2023 May 13 EAMCET Engineering Forenoon Mathematics Practice Test

Test Description

This EAMCET Engineering Mathematics Practice Test was a previous year EAMCET exam conducted on 2023 May 13 Shift 1. This test consists of 80 objective type questions from both Intermediate First Year and Intermediate Second Year Mathematics. The questions are given in the same format as in the exam conducted by Telangana (AP) EAMCET exam in the year 2023.

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

Test Instructions

The test contains 80 multiple-choice questions.
Total time for the test is 1h 30m.
Each question carries equal marks.
There is no negative marking for wrong answers.
Use of calculator is not allowed.
Do not refresh the page during the test.
Make sure you have a stable internet connection.

Quick Test

(1 of 80) If the function

f : R \to R

is defined by

f (x) = \{\begin{cases} 2 x - 3, & i f x < - 2 \\ x^{2} - 1, & i f - 2 \leq x \leq 2 \\ 3 x + 2, & i f x > 2 \end{cases}

then f is

an injection but not a surjection
a surjection but not an injection
a bijection
neither injection nor surjection

(2 of 80)

The domain of the real valued function $f (x) = \frac{\sqrt{\log_{10} (\frac{x}{x - 2})}}{\sqrt{{[x]}^{2} - 5 [x] + 6}}$ is

(Here [x] denotes the greatest integer function)

$(- \infty, 0) \cup (2, \infty)$
$(2, \infty)$
$(- \infty, 2) \cup (4, \infty)$
$(4, \infty)$

(3 of 80) The range of the real valued function

f (x) = \frac{1}{x - |x|}

$(0, \infty)$
$(- \infty, 0)$
$(- \infty, 0) \cup (0, \infty)$
$(- \infty, \infty)$

(4 of 80) If

A = [\begin{matrix} 1 & 2 & - 1 \\ - 1 & 0 & 2 \\ 1 & 2 & 0 \end{matrix}]

and

B = [\begin{matrix} - 3 & - 2 & 4 \\ 2 & 2 & - 1 \\ - 2 & 0 & 3 \end{matrix}]

, then

A^{2} =

A-B
B-A
A+B
$B^{2}$

(5 of 80)

|\begin{matrix} 2 & 3 & 5 \\ 3 & 5 & 2 \\ 5 & 2 & 3 \end{matrix}| + |\begin{matrix} 1 & 1 & 1 \\ 7 & 11 & 13 \\ 49 & 121 & 169 \end{matrix}| =

(6 of 80) If

A = [\begin{matrix} k & 5 & 2 \\ 2 & - k & 5 \\ 5 & 2 & - k \end{matrix}]

and det A=190 then Adj A=

$[\begin{matrix} - 1 & 19 & 31 \\ 31 & - 19 & - 11 \\ 19 & 19 & - 19 \end{matrix}]$
$[\begin{matrix} - 1 & 31 & 19 \\ 19 & - 19 & 19 \\ 31 & - 11 & - 19 \end{matrix}]$
$[\begin{matrix} - 1 & 19 & 31 \\ - 31 & - 19 & - 11 \\ 19 & 19 & - 19 \end{matrix}]$
$[\begin{matrix} - 1 & - 31 & 19 \\ 19 & - 19 & 19 \\ 31 & - 11 & - 19 \end{matrix}]$

(7 of 80)

If the unique solution of the simultaneous linear equations 3x-2y+z=5k,

2x+3y-2z= -5k, x+4y+3z=k is $x = α, y = β, z = 3$ , then k=

1
2
-1
-2

(8 of 80) If the value of

\sqrt{- 5 - 12 i} + \sqrt{7 + 24 i}

is a negative real number k, then k=

-5
-7
-6
-4

(9 of 80) Let z=x+iy be a point in the Argand plane. If the amplitude of

(\frac{z - 3}{z + 2 i})

\frac{π}{2}

, then the locus of z is

a cirlce
a straight line
a semicircular are not containing the origin
a semicircular are containing the origin

(10 of 80) If a point P denotes the complex number z=x+iy in the Argand plane and if

\frac{z - (2 + i)}{z + (1 - 2 i)}

is purely real, then the locus of P is

the line x+3y-5=0 excluding the point (-1, 2)
the circle $x^{2} + y^{2} - x - 3 y = 0$ excluding the point (-1, 2)
the line x+3y-5=0 and the circle $x^{2} + y^{2} - x - 3 y = 0$ excluding the point (-1, 2)
the circle $x^{2} + y^{2} - 2 x - 6 y + 5 = 0$ excluding the point (-1, 2)