[{"id":19913,"question":"If the vector 2i+4j-2k and 2i +6j+xk are perpendicular then x-7","choices":[{"text":"4","value":"A"},{"text":"8","value":"B"},{"text":"14","value":"C"},{"text":"7","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19912,"question":"If the angle between two vectors with magnitude 8 and 2 is 60° then their scalar product is","choices":[{"text":"12","value":"A"},{"text":"8","value":"B"},{"text":"16","value":"C"},{"text":"1","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19911,"question":"The direction cosines of y-axis are","choices":[{"text":"1,0,0","value":"A"},{"text":"0,1,0","value":"B"},{"text":"0,0,1","value":"C"},{"text":"1,1,1","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19910,"question":"If i,m,n are the direction cosines of a vector O̅P̅ then","choices":[{"text":"I<sup>2</sup>&nbsp;+ m<sup>2</sup>&nbsp;+ n<sup>2</sup>&nbsp;=0","value":"A"},{"text":"I<sup>2</sup>&nbsp;- m<sup>2</sup>&nbsp;+ n<sup>2</sup>&nbsp;=1","value":"B"},{"text":"I<sup>2</sup>&nbsp;+ m<sup>2</sup>&nbsp;+ n<sup>2</sup>&nbsp;=1","value":"C"},{"text":"I<sup>2</sup>&nbsp;+ m<sup>2</sup>&nbsp;- n<sup>2</sup>&nbsp;=0","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19909,"question":"The magnitude of a vector can never be","choices":[{"text":"Zero","value":"A"},{"text":"Negative","value":"B"},{"text":"Positive","value":"C"},{"text":"Absolute","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19908,"question":"Unit vector in the positive direction of x-axis is","choices":[{"text":"î","value":"A"},{"text":"ĵ","value":"B"},{"text":"k̂","value":"C"},{"text":"All","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19907,"question":"The two different parts of the hyperbola are called is","choices":[{"text":"Vertices","value":"A"},{"text":"Directrices","value":"B"},{"text":"Nappes","value":"C"},{"text":"Branches","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19906,"question":"The line through the center and perpendicular to the transverse axis is called the","choices":[{"text":"Major axis","value":"A"},{"text":"Minor axis","value":"B"},{"text":"Focal axis","value":"C"},{"text":"Conjugate axis","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19905,"question":"The vertices of the ellipse x<sup>2</sup> + 4y<sup>2</sup> = 16 are","choices":[{"text":"(±,4,0)","value":"A"},{"text":"(0,±,4)","value":"B"},{"text":"(± 2,0)","value":"C"},{"text":"(0,± 2)","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19904,"question":"The end points of the major axis of the ellipse are called its","choices":[{"text":"foci","value":"A"},{"text":"Vertices","value":"B"},{"text":"Co-vertices","value":"C"},{"text":"eccentricity","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19903,"question":"The axis of the parabola y<sup>2</sup> = 4ax is","choices":[{"text":"x =0","value":"A"},{"text":"Y =0","value":"B"},{"text":"X = y","value":"C"},{"text":"X = -y","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19902,"question":"The conic is a parabola if","choices":[{"text":"e &lt;1","value":"A"},{"text":"e &gt; 1","value":"B"},{"text":"e = 1","value":"C"},{"text":"e = 0","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19901,"question":"The perpendicular bisector of any chord of a circle","choices":[{"text":"Passes through the center of the circle","value":"A"},{"text":"Does not pass through the center of the circle","value":"B"},{"text":"May or may not pass through the center of the circle","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19900,"question":"The equation of the normal to the circle x<sup>2</sup>&nbsp;+ 2<sup>2</sup>&nbsp;= 25 at (4,3) is","choices":[{"text":"3x -4y =0","value":"A"},{"text":"3x -4y= 5","value":"B"},{"text":"4x + 3y=5","value":"C"},{"text":"4x - 3y =25","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19899,"question":"The circle (x -2)<sup>2</sup> + (y + 3)<sup>2</sup> =4 is not concentric with the circle","choices":[{"text":"(x -2)<sup>2</sup>&nbsp;+ (y + 3)<sup>2</sup>&nbsp;=9","value":"A"},{"text":"(x +2)<sup>2</sup>&nbsp;+ (y - 3)<sup>2</sup>&nbsp;=4","value":"B"},{"text":"(x -2)<sup>2</sup>&nbsp;+ (y + 3)<sup>2</sup>&nbsp;=8","value":"C"},{"text":"(x -2)<sup>2</sup>&nbsp;+ (y + 3)<sup>2</sup>&nbsp;=5","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19898,"question":"The radius of the circle (x- 1)<sup>2</sup> + (y + 3)<sup>2</sup> =64 is","choices":[{"text":"8","value":"A"},{"text":"2√2","value":"B"},{"text":"4","value":"C"},{"text":"64","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19897,"question":"The equation of the circle with center origin and radius 2√2 is","choices":[{"text":"x<sup>2</sup> + y<sup>2</sup> = 2√2","value":"A"},{"text":"x<sup>2</sup>&nbsp;+ y<sup>2</sup>&nbsp;= 8","value":"B"},{"text":"x<sup>2</sup>&nbsp;- y<sup>2</sup>&nbsp;= 2√2","value":"C"},{"text":"x<sup>2</sup>&nbsp;- y<sup>2</sup>&nbsp;= 8","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19896,"question":"If a cone is cut by a plane perpendicular to the axis of the cone then the section is a","choices":[{"text":"Parabola","value":"A"},{"text":"Circle","value":"B"},{"text":"Hyperbola","value":"C"},{"text":"Ellipse","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19895,"question":"8 &gt; t then","choices":[{"text":"(s -t) <sup>2</sup>&gt;(t -8)<sup>2</sup>","value":"A"},{"text":"(s -t)&nbsp;<sup>2</sup>&lt;(t -8)<sup>2</sup>","value":"B"},{"text":"(s -t)&nbsp;<sup>2</sup>=(t -8)<sup>2</sup>","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19894,"question":"Ab &gt; 0 and a &gt; 0 then","choices":[{"text":"a &gt; b","value":"A"},{"text":"a &lt; b","value":"B"},{"text":"a = b","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19893,"question":"r + 3 &gt; 5 then which is true","choices":[{"text":"r + 2 &gt; 4","value":"A"},{"text":"r + 2 &lt; 4","value":"B"},{"text":"r + 2 + 4","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19892,"question":"x is a member of the set {-1,0,3,5} y is a member of the set {-2,1,2,4} which is possible?","choices":[{"text":"x- y =-6","value":"A"},{"text":"x -y &lt; -6","value":"B"},{"text":"x -y &gt; 6","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19891,"question":"The total cost of 2 apples and 3 oranges is $1.70,which of the following is true","choices":[{"text":"The cost of one apple","value":"A"},{"text":"The cost of one orange","value":"B"},{"text":"Both have equal cost per item","value":"C"},{"text":"Cost of each single item can not be determined","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19890,"question":"If p and r are integers P = 0, and p ≠ -r, which of the following must be true?","choices":[{"text":"p &lt; r","value":"A"},{"text":"p &gt; r","value":"B"},{"text":"p + r &lt; 0","value":"C"},{"text":"p - r &lt; -0","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19889,"question":"If -1 &lt; x &lt; 0, which of the following statement must be true?","choices":[{"text":"x &lt; x<sup>2</sup> &lt; x<sup>2</sup>","value":"A"},{"text":"x &lt; x<sup>3</sup>&nbsp;&lt; x<sup>2</sup>","value":"B"},{"text":"x<sup>2</sup>&nbsp;&lt; x<sup>3</sup>&nbsp;&lt; x","value":"C"},{"text":"x<sup>2&nbsp;</sup>&lt;&nbsp;x &lt;&nbsp;x<sup>3</sup>","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19888,"question":"For which of the following ordered pairs (s,t) is s + t&gt; and s- t &lt; -3?","choices":[{"text":"(3,2)","value":"A"},{"text":"(2,3)","value":"B"},{"text":"(1,8)","value":"C"},{"text":"(0,3)","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19887,"question":"Which is in the solution set of 4x - 3y &lt;2","choices":[{"text":"(3,0)","value":"A"},{"text":"(4,1)","value":"B"},{"text":"(1,3)","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19886,"question":"A point of a solution region where two of its boundary lines intersect is called","choices":[{"text":"Boundary","value":"A"},{"text":"Inequality","value":"B"},{"text":"Half plane","value":"C"},{"text":"Vertex","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19885,"question":"Which is not a half plane","choices":[{"text":"ax + by &lt; c","value":"A"},{"text":"ax + by &gt; c","value":"B"},{"text":"Both A and B","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19884,"question":"If 4 - x &gt; 5, then","choices":[{"text":"x &gt; 1","value":"A"},{"text":"x &gt; -1","value":"B"},{"text":"x &lt; 1","value":"C"},{"text":"x &lt; -1","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19883,"question":"If ab &gt; 0 and a &lt; 0, which of the following is negative?","choices":[{"text":"b","value":"A"},{"text":"-b","value":"B"},{"text":"-a","value":"C"},{"text":"(a - b)<sup>2</sup>","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19882,"question":"If x &lt; y, 2x = A and 2y = B then","choices":[{"text":"A =B","value":"A"},{"text":"A &lt; B","value":"B"},{"text":"A&lt; X","value":"C"},{"text":"B &lt; y","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19881,"question":"If a line passes through origin then the equation of the line is","choices":[{"text":"y = m/x","value":"A"},{"text":"y = mx","value":"B"},{"text":"x = my","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19880,"question":"The angle a (0° &lt; a&lt; 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the","choices":[{"text":"Rotation","value":"A"},{"text":"Inclination","value":"B"},{"text":"Radian","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19879,"question":"The center of a circle of radius 10 is on the origin which of the following points lies with in the circle","choices":[{"text":"(10,0)","value":"A"},{"text":"(8,8)","value":"B"},{"text":"(8,4)","value":"C"},{"text":"(0,10)","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19878,"question":"If k<sub>1</sub> : k<sub>2</sub> = 1:1 then the point P dividing the line is","choices":[{"text":"Mid point","value":"A"},{"text":"Extreme left point","value":"B"},{"text":"Extreme Right point","value":"C"},{"text":"Plies out side k<sub>1</sub> and k<sub>2</sub>","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19877,"question":"If the diagonal of a square has coordinates (1,2) and(5,6) the length of a side is","choices":[{"text":"3","value":"A"},{"text":"4","value":"B"},{"text":"1","value":"C"},{"text":"5","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19876,"question":"Which of the following is the equation of a line with slope 0 and passing through the point (4,3)","choices":[{"text":"X =4","value":"A"},{"text":"X = -4","value":"B"},{"text":"Y = 3","value":"C"},{"text":"Y = -6","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19875,"question":"The curves y =x<sup>2</sup>, y= x interest at","choices":[{"text":"(0,0) ,(1,1)","value":"A"},{"text":"(2,4)","value":"B"},{"text":"(0,),(2,4)","value":"C"},{"text":"(0,3),(-1,1)","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19874,"question":"The equation of the line with gradient 1 passing through the point (h,k) is","choices":[{"text":"Y = x+ k-h","value":"A"},{"text":"Y = k/hx +1","value":"B"},{"text":"Y = x + h -l","value":"C"},{"text":"Ky = hx =1","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19873,"question":"The line joining (1,3) to (a,b) has unit gradient then","choices":[{"text":"a-b =-2","value":"A"},{"text":"a+b = 0","value":"B"},{"text":"A-b =5","value":"C"},{"text":"2a + 3b =1","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19872,"question":"The gradient of the line joining (1,4) and (-2,5) is","choices":[{"text":"3/8","value":"A"},{"text":"-2 2/3","value":"B"},{"text":"-1/3","value":"C"},{"text":"2","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19871,"question":"The mid point of the line joining (=1,-3) to(3,-5) is","choices":[{"text":"(1, 1)","value":"A"},{"text":"(1,-1)","value":"B"},{"text":"(2, -8)","value":"C"},{"text":"(1, -4)","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19870,"question":"The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is","choices":[{"text":"2","value":"A"},{"text":"13","value":"B"},{"text":"7","value":"C"},{"text":"8","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19869,"question":"The general solution of the differential equation dy/dx = log x is","choices":[{"text":"Y = -x log x- x +c","value":"A"},{"text":"Y = x log x + x<sup>2</sup>","value":"B"},{"text":"Y = x log x -x +c","value":"C"},{"text":"Y= 2x log x + 2x +c","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19868,"question":"∫cot (ax + b) dx =","choices":[{"text":"1/a log |sin (ax + b)| +c","value":"A"},{"text":"1/a log |cos ax + b)","value":"B"},{"text":"1/b |sin (ax + b)|","value":"C"},{"text":"1/a log |sin (bx + a)|","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19867,"question":"∫sec (ax + b) tan(ax + b) dx=_______","choices":[{"text":"sec(ax + b)/a","value":"A"},{"text":"sec<sup>2</sup> (ax + b)/2","value":"B"},{"text":"sec(ax + b)/x","value":"C"},{"text":"1/2","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19866,"question":"If f<sub>1</sub>&nbsp;(x) and f<sub>2</sub>&nbsp;&nbsp;(x) are any two anti derivatives of a function F (x) then the value of f<sub>1</sub>&nbsp;(x) = f<sub>2</sub>&nbsp;(x)","choices":[{"text":"A variable","value":"A"},{"text":"A constant","value":"B"},{"text":"Undefined","value":"C"},{"text":"Infinity","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19865,"question":"d/dx&nbsp;∫x<sup>1</sup> dx =________.","choices":[{"text":"1/4 x<sup>4</sup>","value":"A"},{"text":"X<sup>3</sup>","value":"B"},{"text":"3x<sup>3</sup>","value":"C"},{"text":"x<sup>4</sup>/4","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19864,"question":"∫1/ax +b dx =","choices":[{"text":"1/a log |ax + b| +c","value":"A"},{"text":"Log |ax + b| +c","value":"B"},{"text":"1/b log |ax +b| +c","value":"C"},{"text":"1/x log |ax + b| +c","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19863,"question":"If y = sin(ax + b) then fourth derivative of y with respect to x=","choices":[{"text":"a<sup>4</sup> cos (ax + b)","value":"A"},{"text":"a<sup>4</sup> sin (ax + b)","value":"B"},{"text":"-a<sup>4</sup> sin(ax +b)","value":"C"},{"text":"a4 tan (ax + b)","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19862,"question":"Any point where f is neither increasing nor decreasing and f(x) =0 at that point is called a","choices":[{"text":"Minimum","value":"A"},{"text":"Maximum","value":"B"},{"text":"Stationary point","value":"C"},{"text":"Constant","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19861,"question":"Derivative of strictly increasing function is always","choices":[{"text":"Zero","value":"A"},{"text":"Positive","value":"B"},{"text":"Negative","value":"C"},{"text":"Both A and B","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19860,"question":"Second derivative of y = x<sup>9</sup> + 10x<sup>2</sup> + 2x -1 at x = 0 is","choices":[{"text":"10","value":"A"},{"text":"20","value":"B"},{"text":"12","value":"C"},{"text":"1","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19859,"question":"d/dx [cos x<sup>2</sup>] =________","choices":[{"text":"-2x cos x<sup>2</sup>","value":"A"},{"text":"-2x<sup>2</sup> sin x<sup>2</sup>","value":"B"},{"text":"x<sup>2</sup>&nbsp;sin x","value":"C"},{"text":"-2x<sup>2</sup>&nbsp;sin x<sup>2</sup>","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19858,"question":"If y = (ax)<sup>m</sup>&nbsp;+ b<sup>m</sup>, then dy/dx equals","choices":[{"text":"m (ax)<sup>m</sup>&nbsp;x<sup>m-1</sup>","value":"A"},{"text":"ma<sup>m</sup>&nbsp;x<sup>m-1</sup>","value":"B"},{"text":"m a<sup>m</sup>&nbsp;x<sup>m-1</sup>","value":"C"},{"text":"m a<sup>m</sup>&nbsp;x<sup>m-2</sup>","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19857,"question":"d/dx (3y<sup>4</sup>) =","choices":[{"text":"12y<sup>3</sup> dy/dx","value":"A"},{"text":"8y<sup>3</sup>","value":"B"},{"text":"8y<sup>3</sup> dy/dx","value":"C"},{"text":"12y<sup>3</sup>","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19856,"question":"d/dx (√x) =","choices":[{"text":"2√x","value":"A"},{"text":"1/√x","value":"B"},{"text":"1/2√x","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19855,"question":"d/dx a<sup>x</sup> is","choices":[{"text":"xa<sup>x-1</sup>","value":"A"},{"text":"a<sup>x</sup>","value":"B"},{"text":"x in a","value":"C"},{"text":"a<sup>x</sup> in a","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19854,"question":"If x<sup>2</sup> +y<sup>2</sup> = 4, Then dy/dx =","choices":[{"text":"2x +2y","value":"A"},{"text":"4 -x<sup>2</sup>","value":"B"},{"text":"-x/y","value":"C"},{"text":"y/x","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19853,"question":"The parametric equation of a curve are x = t<sup>2</sup>, y = t<sup>2&nbsp;</sup>then","choices":[{"text":"dy/dx =3t/2","value":"A"},{"text":"dy/dx =t<sup>5</sup>","value":"B"},{"text":"dy/dx =5t<sup>4</sup>","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19852,"question":"In the function v = 4/3 π r<sup>3</sup>, V is a function of","choices":[{"text":"3/4","value":"A"},{"text":"r","value":"B"},{"text":"v","value":"C"},{"text":"π","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19851,"question":"F(x) = xx decreases in the interval","choices":[{"text":"(0,e)","value":"A"},{"text":"(0.1)","value":"B"},{"text":"(-∞.0)","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19850,"question":"The area of circle of unit radius=","choices":[{"text":"0","value":"A"},{"text":"1","value":"B"},{"text":"4","value":"C"},{"text":"π","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19849,"question":"Domain of Y = csc x is","choices":[{"text":"R - nπ, n&nbsp;ε I","value":"A"},{"text":"R","value":"B"},{"text":"R -nπ/2,nεI","value":"C"},{"text":"All negative Integers","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19848,"question":"Graph of the equation X<sup>2</sup> + y<sup>2</sup> = 4 is","choices":[{"text":"a circle","value":"A"},{"text":"an ellipse","value":"B"},{"text":"a parabola","value":"C"},{"text":"A square","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":19847,"question":"The range of inequality x + 2 &gt; 4 is","choices":[{"text":"(-1,2)","value":"A"},{"text":"(-2,2)","value":"B"},{"text":"(1,∞)","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":19846,"question":"A function F(x) is called even if","choices":[{"text":"F(x) = F(-x)","value":"A"},{"text":"F(x) = F(-x)","value":"B"},{"text":"F(x) = -F(x)","value":"C"},{"text":"2F(x) = 0","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":19845,"question":"The Domain of f(x) = log x is","choices":[{"text":"[0,∞]","value":"A"},{"text":"(0,&nbsp;∞)","value":"B"},{"text":"[0,∞[","value":"C"},{"text":"[∞ ,∞]","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":19844,"question":"If f(x) : A&nbsp;→ B and g (x) : A&nbsp;→ B then Dom [f(x) + g(x)] is","choices":[{"text":"Dom f(x)&nbsp;∩ Dom g (x)","value":"A"},{"text":"Dom f(x)&nbsp;∪ Dom g(x)","value":"B"},{"text":"[Domf(x)]<sup>2</sup> - [Dom g(x)]<sup>2</sup>","value":"C"},{"text":"[Dom g(x)]<sup>2 </sup>-[Domf(x)]<sup>2</sup>","value":"D"},{"value":"E"}],"correctAnswer":1}]