NTS Educators ESE (Science) Jobs Test With Answers

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NTS Educators ESE (Science) Jobs Test

Sr. # Questions Answers Choice
1 If ab > 0 and a < 0, which of the following is negative? b -b -a (a - b)<sup>2</sup>
2 If x < y, 2x = A and 2y = B then A =B A &lt; B A&lt; X B &lt; y
3 If a line passes through origin then the equation of the line is y = m/x y = mx x = my None
4 The angle a (0° < a< 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the Rotation Inclination Radian None
5 The center of a circle of radius 10 is on the origin which of the following points lies with in the circle (10,0) (8,8) (8,4) (0,10)
6 If k1 : k2 = 1:1 then the point P dividing the line is Mid point Extreme left point Extreme Right point Plies out side k<sub>1</sub> and k<sub>2</sub>
7 If the diagonal of a square has coordinates (1,2) and(5,6) the length of a side is 3 4 1 5
8 Which of the following is the equation of a line with slope 0 and passing through the point (4,3) X =4 X = -4 Y = 3 Y = -6
9 The curves y =x2, y= x interest at (0,0) ,(1,1) (2,4) (0,),(2,4) (0,3),(-1,1)
10 The equation of the line with gradient 1 passing through the point (h,k) is Y = x+ k-h Y = k/hx +1 Y = x + h -l Ky = hx =1
11 The line joining (1,3) to (a,b) has unit gradient then a-b =-2 a+b = 0 A-b =5 2a + 3b =1
12 The gradient of the line joining (1,4) and (-2,5) is 3/8 -2 2/3 -1/3 2
13 The mid point of the line joining (=1,-3) to(3,-5) is (1, 1) (1,-1) (2, -8) (1, -4)
14 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
15 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
16 ∫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)|
17 ∫sec (ax + b) tan(ax + b) dx=_______ sec(ax + b)/a sec<sup>2</sup> (ax + b)/2 sec(ax + b)/x 1/2
18 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
19 d/dx ∫x1 dx =________. 1/4 x<sup>4</sup> X<sup>3</sup> 3x<sup>3</sup> x<sup>4</sup>/4
20 ∫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
21 If y = sin(ax + b) then fourth derivative of y with respect to x= a<sup>4</sup> cos (ax + b) a<sup>4</sup> sin (ax + b) -a<sup>4</sup> sin(ax +b) a4 tan (ax + b)
22 Any point where f is neither increasing nor decreasing and f(x) =0 at that point is called a Minimum Maximum Stationary point Constant
23 Derivative of strictly increasing function is always Zero Positive Negative Both A and B
24 Second derivative of y = x9 + 10x2 + 2x -1 at x = 0 is 10 20 12 1
25 d/dx [cos x2] =________ -2x cos x<sup>2</sup> -2x<sup>2</sup> sin x<sup>2</sup> x<sup>2</sup>&nbsp;sin x -2x<sup>2</sup>&nbsp;sin x<sup>2</sup>
26 If y = (ax)m + bm, then dy/dx equals m (ax)<sup>m</sup>&nbsp;x<sup>m-1</sup> ma<sup>m</sup>&nbsp;x<sup>m-1</sup> m a<sup>m</sup>&nbsp;x<sup>m-1</sup> m a<sup>m</sup>&nbsp;x<sup>m-2</sup>
27 d/dx (3y4) = 12y<sup>3</sup> dy/dx 8y<sup>3</sup> 8y<sup>3</sup> dy/dx 12y<sup>3</sup>
28 d/dx (√x) = 2√x 1/√x 1/2√x None of these
29 d/dx ax is xa<sup>x-1</sup> a<sup>x</sup> x in a a<sup>x</sup> in a
30 If x2 +y2 = 4, Then dy/dx = 2x +2y 4 -x<sup>2</sup> -x/y y/x
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