NAT I General Science Mathematics With Answers

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NAT I General Science Mathematics

Sr. # Questions Answers Choice
1 The line joining (1,3) to (a,b) has unit gradient then a-b =-2 a+b = 0 A-b =5 2a + 3b =1
2 The gradient of the line joining (1,4) and (-2,5) is 3/8 -2 2/3 -1/3 2
3 The mid point of the line joining (=1,-3) to(3,-5) is (1, 1) (1,-1) (2, -8) (1, -4)
4 The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is 2 13 7 8
5 The general solution of the differential equation dy/dx = log x is Y = -x log x- x +c Y = x log x + x<sup>2</sup> Y = x log x -x +c Y= 2x log x + 2x +c
6 ∫cot (ax + b) dx = 1/a log |sin (ax + b)| +c 1/a log |cos ax + b) 1/b |sin (ax + b)| 1/a log |sin (bx + a)|
7 ∫sec (ax + b) tan(ax + b) dx=_______ sec(ax + b)/a sec<sup>2</sup> (ax + b)/2 sec(ax + b)/x 1/2
8 If f1 (x) and f2  (x) are any two anti derivatives of a function F (x) then the value of f1 (x) = f2 (x) A variable A constant Undefined Infinity
9 d/dx ∫x1 dx =________. 1/4 x<sup>4</sup> X<sup>3</sup> 3x<sup>3</sup> x<sup>4</sup>/4
10 ∫1/ax +b dx = 1/a log |ax + b| +c Log |ax + b| +c 1/b log |ax +b| +c 1/x log |ax + b| +c
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