NDA Previous Year Question Paper 2009 Exam II – Shift I |

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1. If (1+3+5+……+p)+(1+3+5+……+q)=(1+3+5+……+r) where each set of parentheses contains the sum of consecutive odd integers as shown, what is the smallest possible value of (p+q+r) where p>6?
   (a) 12 (b) 21 (c) 45 (d) 54
2. Let A={x | x≤9, x∈N}. Let B={a,b,c} be the subset of A where (a+b+c) is a multiple of 3. What is the largest possible number of subsets like B?
   (a) 12 (b) 21 (c) 27 (d) 30
3. Let A={−1,2,5,8}, B={0,1,3,6,7} and R be the relation ‘is one less than’ from A to B, then how many elements will R contain?
   (a) 2 (b) 3 (c) 5 (d) 9
4. A mapping f:R→R which is defined as f(x)=cos x; x∈R is:
   (a) One-one only (b) Onto only (c) One-one onto (d) Neither one-one nor onto
5. If α is a complex number such that α²+α+1=0, then what is α³ equal to?
   (a) α (b) α² (c) 0 (d) 1
6. If x²,y²,z² are in AP, then y+z,z+x,x+y are
   (a) in AP (b) in HP (c) in GP (d) neither in AP nor in HP nor in GP
7. Natural numbers are divided into groups as (1),(2,3),(4,5,6),(7,8,9,10) and so on. What is the sum of the numbers in the 11th group?
   (a) 605 (b) 615 (c) 671 (d) 693
8. If α,β are the roots of ax²+bx+b=0, then what is √α/√β + √β/√α + √b/√a equal to?
   (a) 0 (b) 1 (c) 2 (d) 3

NDA Previous Year Question Paper

1. If the roots of ax²+bx+c=0 are sin α and cos α for some α, then which one of the following is correct?
   (a) a²+b²=2ac (b) b²−c²=2ab (c) b²−a²=2ac (d) b²+c²=2ab
2. What is the coefficient of x⁴ in the expansion of (1+2x+3x²+4x³+……)¹²?
   (a) 1/4 (b) 1/16 (c) 1 (d) 1/128
3. If x=2+2^{1/3}+2^{2/3}, then what is the value of x³−6x²+6x?
   (a) 1 (b) 2 (c) 3 (d) −2
4. What is the value of (log₂ 9)(log₁₆ 64)/log₄ √2?
   (a) 1 (b) 2 (c) 4 (d) 8
5. If X and Y are the matrices of order 2×2 each and 2X−3Y=[−7 0; 7 −13] and 3X+2Y=[9 13; 4 13], then what is Y equal to?
   (a) [1 3; −2 1] (b) [1 3; 2 1] (c) [3 2; −1 5] (d) [3 2; 1 −5]
6. If a,b,c are non-zero real numbers and |1+a 1 1; 1 1+b 1; 1 1 1+c|=0, then what is the value of 1/a+1/b+1/c?
   (a) 2 (b) 1 (c) −1 (d) 0
7. If a matrix A is symmetric as well as anti-symmetric, then which one of the following is correct?
   (a) A is a diagonal matrix. (b) A is a null matrix. (c) A is a unit matrix. (d) A is a triangular matrix.
8. If A=[1 −2 −3; 2 1 −2; 3 2 1], then which one of the following is correct?
   (a) A is symmetric matrix. (b) A is anti-symmetric matrix. (c) A is singular matrix. (d) A is non-singular matrix.
9. If |2a 3r x; 4b 6s 2y; −2c −3t −z|=λ|a r x; b s y; c t z|, then what is the value of λ?
   (a) 12 (b) −12 (c) 7 (d) −7
10. What is the value of |1−i ω² −ω; ω²+i ω −i; 1−2i−ω² ω²−ω i−ω| where ω is the cube root of unity?
    (a) −1 (b) 1 (c) 2 (d) 0
11. What is the length of arc of a circle of radius 5 cm subtending a central angle measuring 15°?
    (a) 5π/12 cm (b) 7π/12 cm (c) π/12 cm (d) π/5 cm
12. What is the maximum value of sinθ cosθ?
    (a) 1 (b) 1/2 (c) 1/√2 (d) √3/2
13. If sin x + cosec x =2, then what is the value of sin⁴x + cosec⁴x?
    (a) 2 (b) 4 (c) 8 (d) 16
14. What is the value of tan15° + cot15°?
    (a) √3 (b) 2√3 (c) 4 (d) 2

NDA Previous Year Question Paper

1. If A+B+C=π/2, then what is the value of tan A tan B + tan B tan C + tan C tan A?
   (a) 0 (b) 1 (c) −1 (d) tan A tan B tan C
2. If angles of a triangle are in the ratio 1:2:3, then what is the ratio of its corresponding sides?
   (a) 3:2:1 (b) 1:√2:√3 (c) 1:√3:2 (d) 2:√3:4
3. If C(n,12)=C(n,8), then what is the value of C(22,n)?
   (a) 131 (b) 231 (c) 256 (d) 292
4. If A=[ω 0; 0 ω] where ω is cube root of unity, then what is A¹⁰⁰ equal to?
   (a) A (b) −A (c) Null matrix (d) Identity matrix
5. What is the modulus of (1+2i)/[1−(1−i)²] equal to?
   (a) 5 (b) 4 (c) 3 (d) 1
6. What is the value of (−√−1)^{4n+3} + (i⁴¹ + i^{−257})⁹, where n∈N?
   (a) 0 (b) 1 (c) i (d) −i
7. If x=(1101)₂ and y=(1100)₂, then what is the value of x²−y²?
   (a) (1000101)₂ (b) (100000101)₂ (c) (100011101)₂ (d) (10010101)₂
8. If (10×010)₂ − (11y1)₂ = (10z11)₂, then what are the possible values of the binary digits x,y,z respectively?
   (a) 0,0,1 (b) 0,1,0 (c) 1,1,0 (d) 0,0,0
9. The roots of the equation (x−p)(x−q)=r², where p,q,r are real are
   (a) always complex (b) always real (c) always purely imaginary (d) None of the above
10. If (sin x + cosec x)² + (cos x + sec x)² = k + tan²x + cot²x, then what is the value of k?
    (a) 8 (b) 7 (c) 4 (d) 3
11. A matrix X has (a+b) rows and (a+2) columns; and a matrix Y has (b+1) rows and (a+3) columns. If both XY and YX exist, then what are the values of a,b respectively?
    (a) 3,2 (b) 2,3 (c) 2,4 (d) 4,3
12. In a football championship 153 matches were played. Every team played one match with each other team. How many teams participated in the championship?
    (a) 21 (b) 18 (c) 17 (d) 15
13. The equation x−2(x−1)⁻¹=1−2(x−1)⁻¹ has
    (a) no roots (b) one root (c) two equal roots (d) infinite roots
14. The number 0.0011 in binary system represents
    (a) rational number 3/8 in decimal system (b) rational number 1/8 in decimal system (c) rational number 3/16 in decimal system (d) rational number 5/16 in decimal system
15. The function y=tan⁻¹x − x
    (a) is always decreasing (b) is always increasing (c) first increases and then decreases (d) first decreases and then increases
16. If n(A)=115, n(B)=326, n(A−B)=47, then what is n(A∪B) equal to?
    (a) 373 (b) 165 (c) 370 (d) 394
17. What does the equation x dy = y dx represent?
    (a) A family of circles (b) A family of parabolas (c) A family of hyperbolas (d) A family of straight lines

NDA Previous Year Question Paper

1. What is the value of k if the area bounded by the curve y=sin kx, y=0, x=π/k, x=π/(3k) is 3 square units?
   (a) 1/2 (b) 1 (c) 3/2 (d) 2
2. What is the solution of the differential equation x dy − y dx = xy² dx?
   (a) y+x²=c (b) y²+2x⁻¹=c (c) y+x⁻¹=c (d) x²+2xy⁻¹=c where c is a constant.
3. If f(x)=a+bx+cx², then what is ∫₀¹ f(x) dx equal to?
   (a) [f(0)+4f(1/2)+f(1)]/6 (b) [f(0)+4f(1/2)+f(1)]/3 (c) [f(0)+4f(1/2)+f(1)] (d) [f(0)+2f(1/2)+f(1)]/6
4. What is ∫ (a + b sin x)/cos²x dx equal to?
   (a) a sec x + b tan x + c (b) a tan x + b sec x + c (c) a cot x + b cosec x + c (d) a cosec x + b cot x + c where a,b,c are constants.
5. If eʸ + xy = e, then what is the value of d²y/dx² at x=0?
   (a) e⁻¹ (b) e⁻² (c) e (d) 1
6. What is ∫ (ln x)/(1+ln x)² dx equal to?
   (a) 1/(1+ln x)³ + c (b) 1/(1+ln x)² + c (c) x/(1+ln x) + c (d) x/(1+ln x)² + c where c is a constant.
7. If P(A) denotes the power set of A and A is the void set, then what is number of elements in P{P{P{P(A)}}}?
   (a) 0 (b) 1 (c) 4 (d) 16
8. What is lim x→∞ (x/(3+x))^{3x} equal to?
   (a) e (b) e³ (c) e⁻⁹ (d) e⁹
9. Consider the following function f:R→R such that f(x)=x if x≥0 and f(x)=−x² if x<0. Then which one of the following is correct?
   (a) f(x) is continuous at every x∈R. (b) f(x) is continuous at x=0 only. (c) f(x) is discontinuous at x=0 only. (d) f(x) is discontinuous at every x∈R.
10. If √(1−x²)+√(1−y²)=a, then what is dy/dx equal to?
    (a) √[(1−x²)(1−y²)] (b) √[(1−y²)/(1−x²)] (c) √[(1−x²)/(1−y²)] (d) None of the above
11. If x=ln t and y=t²−1, then what is d²y/dx² at t=1 equal to?
    (a) 2 (b) 3 (c) −4 (d) 4
12. Which one of the following functions f:R→R is injective?
    (a) f(x)=|x| for all x∈R (b) f(x)=x² for all x∈R (c) f(x)=11 for all x∈R (d) f(x)=−x for all x∈R
13. What is the derivative of log₅ 5 with respect to log₅ x?
    (a) −(log₅ x)⁻² (b) (log₅ x)⁻² (c) −(log₅ 5)⁻² (d) (log₅ 5)⁻²
14. The velocity v of a particle at any instant t moving in a straight line is given by v=s+1 where s meter is the distance travelled in t second. What is the time taken by the particle to cover a distance of 9 meter?
    (a) 1 s (b) (ln 10) s (c) 2(ln 10) s (d) 10 s
15. The curve y²=−4ax (a>0) lies in:
    (a) First and fourth quadrants (b) First and second quadrants (c) Second and third quadrants (d) Third and fourth quadrants

NDA Previous Year Question Paper

1. The circle x²+y²+4x−4y+4=0 touches:
   (a) Only the x-axis (b) Only the y-axis (c) Both the axes (d) Neither of the axes
2. What is the value of n so that the angle between the lines having direction ratios (1,1,1) and (1,−1,n) is 60°?
   (a) √3 (b) √6 (c) 3 (d) None of the above
3. What is the product of the perpendiculars from the two points (±√(b²−a²),0) to the line ax cos φ + by sin φ = ab?
   (a) a² (b) b² (c) ab (d) a/b
4. The middle point of the segment of the straight line joining the points (p,q) and (q,−p) is (r/2,s/2). What is the length of the segment?
   (a) [(s²+r²)^{1/2}]/2 (b) [(s²+r²)^{1/2}]/4 (c) (s²+r²)^{1/2} (d) s+r
5. The direction cosines of a line are proportional to (2,1,2) and the line intersects a plane perpendicularly at the point (1,−2,4). What is the distance of the plane from the point (3,2,3)?
   (a) √2 (b) 2 (c) 2√2 (d) 4
6. The foot of the perpendicular drawn from the origin to a plane is the point (1,−3,1). What is the intercept cut on the x-axis by the plane?
   (a) 1 (b) 3 (c) √11 (d) 11
7. A line makes the same angle α with each of the x and y-axes. If the angle θ, which it makes with the z-axis, is such that sin²θ=2 sin²α, then what is the value of α?
   (a) π/4 (b) π/6 (c) π/3 (d) π/2
8. What is the locus of a point which is equidistant from the point (m+n,n−m) and the point (m−n,n+m)?
   (a) mx=ny (b) nx=−my (c) nx=my (d) mx=−ny
9. What is the equation of the sphere which has its centre at (6,−1,2) and touches the plane 2x−y+2z−2=0?
   (a) x²+y²+z²+12x−2y+4z+16=0 (b) x²+y²+z²+12x−2y+4z−16=0 (c) x²+y²+z²−12x+2y−4z+16=0 (d) x²+y²+z²−12x+2y−4z+25=0
10. What are the direction ratios of the line determined by the planes x−y+2z=1 and x+y−z=3?
    (a) (−1,3,2) (b) (−1,−3,2) (c) (2,1,3) (d) (2,3,2)
11. The ellipse x²/169 + y²/25 =1 has the same eccentricity as the ellipse x²/a² + y²/b² =1. What is the ratio of a to b?
    (a) 5/13 (b) 13/5 (c) 7/8 (d) 8/7
12. If â and ˆb are the unit vectors along ā and ˉb respectively, then what is the projection of ˉb on ā?
    (a) ā·ˉb (b) â·ˆb (c) â·ˉb (d) |ā×ˉb|
13. What are the unit vectors parallel to xy-plane and perpendicular to the vector 4î−3ĵ+ˆk?
    (a) ±(3î+4ĵ)/5 (b) ±(4î+3ĵ)/5 (c) ±(3î−4ĵ)/5 (d) ±(4î−3ĵ)/5
14. What is the vector in the xy-plane through origin and perpendicular to the vector ˉr=aî+bĵ and of the same length?
    (a) −aî−bĵ (b) aî−bĵ (c) −aî+bĵ (d) bî−aĵ

NDA Previous Year Question Paper

1. Given ā=2î−3ĵ+4ˆk and ˉb is a unit vector co-directional with ā. If m is a scalar such that ˉb=mā, then what is the value of m?
   (a) 1/5 (b) 1/√5 (c) 1/29 (d) 1/√29
2. The magnitude of the vectors ā and ˉb are equal and the angle between them is 60°. If the vectors λā+ˉb and ā−λˉb are perpendicular to each other, then what is the value of λ?
   (a) 1 (b) 2 (c) 3 (d) 4
3. If |ā|=3, |ˉb|=4 and |ā−ˉb|=7, then what is the value of |ā+ˉb|?
   (a) 3 (b) 2 (c) 1 (d) 0
4. Consider the diagonals of a quadrilateral formed by the vectors 3î+6ĵ−2ˆk and 4î−ĵ+3ˆk. The quadrilateral must be a:
   (a) Square (b) Rhombus (c) Rectangle (d) None of the above
5. If p=sin(989°) cos(991°), then which one of the following is correct?
   (a) p is finite and positive (b) p is finite and negative (c) p=0 (d) p is undefined
6. If A=41π/12, then what is the value of (1−3 tan²A)/(3 tan A − tan³A)?
   (a) −1 (b) 1 (c) 1/3 (d) 3
7. If ω is the cube root of unity, then what is the conjugate of 2ω²+3i?
   (a) 2ω−3i (b) 3ω+2i (c) 2ω+3i (d) 3ω−2i
8. Consider the following statements:
9. If θ=1200°, then (sec θ + tan θ)⁻¹ is positive.
10. If θ=1200°, then (cosec θ − cot θ) is negative.
    Which of the statements given above is/are correct?
    (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2
11. If cot θ=2 cos θ, where (π/2)<θ<π, then what is the value of θ?
    (a) 5π/6 (b) 2π/3 (c) 3π/4 (d) 11π/12
12. If cot θ=5/12 and θ lies in the third quadrant, then what is (2 sin θ + 3 cos θ) equal to?
    (a) −4 (b) −p² for some odd prime p (c) (−q/p) where p is an odd prime and q a positive integer with (q/p) not an integer. (d) −p for some odd prime p.
13. What is the value of cos(π/9)+cos(π/3)+cos(5π/9)+cos(7π/9)?
    (a) 1 (b) −1 (c) −1/2 (d) 1/2
14. If in a triangle ABC, cos B=(sin A)/(2 sin C), then the triangle is:
    (a) Isosceles triangle (b) Equilateral triangle (c) Right angled triangle (d) Scalene triangle
15. During a certain plan period a state out of a total budget of Rs. 1400 crores had spent 28% of the total amount on Agriculture, 35% on Industry, 12% on Energy and 8% on Social Welfare, 105 crores on Education and the balance amount on Transport. What is the amount spent on Transport in crores of rupees?
    (a) 123 (b) 145 (c) 165 (d) 133
16. A class consists of 3 sections A, B and C with 35, 35 and 30 students respectively. The arithmetic means of the marks secured by students of sections A and B, who appeared for a test of 100 marks are 74 and 70 respectively. The arithmetic mean of the marks secured by students of section C, who appeared for a test in the same subject which carried 75 marks is 51. What is the average percentage of marks secured by all the 100 students of the three sections?
    (a) 70.0 (b) 70.8 (c) 65.0 (d) 67.5

NDA Previous Year Question Paper

1. In a town 35.4% of the people are not literates, 27% have education up to primary school, 18.6% have education up to middle school. The people with education up to high school are twice the number of people with education up to Pre-University. Of the remaining, 660 are graduates. If the population of the town is 15,000, then what is the number of people with education up to high school?
   (a) 3120 (b) 1560 (c) 1460 (d) None of the above
2. Three letters are randomly selected from the 26 capital letters of the English Alphabet. What is the probability that the letter ‘A’ will not be included in the choice?
   (a) 1/2 (b) 23/26 (c) 12/13 (d) 25/36
3. A coin is tossed 10 times. The number of heads minus the number of tails in 10 tosses is considered as the outcome of the experiment. What is the number of points in the sample space?
   (a) 10 (b) 11 (c) 21 (d) 99
4. In a study on the relationship between investment (X) and profit (Y), the following two regression equations were obtained based on the data on X and Y:
   3X + Y −12=0
   X + 2Y −14=0.
   What is the mean X̄?
   (a) 6 (b) 5 (c) 4 (d) 2
5. Following table gives the mean and variance of monthly demand for four products A, B, C and D in a supermarket:
   Product A B C D
   Mean demand 60 90 80 120
   Variance 12 25 36 16
   For which product the demand is consistent?
   (a) Product A (b) Product B (c) Product C (d) Product D
6. What is the least value of the standard deviation of 5 integers, no two of which are equal?
   (a) √5 (b) 2 (c) √2 (d) No such least value can be computed
7. Two numbers are successively drawn from the set {1,2,3,4,5,6,7} without replacement and the outcomes recorded in that order. What is the number of elementary events in the random experiment?
   (a) 49 (b) 42 (c) 21 (d) 14
8. The probabilities of two events A and B are given as P(A)=0.8 and P(B)=0.7. What is the minimum value of P(A∩B)?
   (a) 0 (b) 0.1 (c) 0.5 (d) 1
9. Two numbers X and Y are simultaneously drawn from the set {1,2,3,4,5,6,7,8,9,10}. What is the conditional probability of exactly one of the two numbers X and Y being even, given (X+Y)=15?
   (a) 1 (b) 3/4 (c) 1/2 (d) 1/4
10. If x, 2x+2, 3x+3 are the first three terms of a GP, then what is its fourth term?
    (a) −27/2 (b) 27/2 (c) −33/2 (d) 33/2
11. Correlation between two variables is said to be perfect if
    (a) one variable increases, the other also increases (b) one variable increases, the other decreases (c) one variable increases, the other also increases proportionally (d) one variable increases, the other decreases proportionally
12. Consider the following statements:
13. The data, which are collected from the units or individual respondents directly for the purpose of certain study or information are known as primary data.
14. The data obtained in a census study are primary data.
    Which of the above statements is/are correct?
    (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2
15. Given that P(A)=1/3, P(B)=3/4 and P(A∪B)=11/12, then what is P(B|A)?
    (a) 1/6 (b) 4/9 (c) 1/2 (d) 1/3

NDA Previous Year Question Paper

1. If a,b and c are real numbers then the roots of the equation (x−a)(x−b)+(x−b)(x−c)+(x−c)(x−a)=0 are always
   (a) real (b) imaginary (c) positive (d) negative
2. If (logₖ x)(logₖ 2x)(logₖ y)=logₖ x², then what is the value of y?
   (a) 9/2 (b) 9 (c) 18 (d) 27
3. If logₖ x log₅ k=3 then what is x equal to?
   (a) k³ (b) 5k³ (c) 243 (d) 125
4. Which term of the sequence 20, 19 1/4, 18 1/2, 17 3/4, …… is the first negative term?
   (a) 27th (b) 28th (c) 29th (d) No such term exists
5. If sin⁻¹x + cot⁻¹(1/2)=π/2, then what is the value of x?
   (a) 0 (b) 1/√5 (c) 2/√5 (d) √3/2
6. For the two equations x²+mx+1=0 and x²+x+m=0, what is/are the value/values of m for which these equations have at least one common root?
   (a) −2 only (b) 1 only (c) −2 and 1 (d) −2 and −1
7. Looking from the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its bottom is 30°. What is the height of the tower?
   (a) 50 m (b) 60 m (c) 70 m (d) 80 m
8. What is the value of √3 cosec 20° − sec 20°?
   (a) 4 (b) 3 (c) 2 (d) 1
9. Match List-I with List-II and select the correct answer using the code given below the lists:
   List-I List-II
   A. tan 15° 1. −2−√3
   B. tan 75° 2. 2+√3
   C. tan 105° 3. −2+√3 4. 2−√3
   Code: A B C
   (a) 4 1 2 (b) 4 2 1 (c) 3 2 1 (d) 2 1 4
10. In a triangle ABC, a+b=3(1+√3) cm and a−b=3(1−√3) cm. If angle A is 30°, then what is the angle B?
    (a) 120° (b) 90° (c) 75° (d) 60°
11. If Nₐ={ax | x∈N}, then what is N₁₂ ∩ N₈ equal to?
    (a) N₁₂ (b) N₂₀ (c) N₂₄ (d) N₄₈
12. If X={(4ⁿ−3n−1)|n∈N} and Y={9(n−1)|n∈N}, then what is X∪Y equal to?
    (a) X (b) Y (c) N (d) A null set
13. Sets A and B have n elements in common. How many elements will (A×B) and (B×A) have in common?
    (a) 0 (b) 1 (c) n (d) n²
14. If z is a complex number such that z+z⁻¹=1, then what is the value of z⁹⁹ + z⁻⁹⁹?
    (a) 1 (b) −1 (c) 2 (d) −2
15. In an AP, the mth term is 1/n and nth term is 1/m. What is its (mn)th term?
    (a) 1/(mn) (b) m/n (c) n/m (d) 1
16. How many times does the digit 3 appear while writing the integers from 1 to 1000?
    (a) 269 (b) 271 (c) 300 (d) None of the above

NDA Previous Year Question Paper

1. Consider the following statements:
2. The coefficient of the middle term in the expansion of (1+x)⁸ is equal to the middle term of (x+1/x)⁸.
3. The coefficient of the middle term in the expansion of (1+x)⁸ is less than the coefficient of the fifth term in the expansion of (1+x)⁷.
   Which of the above statements is/are correct?
   (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2
4. When a and b are eliminated from the equation xy=aeˣ + be⁻ˣ, the resulting differential equation is of:
   (a) first order and first degree (b) first order and second degree (c) second order and first degree (d) second order and second degree
5. If y=(1+x^{1/4})(1+x^{1/2})(1−x^{1/4}), then what is dy/dx equal to?
   (a) 1 (b) −1 (c) 0 (d) −2x
6. The velocity of telegraphic communication is given by v=x² ln(1/x) where x is the displacement. For maximum velocity, x equals to?
   (a) e^{1/2} (b) e^{−1/2} (c) (2e)⁻¹ (d) 2e^{−1/2}
7. What is the area bounded by the curve y=4x−x²−3 and the x-axis?
   (a) 2/3 square units (b) 4/3 square units (c) 5/3 square units (d) 4/5 square units
8. A function f is such that f′(x)=6−4 sin 2x and f(0)=3. What is f(x) equal to?
   (a) 6x+2 cos 2x (b) 6x−2 cos 2x (c) 6x−2 cos 2x+1 (d) 6x+2 cos 2x+1
9. If f(x)=eˣ and g(x)=ln x, then what is the value of (g∘f)′(x)?
   (a) 0 (b) 1 (c) e (d) None of the above
10. Let g(x)=x³−4x+6. If f′(x)=g′(x) and f(1)=2, then what is f(x) equal to?
    (a) x³−4x+3 (b) x³−4x+6 (c) x³−4x+1 (d) x³−4x+5
11. Let f:R→R be defined by f(x)=|x|/x, x≠0, f(0)=2. What is range of f?
    (a) {1,2} (b) {1,−1} (c) {−1,1,2} (d) {1}

NDA Previous Year Question Paper 2009 Exam II Shift 1 & 2

NDA Previous Year Question Paper 2009 exam 1 shift 1

NDA Previous Year Question paper 2009 SHift II

NDA Previous year Question paper 2009 to 2025 Free PDF download

JEE MAIN Previous Year Question paper