2023 May 15 EAPCET Engineering Afternoon Mathematics Practice Test

Test Description

This EAPCET Engineering Mathematics Practice Test was a previous year EAPCET exam conducted on 2023 May 15 Shift 2. 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 Andhra Pradesh (AP) EAPCET 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 Andhra Pradesh.

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

f (a) = \log |\frac{1 - a}{1 + a}|

for

a \neq \{- 1, 1\}

, then the set of values of all 'a', for which

f (\frac{2 a}{1 + a^{2}}) > 0

$(0, \infty) - \{1\}$
$(- \infty, 0) - \{- 1\}$
$(- \infty, \infty) - \{- 1, 1\}$
$(- 1, 1)$

(2 of 80) If a real valued function f is defined by

f (x) = \frac{ax + \sqrt{a^{2} - x^{2}}}{bx}

, then f is

only one - one
only onto
both one - one and onto
neither one - one nor onto

(3 of 80) If the cofactors of the elements 3, 7 and 6 of the matrix

[\begin{matrix} 1 & 2 & 3 \\ 4 & - 1 & 7 \\ 2 & 4 & 6 \end{matrix}]

are a, b and c respectively, then

[\begin{matrix} a & b & c \end{matrix}] [\begin{matrix} 1 \\ 4 \\ 2 \end{matrix}] + [\begin{matrix} a & b & c \end{matrix}] [\begin{matrix} 3 \\ 7 \\ 6 \end{matrix}] =

-1
1
0
3

(4 of 80) Let

B = (\begin{matrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ - 1 & 1 & - 1 \end{matrix})

and

C = (\begin{matrix} - 1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{matrix})

. If a matrix A is such that BAC=I, then

A^{- 1} =

$(\begin{matrix} - 3 & - 5 & 5 \\ 0 & 9 & 14 \\ 2 & 2 & 6 \end{matrix})$
$(\begin{matrix} - 3 & - 5 & 5 \\ 0 & 0 & 9 \\ 2 & 14 & 16 \end{matrix})$
$(\begin{matrix} - 3 & - 5 & - 6 \\ 0 & 9 & 2 \\ 2 & 14 & 6 \end{matrix})$
$(\begin{matrix} - 3 & - 5 & - 5 \\ 0 & 9 & 2 \\ 2 & 14 & 6 \end{matrix})$

(5 of 80) If

\det (AB) = (\det A) (\det B)

and A is a non-singular matrix of order

3 \times 3

, then

\det (adj A) =

$\det (A)$
${(\det (A))}^{- 1}$
${(\det (A))}^{2}$
${(\det (A))}^{3}$

(6 of 80)

S = \{z \in C / |z - 1 + i| = 1\}

represents

a circle with centre (-1, 1) and radius 1 unit
a circle with centre (1, 2) and radius 5 units
a circle with centre (1, -1) and radius 1 unit
an ellipse with centre (1, -1)

(7 of 80) If

|z - \frac{2}{z}| = 2

, then the greatest value of

|z|

$\sqrt{3} - 1$
$\sqrt{3}$
$\sqrt{3} + 1$
$\sqrt{3} + 2$

(8 of 80) One of the

15^{th}

roots of -1 is

$cis 0$
$cis \frac{14 π}{15}$
$cis \frac{13 π}{15}$
$cis \frac{8 π}{15}$

(9 of 80) The product of the four values of

{(1 + i \sqrt{3})}^{\frac{3}{4}}

-8i
i
-8
8

(10 of 80) If one root of the equation

{ax}^{3} + bx + c = 0

is twice another root, then

$36 b^{3} = 343 {ac}^{2}$
$36 b^{3} + 343 {ac}^{2} = 0$
$36 b^{3} + 729 {ac}^{2} = 0$
$36 b^{3} = 729 {ac}^{2}$

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Test Details

Duration

1h 30m

Questions

80 Multiple Choice Questions

Passing Score

N/A% or higher to pass

Attempts

Unlimited attempts allowed

Total Runs

100