Union Public Service Commission had successful conduct the **National Defence Academy (NDA) & Naval Academy (NA)** on **27 September 2015**. A lot of aspirants has attended** NDA NA exam** which held All over India in the various cities. Official **NDA NA Answer Key **will be released soon on official site upsc.gov.in set wise, set A, set B, set C, set D.

Until You can check Unofficial **Answer Key NDA NA **and calculate their performance in Examination. This Unofficial **NDA NA** **Answer Sheet** is prepared by the solved paper educational web portal. You can also check solved Mathematics and General Ability Test on **Edupil. **

There is two paper, first is mathematics with 300 marks and second paper fo general ability with 600 marks (General Ability including General Knowledge, Physics, Chemistry and English). There is also a negative marking.

This is good chance for those candidates who want to do something for the Country and can be proved his patriotism in the defence field. This Exam conducted by two times in a year. After qualify the **NDA NA Exam** candidate get admission in 3 years training course in Defence.

## NDA NA 2015 Exam Paper and Answer Key:

### Mathematics paper – I

- The eccentricity of the hyperbola 16x
^{2}– 9y^{2}=1 is

(a) 3/5

(b)**5/3**

(c) 4/5

(d) 5/4 - The product of perpendiculars from the two points (±4, 0) to the line 3x cos Æ + 5y sin Æ = 15 is

(a) 25

(b) 16

(c)**9**

(d) 8 - If the centre of the circle passing through the origin is (3,4) then the intercepts cut off by the circle on
*x*-axis and*y-*axis respectively are(a)

**3 unit and 4 unit**

(b) 6 unit and 4 unit

(c) 3 unit and 8 unit

(d) 6 unit and 8 unit - The lines 2x=3y=-z and 6x=-y=-4z

(a)**are perpendicular**

(b) are parallel

(c) intersect at an angle 45^{o}

(d) intersect at an angle 60^{o} - Two straight lines passing through the point
*A*(3,2) cut the line 2y=x+3 and*x-*axis perpendicularly at*P and Q*The equation of the line PQ is

(a) 7x + y -21 +0

(b)**x + 7y +21 +0**

(c) 2x + y – 8 + 0

(d) x = 2y +8 = 0 - The radius of the sphere

3x^{2}+3y^{2}+3z^{2}– 8x + 4y + 8z -15 = 0 is

(a) 2

(b)**3**

(c) 4

(d) 5 - The direction ratios of the line perpendicular to the lines with direction ratios <1, -2, -2> and <0, 2, 1> are

(a)**<2, -1, 2>**

(b) <-2, 1, 2>

(c) <2, 1, -2>

(d) <-2, -1, -2> - What are the co-ordinates of the foot of the perpendicular drawn from the point (3, 5, 4) on the plane z=0?

(a) (0, 5, 4)

(b)**(3, 5, 0)**

(c) (3, 0, 4)

(d) (0, 0, 4) - The lengths of the intercepts on the co-ordinate axes made by the plane 5x+2y+z-13=0 are

(a) 5, 2, 1 unit

(b)**13/5, 13/2, 13 unit**

(c) 5/13, 2/13, 1/13 unit

(d) 1,2, 5 unit**For the next three (03) items that follow:**

Consider the expansion of (1+x)^{2n+1 } - The sum of the coefficients of all the terms in the expansion is

(a)**2**^{2n-1 }(b)4^{ n-1}

(c) 2 x 4^{n}

(d) None of the above - If the coefficients of x
^{r}and x^{r+1}are equal in the expansion, then r is equal to

(a) n

(b) 2n-1/2

(c)**2n+1/2**

(d) n+1 - The average of the coefficients of the two middle terms in the expansion is

(a)^{2n+1}C_{n+2}

(b)^{2n+1}C_{n}^{ }(c)^{2n+1}C_{n-1}^{ }

(d)^{2n}C_{n+1} - The
*n*th term of an A.P. is (3+n)/4, then the sum of first 105 terms is

(a) 270

(b) 735

(c) 1409

(d)**1470** - The polygon has 44 diagonals. The number of its sides is

(a)**11**

(b) 10

(c) 8

(d) 7