:- (d)