#### 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 – 1}C_{3} + ^{n – 1}C_{4} > ^{n}C_{3} 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 4A^{3} + 2A^{2} + 7A + I = O, then A^{–1} equals

(a) (4A^{2} + 2A + 7I)

(b) –(4A^{2} + 2A + 7I)

(c) –(4A^{2} – 2A + 7I)

(d) (4A^{2} + 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 + sin^{2} x = 1, then the value of expression cos^{12} x + 3 cos^{10} x + 3 cos^{8} x + cos^{6} 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 x^{2} + y^{2} – 10x = 0, then the equation of the circle of which this chord is a diameter, is

(a) x^{2} + y^{2} – 2x + 4y = 0

(b) x^{2} + y^{2} + 2x + 4y = 0

(c) x^{2} + y^{2} – 2x + 4y = 0

(c) x^{2} + y^{2} – 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 r_{xy} 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 x^{3} + 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)

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