Find **UPSEE 2017 Solved Mathematics Sample Paper Set-V**. This sample paper will be very helpful for those engineering aspirants who are going to appear for UPSEE-2017 Exam. Solving sample papers and previous year question papers are must do activities to do good in any entrance examination. Questions in this paper are prepared with great expertise and every question of this paper is important for UPSEE 2017 Examination. Also, many a times question is repeated in UPSEE/UPTU examination. So, practicing more questions will certainly give you an extra edge over other students.

This paper consists of 50 questions. Each correct answer will give 4 marks. There is no negative marking in this paper. Questions given in this paper cover complete syllabus of UPSEE. All questions are very important as they are developed with great expertise.

**About Exam:**

UPSEE is a state level entrance examination for various disciplines. Many prestigious government and private college is associated with this university. UPSEE engineering entrance exam paper is easier than JEE Main and Advanced. It provides good opportunity for those who cannot make to IITs or NITs.

**Few random questions from the sample paper are given below:**

**Q. **If *a*_{1}.*a*_{2} *a*_{3},... are terms of AP such that *a*_{1} + *a*_{5} + *a*_{10} + *a*_{15} + *a*_{20} + *a*_{24} = 225, then the sum of first 24 terms is

(a) 9 × 10^{2} (b) 9 × 10^{3}

(c) 10 × 9^{2} (d) 10 × 9^{3}

**Correct Option: (a)**

**Sol**.

We know that,

*a*_{l} + *a*_{24} = *a*_{5} + *a*_{20} = *a*_{10} + *a*_{15} ...(i)

Given,

*a*_{1} + *a*_{5} + *a*_{10} + *a*_{15} + *a*_{20} + *a*_{24} = 225

From equation (i)

3(*a*_{1} + *a*_{24}) = 225

*a*_{1} + *a*_{24} = 75

Sum of first *n* terms of an AP is given as:

= 12 (75)

= 900

= 9 × l0^{2}

**Q. **The probabilities that Mr. *A *and Mr. *B *will die within a year are 1/2 and 1/3 respectively, then the probability that only one of them will be alive at the end of the year, is

(a) 5/6

(b) 1/2

(c) 2/3

(d) None of the above

**Correct Option: (b)**

**Sol**.

Given,

Probability that Mr. *A *will die within a year P(A) = 1/2

**Q. **The number of solutions of the system ofequations 2*x* + *y* -*z *= 7, *x* *-*3y *+ *2*z* =* *1* *and *x + *4*y* -3*z* = 5 is

(a) 0 (b) 1

(c) 2 (d) 3

** **

**Correct Option: (a)**

**Sol**.

Given,

2*x* + *y *-z = 7 ...(i)

*x* -3*y* + 2*z* = l ...(ii)

and *x* + 4*y* -3*z* = 5 ...(iii)

Multiplying (i) by 2 and then adding (i) and (ii), we get

5*x* -*y* = 15 ...(iv)

Multiplying (i) by 3 and then subtracting (iii) from (i), we get

5*x* -*y* = 16 ...(v)

Eqs. (iv) and (v) shows that they are parallel and so solution does not exist.

**Q. **In a right angle Δ*ABC*, *angle A *= 90°* *and sides *a,* *b,* *c *are respectively 10 cm, 8 cm and 6c.m.If a force **F** has moments 0, 64* *and 36 N-cm respectively about vertices *A, B *and *C*, then magnitude of **F** is

(a) 9

(b) 4

(c) 10

(d) 8

** **

**Correct Option: (c)**

**Sol**. ** **

Since, moment of** F** about *A* is 0, therefore **F** passes through *A. *Let the components of **F** along *AB *and *AC *be* X *and *Y *respectively, then moment of **F **about *B* = 36.

6*Y* = 36

*Y *= 6

Also, moment of **F** about *C *= 64

8X = 64

*X = 8*

Hence, *F*^{2 }= *X*^{2 }+ *Y*^{2}

= 64 +36 = 100

*F* = 10

**Q. **A train of length 100 m travelling at 20 m/s overtakes another train of length 200 m travelling at 10 m/s. The time taken by the first train to pass the second train is

(a) 30 s (b) 50 s

(c) 10 s (d) 40 s

**Correct Option: (a)**

**Sol**. ** **

Total distance travelled by the first train to pass the second train = (100 + 200)m = 300m

Since first train overtakes second train that means both trains are travelling in the same direction.

So, the relative velocity of the first train = (20 - 10) m/s = 10 m/s

So the time taken by the first train to pass the second train = 300/10 = 30 sec

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