### UPSEE Sample Paper for MCA:

**Question:** The straight lines x + y – 4 = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a traigle which is

(a) isosceles

(b) right angled

(c) equilateral

(d) None of these

**Ans. **(a)

**Question:** The line y = mx + 1 is a tangent to the parabola y^{2} = 4x if

(a) m = 1

(b) m = 2

(c) m = 3

(d) m = 4

**Ans. **(a)

**Question:** The length of the median through A of a triangle whose vertices are A (–1,3) ,B (1, –1) and C (5, 1) is

(a) 5

(b) 4

(c) 1

(d) None of these

**Ans. **(a)

**Question:** If the sum of three numbers in A.P. is 12 and the sum of their cubes is 288, then the numbers are

(a) 2, 4, 6

(b) 1, 4, 7

(c) 1, 3, 5

(d) None of these

**Ans. **(a)

**Question:** If a, b, c be in H.P., then

(a) a^{2} + c^{2} > b^{2
}(b) a^{2} + b^{2} > 2c^{2
}(c) a^{2} + c^{2} > 2b^{2
}(d) a^{2} + b^{2} > c^{2}

**Ans:** (c)

**Question:** The locus of a point whose sum of the distances from the origin and the line x = 2 is 4 units is

(a) y^{2} = – 12(x – 3)

(b) y^{2} = 12 (x – 3)

(c) x^{2} = 12 (y – 3)

(d) x^{2} = –12(y – 3)

**Ans. **(a)

**Question:** Sukhbir is taller than Randhir but not as tall as Ajit. If Manoj is taller than Nitin, who is shorter than Ajit, then who among them is the shortest?

(a) Nitin

(b) Sukhbir

(c) Manoj

(d) Data inadequate

**Ans. **(d)

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**Question:** If S_{n} denotes the sum of n terms of an arithmetic progression, then the value of (S_{2n} – S_{n}) is equal to

(a) 2S_{n}

(b) S_{3n}

(c) 1/3 S_{3n}

(d) 1/2S_{n
}**Ans:** (c)

**Question:** Ten men can finish construction of a wall in eight days. How much men are needed to finish the work in half-a-day?

(a) 80

(b) 100

(c) 120

(d) 160

**Ans. **(d)

**Question:** It was Wednesday on July 15, 2019. What was the day on July 15, 2019?

(a) Thursday

(b) Tuesday

(c) Friday

(d) None of these

**Ans. **(a)

**Question:** How is ½ % expressed as a decimal fraction?

(a) 0.5

(b) 0.05

(c) 0.005

(d) 0.0005

**Ans. **(c)

**Question:** The smallest number of 5 digits beginning with 3 and ending with 5 will be:

(a) 31005

(b) 30015

(c) 30005

(d) 30025

**Ans. **(c)

**Question:** The Range of the function f(x) = x – 2 / 2 – x is

(a) R

(b) R – {1}

(c) (-1)

(d) R – {-1}

**Ans. **(c)

**Question:** A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is

(a) 112

(b) 140

(c) 164

(d) None of these

**Ans. **(b)

**Question:** Convert 103 of base to a number of base 3 is

(a) 12011

(b) 10211

(c) 10221

(d) 10031

**Ans. **(b)

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**Question:** If (2311)_{4} – (1111)_{2} = (×)_{5}, then ×

(a) 1131

(b) 1130

(c) 1129

(d) None of these

**Ans. **(a)

**Question:** The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

(a) 7/2

(b) 7/3

(c) 7/5

(d) 7/10

**Ans. **(d)

**Question:** A circle is circumscribed around a square (shown in figure). The area of one of the four shaded portions is equal to 4/7. The radius of the circle is:

(a) 3

(b) 2

(c) √2

(d) ½

**Ans. **(c)

**Question:** A shopkeeper buys 144 eggs at 90 paise each. In the way 20 eggs were broken. He sold the remaining eggs at Rs. 1.20 each. The percentage gain or loss is

(a) 14.8% gain

(b) 12.9% gain

(c) 8.5% gain

(d) 4.8% gain

**Ans. **(b)

**Question:** “Some stones are rocks” and “Some rocks are clouds”. If both the statements are true, then which of the following statements is DEFINITELY TRUE?

(a) Some clouds are stones

(b) All clouds are rocks

(c) No rock is stone

(d) None of that

**Ans. **(d)

**Question:** The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is

(a) 1/39

(b) 1/28

(c) 1/17

(d) 1/6

**Ans. **(d)

**Question:** If the product of n positive numbers in 1, then their sum is

(a) a positive integer

(b) divisible by n

(c) equal to n + 1/n

(d) never less than n

**Ans. **(d)

**Question:** The equation of the straight line, passing through the point (1, -2) and parallel to the line 8x – 4y + 7 = 0 is

(a) 2x + y – 4 = 0

(b) 2x – y + 4 = 0

(c) 2x – y – 4 = 0

(d) None of these

**Ans. **(c)

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**Question:** If the line 2x – y + k = 0 is a diameter of the circle x^{2} + y^{2} + 6x – 6y + 5 = 0 then k is equal to

(a) 12

(b) 9

(c) 6

(d) 3

**Ans. **(b)

**Question:** In a group of people 65% speak German and 45 speak French. If 5% of the people speak neither French nor German, then the percentage of people who can speak both German and French is

(a) 5%

(b) 10%

(c) 15%

(d) 20%

**Ans. **(c)

**Question:** Let *A* = {*p*, *q*, *r*}. Which of the following is an equivalence relation on *A
*(a) R

_{1}= {(

*p, q*), (

*q*,

*r*), (

*p, r*), (

*p, p*)}

(b) R

_{2}= {(

*r, q*), (

*r*,

*p*), (

*r, r*), (

*q, q*)}

(c) R

_{3}= {(

*p, p*), (

*q*,

*q*), (

*r, r*), (

*p, q*)}

(d) None of these

**Ans.**(d)

**Question:** If in an A.P. the sum of 10 items, is 11 and the sum to 11 terms is 19 then the sum of 30 terms is:

(a) -20

(b) 20

(c) 30

(d) -30

**Ans. **(d)

**Question:** How many such pairs of letters are there in the word EXPRESSION which have as many letters between them in the word as in the alphabet?

(a) Four

(b) Five

(c) Three

(d) Two

**Ans. **(a)

**Question:** If nC_{12} = nC_{8}, then n has the value

(a) 20

(b) 12

(c) 6

(d) 30

**Ans. **(a)

**Question:** If ‘P’ means ‘×’, ‘Q’ means ‘÷’ T means of and ‘V’ means +, then what will be the value of 85 Q 17 P 3 V ½T 4 = ?

(a) 62

(b) 31

(c) 17

(d) 19

**Ans. **(c)

**Question:** An A.P. consists of 60 items. If the first and the last term be 7 and 125 respectively its 32nd term is:

(a) 64

(b) 65

(c) 66

(d) 69

**Ans. **(d)

**Question:** The number of ways in which 6 rings can be worn on the four fingers of one hand is

(a) 4^{6}

(b) ^{6}C_{4
}(c) 6^{4}

(d) None of these

Ans. (a)

**Question:** In how many ways a committee of 5 members can be selected from 6 men and 5 women, consisting of 3 men and 2 women?

(a) 320

(b) 200

(c) 450

(d) None of these

**Ans. **(b)

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**Question:** On the portion of the straight line x + y = 2 which is intercepted between the axes, a square is constructed away from the origin, with this portion as one of its side, If P denotes the perpendicular distance of a side of this square from the origin then the maximum value of P is

(a)

(b)

(c)

(d)

**Ans. **(c)

**Question:** The set of all integers x such that |x – 3| < 2 is equal to

(a) {1, 2, 3, 4, 5}

(b) {1, 2, 3, 4}

(c) {2, 3, 4}

(d) {-4, -3, -2}

**Ans. **(c)

**Question:** The values of k for which the quadratic equation kx^{2} + 1 = kx + 3x – 11x^{2} has real and equal roots are

(a) {–11, –3}

(b) {5,7}

(c) {5, –7}

(d) None of these

**Ans. **(c)

**Question:** The equation of that diamenter of the circle x^{2} + y^{2} – 6x + 2y – 8 = 0, which passes through the origin, is

(a) x – 3y = 0

(b) x + 3y = 0

(c) 3x – y = 0

(d) None of these

**Ans. **(b)

**Question:** The value of k for which the line x + y + 1 = 0 touches the parabola y^{2} = kx is

(a) -4

(b) 4

(c) 2

(d) -2

**Ans. **(b)

**Question:** 7, 7,14, 42, 168, ?

(a) 840

(b) 672

(c) 504

(d) 336

**Ans. **(a)

**Question:** If ‘M S N’ means ‘M is the father of N’, ‘M ≠ N’ means ‘M is the sister of N’ and ‘M * N’ means ‘M is the brother of N’ then what is the relation of C with A in A # B $ C * D?

(a) Niece

(b) Nephew

(c) Aunt

(d) Data inadequate

**Ans. **(b)

**Question:** It is given that M is either greater than or equal to P. P is smaller than Q and Q is not greater than R. Which of the following is DEFINITELY TRUE?

(a) M is either greater than or equal to R

(b) M is either greater than or equal to Q

(c) R is greater than P

(d) R is either greater than or equal to P

**Ans. **(c)

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