CoordinateGeometry
Question 1 
Let R be the radius of the circle. What is the angle subtended by an arc of length at the center of the circle?
1 degree  
1 radian  
90 degrees  
π radians 
Question 1 Explanation:
A degree (in full, a degree of arc, arc degree, or arc degree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit.Because a full rotation equals 2π radians.
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends;
It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit.Because a full rotation equals 2π radians.
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends;
Question 2 
What is the area bounded by the parabola 2y = x^{2} and the line x = y  4?
18  
36  
72  
6 
Question 2 Explanation:
Given parabola 2y = x^{2}  (1)
and the line x = y – 4  (2)
Then y = x+4
Now, Substitute Y value in Equation(1)
x^{2} = 2 ( x + 4 )  (3)
Solving equation3 we get x = 4,  2.
Place Values of x in equation (1) and (2) we will get y = 8, 2.
Then the points of intersection are (8, 4), (2, –2).
After solving the integration, we will get 18.
and the line x = y – 4  (2)
Then y = x+4
Now, Substitute Y value in Equation(1)
x^{2} = 2 ( x + 4 )  (3)
Solving equation3 we get x = 4,  2.
Place Values of x in equation (1) and (2) we will get y = 8, 2.
Then the points of intersection are (8, 4), (2, –2).
After solving the integration, we will get 18.
Question 3 
A straight line which cuts a curve on two points at an infinite distance from the origin and yet is not itself wholly at infinity is called:
Spiral
 
Asymptote
 
Parallel
 
Polar

Question 3 Explanation:
A straight line which cuts a curve in two points at an infinite distance from the origin, but which is not itself wholly at infinity, is called an asymptote to a curve.
Question 4 
On the parabola y = x ^{2} find the point N least distant from the straight line y = 2 x − 4
N (2, 4 )  
N (1, 1 )  
N (1, 2 )  
N (− 1 , 1 ) 
Question 5 
Three lines 3 x + y − 2 = 0 , p x + 2 y − 3 = 0 and 2 x − y − 3 = 0 intersect at a point. Then, the value of p is
7  
2  
5  
11 
Question 6 
The equation of the plane through the point ( − 1 , 3 , 2 ) and perpendicular to each of the planes x + 2 y + 3 z = 5 and 3 x + 3 y + z = 0 is
7 x − 8 y + 3 z + 2 5 = 0  
7 x + 8 y + 3 z + 2 5 = 0  
7 x − 8 y + 3 z − 2 5 = 0  
7 x − 8 y − 3 z − 2 5 = 0 
Question 7 
For the curve y = x e x the point
x = − 1 is a minimum  
x = 0 is a minimum  
x = − 1 is a maximum  
x = 0 is a maximum 
Question 8 
The line y = m x + c will be tangent to the ellipse x ^{2}/ 9 + y ^{2} / 4 = 1 , if c is equal to
3 / m  
√ 9m ^{2} + 4  
√ 1 + m^{ 2}  
√ 4m ^{2} + 9 
Question 9 
The circle x^{ 2} + y^{ 2} + 2 ax + 1 = 0 (where a > 0 ) is ________.
tangent to the yaxis  
does not meet the yaxis  
intersects the yaxis  
intersects both xaxis and yaxis 
Question 10 
The perpendicular from the origin to the line y = m x + c meets it at the point ( − 1 , 2 ) . Then, the values of m and c are
m = 3/2 , c = 5/2  
m = 1/2 , c = 5/2  
m = 1/2 , c = 5/2  
m = 1/2 , c = 5/2 
Question 11 
Circle has ____________
No vertices  
Only 1 vertex  
∞ vertices  
None of these 
Question 11 Explanation:
In graph theory, a circle graph is the intersection graph of a set of chords of a circle.
→ A circle graph is an undirected graph whose vertices can be associated with chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
→ Circle does not have vertices.
→ A circle graph is an undirected graph whose vertices can be associated with chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
→ Circle does not have vertices.
Question 12 
Find the equation of the circle x^{2}+y^{2}=1 in terms of x'y' coordinates, assuming that the xy coordinate system results from a scaling of 3 units in the x' direction and 4 units in the y' direction.
3(x')^{2} + 4(y')^{2} = 1  
(x'/3)^{2} + (y'/4)^{2} = 1  
(3x')^{2} + 4(y')^{2} = 1  
1/3(x')^{2} + 1/4(y')^{2} = 1 
Question 13 
The end points of a given line are (0, 0) and (6, 18). Compute each value of y as x steps from 0 to 3, by using equation of straight line:
For x = 0, y = 0; x = 1, y = 3; x = 2, y = 6; x = 3, y = 9  
For x = 0, y = 1; x = 1, y = 3; x = 2, y = 4; x = 3, y = 9  
For x = 0, y = 2; x = 1, y = 3; x = 2, y = 6; x = 3, y = 9  
For x = 0, y = 0; x = 1, y = 3; x = 2, y = 4; x = 3, y = 6 
Question 13 Explanation:
Question 14 
Consider a unit square centred at the origin. The coordinates of the square are translated by a factor (1/2, 1) and rotated by an angle of 90°. What shall be the coordinates of the new square?
Question 14 Explanation:
There are 14 questions to complete.