2023 May 14 EAMCET Engineering Afternoon Mathematics Practice Test

Test Description

This EAMCET Engineering Mathematics Practice Test was a previous year EAMCET exam conducted on 2023 May 14 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 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) Let

f : ℝ \to ℝ

be a function defined by

f (x) = \{\begin{cases} x^{2} - 4 x + 3 & if x < 2 \\ x - 3 & if x \geq 2 \end{cases}

Then the number of real numbers x for which

f (x) = 8

(2 of 80) If

f (x)

and

g (x)

are two real valued functions such that

f (x) = 3 x - 2

and

g (x) = x^{2} + 2

then

[(g o f) + (f o g)] (x) =

$2 g (x) + 2 f (x)$
$12 g (x) - 4 f (x) - 22$
$3 g (x) + f (x) - 2$
$2 f (x) + 4 g (x) - 32$

(3 of 80)

If $f (x)$ is a real valued function defined by

f (x) = \frac{a x^{10} + b x^{8} + c x^{6} + d x^{4} + e x^{2} + 12 x + 15}{x} (x \neq 0)

and

f (4) = - 4

then

f (- 4) =

(4 of 80) If

X_{4 \times 3}, Y_{4 \times 3}

and

P_{2 \times 3}

are the matrices then the order of the matrix

{[P {(X^{T} Y)}^{- 1} P^{T}]}^{T}

$4 \times 3$
$3 \times 4$
$3 \times 3$
$2 \times 2$

(5 of 80) If

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

and

α, β \in ℝ

are such that

α A^{2} - β A = 2 I

, then

α^{2} + β =

-8
16
12
20

(6 of 80) If

|\begin{matrix} {(1 + α)}^{2} & {(1 + 2 α)}^{2} & {(1 + 3 α)}^{2} \\ {(2 + α)}^{2} & {(2 + 2 α)}^{2} & {(2 + 3 α)}^{2} \\ {(3 + α)}^{2} & {(3 + 2 α)}^{2} & {(3 + 3 α)}^{2} \end{matrix}| = k

, then

α = - 2

then k=

(7 of 80) If the system of equations

x + y + z = 5, x + 2 y + 2 z = 6

and

x + 3 y + λ z = μ

(λ, μ \in ℝ)

is solvable by Matrix Inversion Method, then

$λ \neq 3, μ \in ℝ$
$λ = 3, μ = 0$
$λ \neq 3, μ \neq 5$
$λ = 3, μ \in ℝ$

(8 of 80) If

x = a + b, y = a α + b β, z = a β + b α

and

α, β

are the complex cube roots of unity, then

x^{3} + y^{3} + z^{3} =

$a^{3} + b^{3}$
$3 (a^{3} + b^{3})$
$a^{3} - b^{3}$
$3 (a^{3} - b^{3})$

(9 of 80) If

Z = \frac{3 + 2 i \cos θ}{1 - 2 i \sin θ}

is a purely imaginary number, then

\sin^{2} θ + \cos^{2} 3 θ =

$\frac{3}{4}$
$\frac{7}{4}$
1
$\frac{5}{4}$

(10 of 80) If

z = x + i y

is a complex number such that

z {\bar{z}}^{3} + \bar{z} z^{3} = 350

and x, y are integers, then

|z| =

$\sqrt{41}$
5
25
$\sqrt{13}$

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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