EAMCET Mathematics Practice Test 013

This Mathematics Practice Test is the thirteenth mock test in the series of many Mathematics tests. This test consists of 40 objective type questions from both Intermediate First Year and Intermediate Second Year Mathematics. This test provides questions in the format of Andhra Pradesh (AP) EAPCET and Telangana (TS) EAMCET.

This test is completely free, and students can attempt as many times as needed and help students in preparing for entrance tests and get admissions into various reputed colleges for Engineering.

Test Instructions

Quick Test

(1 of 40) The locus of the point which is equidistant from the point (1, 1) and the line x+y+1=0 is

$x^{2} - y^{2} + 6 x + 4 y - 3 = 0$
${(x - y)}^{2} - 6 (x + y) + 3 = 0$
${(x + y)}^{2} + 6 (x + y) + 3 = 0$
$x^{2} + y^{2} - 2 x - 2 y + 4 = 0$

(2 of 40) If the y-intercept of the perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) is -4, then a possible value of k is

2
-2
-4
1

(3 of 40) A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of

60 °

with the line x+y=0. Then the equation of the line L is

$(\sqrt{3} + 1) x + (\sqrt{3} - 1) y = 8 \sqrt{2}$
$(\sqrt{3} - 1) x + (\sqrt{3} + 1) y = 8 \sqrt{2}$
$\sqrt{3} x + y = 8$
$x + \sqrt{3} y = 8$

(4 of 40) If p and q are the x and y - intercepts respectively of the line passing through the points

(a \cos α, b \sin α)

and

(a \cos β, b \sin β)

, then

\frac{a^{2}}{p^{2}} + \frac{b^{2}}{q^{2}} =

$\sin^{2} (\frac{α - β}{2})$
$\cos^{2} (\frac{α - β}{2})$
$\sec^{2} (\frac{α - β}{2})$
${cosec}^{2} (\frac{α - β}{2})$

(5 of 40) If

ad \neq 0

and two of the lines represented by

{ax}^{3} + 3 {bx}^{2} y + 3 {cxy}^{2} + {dy}^{3} = 0

are perpendicular, then

$a^{2} + ac + bd + d^{2} = 0$
$a^{2} + 3 ac + 3 bd + d^{2} = 0$
$a^{2} - 3 ac - 3 bd + d^{2} = 0$
$a^{2} + 3 ac - 3 bd + d^{2} = 0$

(6 of 40) The absolute value of the tangent of the difference of the angles made by the lines

4 x^{2} - 24 xy + 11 y^{2} = 0

with the X-axis is

$\frac{4}{11}$
$\frac{24}{11}$
$\frac{4}{3}$
$\frac{11}{24}$

(7 of 40) If the extremities of a diagonal of a square are (1,-2,3) and (2, -3,5), then the length of its side is

$\sqrt{6}$
$\sqrt{3}$
$\sqrt{5}$
$\sqrt{7}$

(8 of 40) Coordinate planes and the planes

π_{1}, π_{2}, π_{3}

which are respectively parallel to YZ, ZX, XY planes at distances a, b, c form a rectangular parallelepiped.

d_{1}

is a diagonal of the face on XY-plane not passing through origin and

d_{2}

is diagonal of plane

π_{2}

coterminous with

d_{1}

. If none of the coordinates of the vertices of the parallelepiped are negative and angle between

d_{1}

and

d_{2}

θ

, then

\cos θ =

$\frac{a^{2}}{\sqrt{a^{2} + b^{2}} \sqrt{a^{2} + c^{2}}}$
$\frac{a}{a^{2} + b^{2} + c^{2}}$
$\frac{π}{2}$
$\frac{a^{2}}{\sqrt{a^{2} + b^{2}} \sqrt{b^{2} + c^{2}}}$

(9 of 40) An equation of a plane parallel to the plane x-2y+2z-5=0 and which is at one unit distance from the origin is

x-2y+2z-1=0
x-2y+2z+5=0
x-2y+2z-3=0
x-2y+2z+1=0

(10 of 40) A circle S touches Y-axis at (0, 3) and makes an intercept of length 8 units on X-axis. If the centre C of the circle S lies in the second quadrant , then the distance of C from the point (-2, -1) is

13
10
5
$\sqrt{2}$

EAMCET Mathematics Practice Test 013

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