NDA MATHEMATICS QUIZ

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Question 1:

The graphs of $a x+b y=c, d x+e y=f $ will be:
1. Parallel is the system has no solution.
2. Coincident if the system has finite number of solutions.
3. Intersecting if the system has only one solution.

Question 2:

From the point $(3,4)$ a line perpendicular to the line $2 x+y+3=0$ is drawn. Find the coordinates of the food of the perpendicular?

Question 3:

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

Question 4:

The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

Question 5:

With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x,y) is either to (x,y+1) or to (x+1,y) is

Question 6:

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

Question 7:

Let S be the set of all points (x,y) in the x-y plane such that |x| + |y| ≤ 2 and |x| ≥ 1. Then, the area, in square units, of the region represented by S equals

Question 8:

A triangle $A B C$ has area 32 sq units and its side $B C$, of length 8 units, lies on the line $x=4$. Then the shortest possible distance between $A$ and the point $(0,0)$ is

Question 9:

The points $\mathrm{A}(-3,4), \mathrm{B}(4,6)$ and $\mathrm{C}(-1,-3)$ are the vertices of

Question 10:

Direction : Refer to the instruction given below and answer the question that follows:
$\Delta(x, y)=$ Mirror image of point $(x, y)$ along X-axis.
$*(x, y)=$ Mirror image of point $(x, y)$ along Y-axis.
$\square(x, y)=$ Distance of point $(x, y)$ from origin.
$\mathrm{O}(x, y)=$ Point $(x, y)$ is shifted 1 unit in the negative direction of $\mathrm{X}$-axis and 2 units in the positive direction of Y-axis. $\mathrm{Y}(x, y)=$ Point $(x, y)$ is shifted 2 units in the positive direction of $\mathrm{X}$-axis and 1 unit in the negative direction of Y-axis.

$\square(\mathrm{O}(\Delta(6,10)))$ equals to

Direction : Refer to the instruction given below and answer the question that follows:
$\Delta(x, y)=$ Mirror image of point $(x, y)$ along X-axis.
$*(x, y)=$ Mirror image of point $(x, y)$ along Y-axis.
$\square(x, y)=$ Distance of point $(x, y)$ from origin.
$\mathrm{O}(x, y)=$ Point $(x, y)$ is shifted 1 unit in the negative direction of $\mathrm{X}$-axis and 2 units in the positive direction of Y-axis. $\mathrm{Y}(x, y)=$ Point $(x, y)$ is shifted 2 units in the positive direction of $\mathrm{X}$-axis and 1 unit in the negative direction of Y-axis.

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