2023 May 17 EAPCET Engineering Forenoon Mathematics Practice Test

Test Description

This EAPCET Engineering Mathematics Practice Test was a previous year EAPCET exam conducted on 2023 May 17 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 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 a set A has n elements, then the number of functions defined from A to A that are not one-one is

${(n)}^{n^{2}}$
$n! - ({}^{n}C_{0} + {}^{n}C_{1} + {}^{n}C_{2} + . . . + {}^{n}C_{n})$
$n^{n} - n!$
$n^{n}$

(2 of 80) If f(x) is the signum function, then in terms of f(x), the constant function g(x)=1,

\forall x \in ℝ

$g (x) = \{\begin{cases} 2 - f (x), & x < 0 \\ f (x), & x \geq 0 \end{cases}$
$g (x) = \{\begin{cases} f (x) + f (- x), & x < 0 \\ f (x) f (- x), & x \geq 0 \end{cases}$
$g (x) = \{\begin{cases} 1 + f (x), & x < 0 \\ 1 - f (x), & x \geq 0 \end{cases}$
$g (x) = \{\begin{cases} f (x) + 2, & x < 0 \\ 1 + f (x), & x = 0 \\ f (x), & x > 0 \end{cases}$

(3 of 80) If

A = [\begin{matrix} 1 & 1 & 3 \\ 5 & 2 & 6 \\ - 2 & - 1 & - 3 \end{matrix}]

, then

A + A^{3} + A^{4} + A^{5} + 3 I =

$[\begin{matrix} 4 & 2 & 1 \\ 2 & 5 & 6 \\ - 3 & 2 & 3 \end{matrix}]$
$[\begin{matrix} 4 & 1 & 3 \\ 5 & 5 & 6 \\ - 2 & - 1 & 0 \end{matrix}]$
$[\begin{matrix} 3 & 1 & 4 \\ 3 & 1 & - 2 \\ - 1 & 2 & - 1 \end{matrix}]$
$[\begin{matrix} 4 & 1 & 3 \\ 2 & 3 & 5 \\ - 3 & - 2 & - 3 \end{matrix}]$

(4 of 80) If the solution for the system of equations x+2y-z=3, 3x-y+2z=1 and 2x-2y+3z=2 is

(α, β, γ)

, then

α^{2} + β^{2} + γ^{2} =

(5 of 80) If

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

, then x=

$- 1 + \sqrt{6}$
$8 \pm \sqrt{5}$
$- 2 \pm \sqrt{10}$
$3 \pm \sqrt{6}$

(6 of 80) For real numbers a and b, if

4 a + i (3 a - b) = b - 6 i

and

z = a + \frac{b}{4} i

, then

\frac{|z|}{a} =

$2 \sqrt{2}$
$6 \sqrt{2}$
$\sqrt{2}$
2

(7 of 80) If

z = {(1 - i)}^{3} (x + i)

is purely imaginary number for

x = x_{1}

and if z is a purely real number for

x = x_{2}

, then

x_{1} x_{2} =

-1
0
1
2

(8 of 80) If 1,

ω

ω^{2}

are the cube roots of unity, k is positive integer and

{(1 - ω + ω^{2})}^{3 k} + {(1 - ω^{2} + ω)}^{3 k} = {(1 - ω + ω^{2})}^{3 k + 1} + {(1 + ω - ω^{2})}^{3 k + 1}

, then k=

$r, r \in ℕ$
$2 r + 1, r \in ℕ$
$4 r + 1, r \in ℕ$
$3 r, r \in ℕ$

(9 of 80) If

α, β

are the two real roots of 4th roots of unity and

γ, δ

are the other two roots of it, then the sum of the eccentricities of the conics

|z - α| + |z - β| = 4

and

|z - γ| + |z - δ| = 6

$\frac{5}{6}$
$\frac{5}{12}$
$\frac{3}{7}$
$\frac{4}{5}$

(10 of 80) The set

\{x \in ℝ : 16 (2^{x}) > 16^{\frac{- 1}{x}}\} =

$\{x \in ℝ : x > 0\}$
$\{x \in ℝ : x < 0\}$
$ℝ$
$\{x \in ℝ : x > 2\}$

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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

Test Description

Test Instructions

Quick Test

Practice Tests

Test Details

Duration

Questions

Passing Score

Attempts

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