NDA I - Mathematics Question Paper 2016 - NDA
120 Questions MCQ Test NDA (National Defence Academy) Past Year Papers - NDA I - Mathematics Question Paper 2016
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Suppose ω is a cube root of unity with ω≠1. Suppose P and Q are the points on the complex plane defined by ω and ω2. If O is the origin, then what is the angle between OP and OQ?
Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?
positive numbers.
(I)2
positive numbers is reflexive, but not transitive and symmetric.If x2+ px + 4 for all real values of x, then which one of thefollowing is correct?
real values of x.If z=x + iy= 
, where i = √-1, then what is the fundamental amplitude of 
If f(x1)- f(x2) is 
for x1, x2 ∈ (-1,1), then what is f(x) equal to?
What is the range of the function 
2 ,where X ∈R?
A straight line intersects x and y axes at P and Q respectively If (3,5) is the middle point of PQ, then what is the area ofthe triangle OPQ?
∵ M is the mid point of PQ
If a circle of radius b units with centre at (0, b) touches the line y = x — a√2 , then what is the value of b?
Consider the function f(θ)= 4(sin2 θ+ cos4 θ)
Q. What is the maximum value of the function f(θ)?
Consider the function f(θ)= 4(sin2 θ+ cos4 θ)
Q. What is the minimum value of the function f(θ)?
Consider the function f(θ)= 4(sin2 θ+ cos4 θ)
Consider the following statements:
f(θ) = 2 has no solution.
f(θ) = 
has a solution.
Q. Which of the above statements is/are correct?
Consider the function 
How many solutions does the function f(x) = 1 have?
then ( 3y + 1) = 0 is a factor o f cubic equation.
Consider the function
How many solutions does the function f(x) = -1 have?
Consider the functions
f(x) = xg(x) and g(x = 
Where [•] is the greatest integer function.
What is 
equal to?
equal to ?
will be 2 and in range
Consider the function f ( x ) = | x - 1 |+ x2 , w here x ∈R .
Which one of the following statements is correct?
x ∈RConsider the function f ( x ) = | x - 1 |+ x2 , w here x ∈R .
Which one of the following statements is correct?
and increasing 
Which one of the following statements is correct?
What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates 
and x = 1 ?
What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and 
Given that an = 
Consider the following statements:
1. The sequence {a2n} is in AP with common difference zero.
2. The sequence {a2n+1} is in AP with common difference zero.
Which of the above statements is/are correct?
Given that an =
What is an-1 - an-4 equal to ?
Consider the equation x + |y| = 2y.
Which of the following statements are not correct?
1. y as a function of x is not defined for all real x.
2. y as a function of x is not continuous at x = 0.
3. y as a function of x is differentiable for all x.
Q. Select the correct answer using the code given below.
Consider the equation x + |y| = 2y.
What is the derivative of y as a function of x with respect to x for x < 0?
Consider the lines y = 3x, y = 6x and y = 9
What is the area of the triangle formed by these lines?
Consider the lines y = 3x, y = 6x and y = 9
The centroid of the triangle is at which one of the following points?
respectively.
Consider the function f(x) = (x - l )2 ( x + 1) (x - 2)3
Q. What is the number of points of local minima of the function f(x)?
Consider the function f(x) = (x - l )2 ( x + 1) (x - 2)3
What is the number of points of local maxima of the function f(x) ?
Let f(x) and g(x) be twice differentiable functions on [0,2] satisfying f"(x) = g"(x), f'(1) = 4, g'(1) = 6,f(2) =3 and g(2) = 9. Then what is f(x) - g(x) at x = 4 equal to ?
Consider the curves y = | x — 1 | and |x| = 2
Q. What is/are the point(s) of intersection of the curves ?
Consider the curves y = | x — 1 | and |x| = 2.
Q. What is the area of the region bounded by the curves and x-axis?
Consider the function
Q. What is the value of f (0)?
Consider the function
Q. What is the value of p for which f"(0)=0?
Consider a tiangle ABC in which
Q. What is the value of sin
Consider a tiangle ABC in which
Q. What is the value of 
Given that tan α and tanβ are the roots of the equation x2 + bx + c = 0 with b ≠ 0.
Q. What is tan(α + β) equal to?
Given that tan α and tanβ are the roots of the equation x2 + bx + c = 0 with b ≠ 0.
What is sin(α+ β)sec α see β equal to?
Consider the two circles (x-l)2 + ( y-3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0
Q. What is the distance between the centres of the two circles?
Consider the two circles (x-l)2 + ( y-3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0
Q. If the circles intersect at two distinct points, then which one of the following is correct?
Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0
Q. What is the equation of the line passing through the point of intersection of the given lines and parallel to x-axis?
Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0
Q. What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis?
Consider the equation
k sinx + cos 2x = 2k - 7
If the equation possesses solution, then what is the minimum value of k?
Consider the equation
k sinx + cos 2x = 2k - 7
If the equation possesses solution, then what is the maximum value of k?
Consider the function f (x) 
where [•] denotes the greatest integer function.
Q. What is 
equal to?
Consider the function f (x) where [•] denotes the greatest integer function.
Q. What is 
equal to?
Let z1, z2 and z3 be non-zero com plex num bers satisfying 
, where i =√- 1 .
Q. What is Z1 + z2 + z3 equal to?
Let z1, z2 and z3 be non-zero com plex num bers satisfying , where i =√- 1 .
Consider the following statements:
1. z1z2z3 is purely imaginary.
2. z1z2 + z2z3 + z3z1 is purely real.
Q. Which of the above statements is/are correct?
Given that logx y, logz x, logy z are in GP, xyz = 64 and x3, y3, z3 are inA.P.
Q. Which one of the following is correct ?
x,y and z are
Given that logx y, logz x, logy z are in GP, xyz = 64 and x3, y3, z3 are inA.P.
Q. Which one of the following is correct?
xy, yz and zx are
Let z be a complex number satisfying
Q. What is |z| equal to?
Let z be a complex number satisfying
Q. What is 
equal to?
A function f(x) is defined as follows:
Consider the following statements:
1. The function f(x) is continuous at x = 0.
2. The function f(x) is continuous at x = 
Q. Which of the above statements is/are correct?
A function f(x) is defined as follows:
Consider the following statements:
1. The function f(x) is differentiable at x = 0. 71
2. The function f(x) is differentiable at x = 
Q. Which of the above statements is/are correct ?
Let α and β (α < β ) be th e roots of the equatio n x2 + bx + c = 0, where b > 0 and c < 0.
Consider the following:
1. β < - α
2. P < | a |
Q. Which of the above is/are correct?
Consider the following:
1. α + β + αβ > 0
2. α2 β + β2α > 0
Which of the above is/are correct?
Consider a parallelogram whose vertices are A (1,2), B (4, y), C (x, 6) and D (3,5) taken in order.
Q. What is the value o f AC2 - BD2 ?
Consider a parallelogram whose vertices are A (1,2), B (4, y), C (x, 6) and D (3,5) taken in order.
Q. What is the point of intersection of the diagonals?
Consider a parallelogram whose vertices are A (1,2), B (4, y), C (x, 6) and D (3,5) taken in order.
Q. What is the area of the parallelogram?
Let f : R → R be a function such that
f(x ) = x3 + x2 f '(1) + xf "(2)+ f "'(3)
for x ∈ R
What is f(1) equal to?
Let f : R → R be a function such that
f(x ) = x3 + x2 f '(1) + xf "(2)+ f "'(3)
for x ∈ R
Q. What is f '(1) equal to?
Let f : R → R be a function such that
f(x ) = x3 + x2 f '(1) + xf "(2)+ f "'(3)
for x ∈ R
Q. What is f'""(10) equal to?
Consider the following:
1. f(2 ) = f(1) - f(0)
2. f "(2) - 2f '(1) = 12
Q. Which of the above is/are correct?
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point (1 ,0 ,1 ).
Q. What are the direction ratios of the line of intersection of the given planes?
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point (1 ,0 ,1 ).
Q. What is the equation of the plane P?
A plane P passes through the line of intersection of the planes 2x - y + 3z = 2, x + y - z = 1 and the point (1 ,0 ,1 ).
Q. If the plane P touches the sphere x2 + y2 + z2 = r2, then what is r equal to?
Consider th e function f (x ) = | x2 - 5x + 6 |
Q. What is f '(4) equal to?
Consider th e function f (x ) = | x2 - 5x + 6 |
Q. What is f"(2.5) equal to?
Let f(x) be the greatest integer function and g(x) be the modulus function.
Q. What is 
equal to?
Let f(x) be the greatest integer function and g(x) be the modulus function.
Q. What is 
equal to?
Consider a circle passing through the origin and the points (a, b) and (-b, -a).
Q. On which line does the centre of the circle lie?
Consider a circle passing through the origin and the points (a, b) and (-b, -a).
Q. What is the sum of the squares of the intercepts cut off by the circle on the axes?
is sum of squares of intercepts 
Let 
be two unit vectors and 0 be the angle between them.
Q. What is cos 
equal to?
Let be two unit vectors and 0 be the angle between them.
What is sin 
equal to?
Consider the following statements:
1. There exists 
2. sin-1 
Q. Which of the above statements is/are correct ?
Consider the following statements:
1. 
2. There exist x ,y ∈[-l, 1], where x ≠ y such that 
Which of the above statements is/are correct ?
What are the order and degree respectively of the differential equation whose solution is y = cx + c2 - 3c3/2 + 2, where c is a parameter?
What is
equal to, where [•] is the greatest integer function?
then what is 
equal to? 
, where a ≠ 0 then what is 
equal to ?
equal to ?
If A is a square matrix, then what is adj(A-1) - (adj A)-1 equal to?
What is the binary equivalent ofthe decimal number 0.3125?
Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'. Then which one of the following is correct?
equal to ?
What is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?
B)
C)
C)
B 
C )
B 
C )(a, 2b) is the mid-point of the line segment joining the points
(10, -6) and (k, 4). If a - 2b = 7, then what is the value of k?
Consider the following statements:
1. If ABC is an equilateral triangle, then 3tan( A+B) tan C =1.
2. If ABC is a triangle in which A= 78°, B =66°, then
3. If ABC is any triangle, then
Q. Which of the above statements is/are correct?
and 
then what is 
equal to ?
What is the mean deviation from the mean of the numbers 10,9,21,16,24?
Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?
Two independent events A and B have P(A) 
and P(B) 
What is the probability that exactly one of the two events A or B occurs?
A coin is tossed three times. What is the probability of getting head and tail alternately?
If the total number of observations is 20 
and 
then what is the variance of the distribution?
A card is drawn from a wel-shuffled deck of 52 cards. What is the probability that it is queen of spade?
If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4?
A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?
For two mutually exclusive events A and B, P(A) = 0.2 and 
= 0.3. What is 
equal to?
What is the probability of 5 Sundays in the month of December?
If m is the geometric mean of
then what is the value of m?
A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?
The mean of the series x1,x2, . . . , xn is 
If x2 is replaced by λ , th en what is the new mean?
For the data
3, 5, 1, 6, 5, 9, 5, 2, 8, 6
the mean, median and mode are x, y and z respectively. Which one of the following is correct?
Consider the following statements in respect of a histogram:
1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequnecy polygon and the x-axis.
2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.
Q. Which of the above statements is/are correct?
A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?
What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?
If one root of the equation (1 - m) x2 +1 x +1 = 0 is double the other and 1 is real, then what is the greatest value of m?
What is the number of four-digit decimal numbers (<1) in which no digit is repeated?
What is a vector of unit length orthogonal to both the vectors
If 
are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?
What is the area of the parallelogram having diagonals 
Consider the following in respect of the matrix
Q. Which of the above is/are correct?
Which of the following determinants have value ‘zero’?
Q. Select the correct answer using the code given below,
What is the acute angle between the lines represented by the equations 
The system of linear equations kx + y + z =1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?
What is the number of different messages that can be represented by three 0’s and two 1 ’s?
If loga(ab) = x, then what is logb(ab) equal to?
then what is 
equal to?
Suppose ω1, and ω2 are two distinct cube roots of unity different from 1. Then what 
equal to?
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