GAT Subject Mathematics Mathematics With Answers

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GAT Subject Mathematics Mathematics

Sr. # Questions Answers Choice
1 Which is an explicit function y = x<sup>2</sup> +2x -1 x<sup>2</sup> +xy +y<sup>2</sup> =2 xy<sup>2</sup> -y +9/xy =1 All are
2 Which is not included in the domain of Cos-1 x 0 1 -1 2
3 P(x) = 2x4 -3x3 +2x-1 is polynomial of degree 1 2 3 4
4 If f (x) = x/x2- 4 then which is not included in the domain of f(x) 0 -2 1 4
5 If f(x) = x3- 2x2 +4x-1, then f(-2) =? 0 -25 5 45
6 Which of the following is the solution of Cot2x = 1/√3 π/5 π/3 π/7 π/9
7 Which of the following is solution of Tan2 x = 1/3 7π/6 5π/6 π/6 All
8 If x lies in {0, 2π} and Cosec x = 2 then x = π/ 6 and 5π/6 π +2nπ nπ 2π/3 and&nbsp;π/3
9 If 1 + Cos x = 0 then x = π +2n&nbsp;π π + nπ π - nπ π/2
10 If θ= 60° then sin&nbsp;θ = 1/2 tan&nbsp;θ = cot 30° θ = π/4 Sec&nbsp;θ =4
11 In which quadrant is the solution of the equation sin x - 1 = 0 II quadrants II and III quadrants III and Iv quadrants I quadrant
12 Cos-1 x = ∏ = sin<sup>-1</sup> x ∏ + sin<sup>-1</sup> x ∏/2 - sin<sup>-1</sup> x ∏/2 +sin<sup>-1</sup> x
13 Sec-1 x= Cos<sup>-1</sup> 1/x Cosec<sup>-1</sup> 1/x Cos-1 (-x) Tan<sup>-1</sup> x
14 Sin-1 (-x) = Cos<sup>-1</sup> 1/x -Sin<sup>-1</sup>&nbsp;X 1/sin-1x Sin<sup>-1</sup> 1/x
15 Tan-1 1/x =______ Sin x Sec<sup>-1</sup> X Cot<sup>-1</sup> X Sin Ix/cos- Ix
16 Sin-1 [-1/2] = ______. ∏/3 -∏/6 -∏/3 ∏/6
17 If Cosθ =0, Then θ= nπ/2 (2n + 1)π/2 (2n - 1)π/2 (n ±1)π/2
18 In the figure angle A is = 15 60 90 20
19 If you looking a high point from the ground then the angle formed is Angle of elevation Angle of depression Right angle Horizon
20 Area of ΔABC= ab sin&nbsp;α 1/2 ab sin&nbsp;α 1/2 ac Sin&nbsp;γ 1/2 ac Sin&nbsp;β
21 In the figure PS is perpendicular to QR, if PQ = PR 26 and P8 = 24,then QR= 10 20 40 26
22 120° degrees are equal to how many radians? π/3 radians 2π/3 radians π/4 radians π/2 radians
23 The principal value of sin-1 [√3/2] is π/3 -π/3 2π/3 5π/3
24 If Sin-1 x + cos-1 y = π, then x and y are Associative angles Complementary angles Reflex angles Supplementary angles
25 Cos-1 (-x) =_______. π +cos<sup>-1</sup>&nbsp;x π -sin<sup>-1</sup>&nbsp;x π +sin<sup>-1</sup>&nbsp;x π -cos<sup>-1</sup>&nbsp;x
26 Which of the following is not defined? Arcsin 1/9 ArcCos (-4/3) Arctan 11/12 Arccot (-4)
27 AreCot √3 =? π/2 π 2π π/6
28 Sin-1 (√2/2)=? π/2 π/3 3π/4 2π
29 Sin-1 √3/2 =? 2π/3 π/2 π/3 v/5
30 Tan (π + Tan-1 x) =? Tan x X -x Cot<sup>-1</sup> x
31 Sin-1 x =? π/2- Sin<sup>-1</sup> x π/2 -Cos<sup>-1</sup> x -Sin<sup>-1</sup> x -Cos<sup>-1</sup> x
32 Sin-1 (-x) =? Sin<sup>-1</sup> x -Sin<sup>-1</sup> x Cos<sup>-1</sup> x -Cos<sup>-1</sup> x
33 Period of Sin 2x = π 4π 2nπ 2π
34 What is the period of Cot x? 2π π π/2 4π
35 What is the domain of y = Cot-1 x? Set of irrational numbers only Set of all real numbers Set of integers only Set of complex numbers only
36 What is the domain of y= Sin-1 x? -1&nbsp;≤ x&nbsp;≤1 1&nbsp;≤ x&nbsp;≤ 1 0&nbsp;≤ x&nbsp;≤&nbsp;π -π/2&nbsp;≤ x&nbsp;≤ π/2
37 If A = (3,8) and B = (5,6) then the distance between A and B is
 2√2 2 1 6
38 Sin x + Cos x=1 x= π π/2 π/3 π/4
39 If Sin θ =Cosθ then θ= 30° 45° 60° 90°
40 Cos 315° = 0.707 0.5 1 0
41 Period is Tan x/5 is 5π 4π 2π π/5
42 Sin(a + b) + Sin(a- b) = Sin a Cos b Sin a Sin b Sin a + Cos b Sin a - 2Cos b
43 The value of Cos (1/2 Cos-1 1/2) is equal to √3/2 -3/4 1/16 1/4
44 If 2 Sin x Cos 2 x = Sin x then? X = nπ+&nbsp;π/6 X = nπ +π/3 X = nπ +1 X = nπ +&nbsp;π/2
45 If Cosα = 3/5, Cosβ = 5/13, then Cos(α +β) =33/65 Sin(α +β) =56/65 sin<sup>2</sup>(α +β/2) =1/65 Cos(α +β) =63/65
46 In the triangle Δ ABC, where C is the right angle Tan A + Tan B= A +B C<sup>2</sup>&nbsp;/AB A<sup>2</sup>/BC B<sup>2</sup>/AC
47 Sin (2π -θ) =______. Cosθ -Sinθ -Sinθ -cosθ
48 Cot 360° =______. Undefined 0.707 -0.5 0
49 Sin 720° = ________ 1 0 2 1/2
50 If sinθ = 1 then θ = 2nπ +π/2 2nπ 2π +n Nπ +π/2
51 If a rectangle has an area 81x2 and length of 27x. then what is its width? 3x 9x 3x<sup>2</sup> 9x<sup>2</sup>
52 Cse π/3 2 1 0 2/√3
53 In 30,60,90 triangle if the smallest side is 6 than the side opposite to the angle of 60o is 12 3 6√3 6
54 Domain of Cosecθ is is R but&nbsp;θ= nπ is R but&nbsp;θ ≠ nπ is R but&nbsp;θ ≠ 2nπ is R but&nbsp;θ ≠ nπ/2
55 If 0 is not an integral multiple of π/2 then Cot4 θ+ Cot2 θ=? Cosec<sup>4</sup>&nbsp;θ -Cosec<sup>2&nbsp;</sup>θ Tan&nbsp;θ - Tan<sup>2</sup>&nbsp;θ Cosec<sup>2</sup>&nbsp;θ + Cosec&nbsp;θ Sinθ Cosθ
56 If in isosceles right angled triangle one side is a then hypotenuse is a√2 a/2 a Cannot be determined by given
57 An angle 0 is such that tan θ = 1 and cos θ is negative then Sin&nbsp;θ is positive Cos&nbsp;θ = √2/4 cosθ = -1 sec&nbsp;θ is negative
58 If sin θ= 3/5 Cos θ= 1/2 3/5 4/5 1
59 The associative angle of 280o is 100<sup>o</sup> 10<sup>o</sup> 80<sup>o</sup> -80<sup>o</sup>
60 An angle of one radian is equivalent to 90<sup>o</sup> 60<sup>o</sup> 67<sup>o</sup> 57<sup>o</sup>, 18<sup>o</sup>
61 1+2+3+......+n=? n(n +1)/2 n +1/2 n(n +1)(2n +1)/6 n<sup>3</sup>
62 There are 30 Red balls and 25 Green balls in a bag of a ball is drawn from the bag randomly what is the probability that a Blue ball comes out? 1 0.5 0 None
63 There are 30 Red, 20 Green and some Blue bells in a bag if the probability of finding a Red ball is 1/3,how many are red balls in the bag 120 20 40 90
64 Given eight points in a plane no three of which are collinear how many lines do the points determine? 16 64 28 36
65 How many different arrangements of the letters in the word QABABA are Possible? 720 40 60 30
66 Corola available in 5 models 8 colours and 3 sizes how many Corola must a local dealer have no hand in order to have one of each kind avialable? 24 120 16 39
67 How many elements are in the sample space of two rolling dies 6 12 18 36
68 A standard deck of 52 cards shuffled what is the probability of choosing the queen of the diamonds 1/5 1/13 5/52 1/52
69 If P(E) is the probability that can event will occur then P(E)= 1 0.5 2 0
70 The number of ways in which 5 distinct toys can be distributed among 3 children is 3<sup>5</sup> 5<sup>3</sup> C<sup>5</sup><sub>3</sub> P<sup>5</sup><sub>3</sub>
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