2023 May 16 EAPCET Engineering Forenoon Mathematics Practice Test

Test Description

This EAPCET Engineering Mathematics Practice Test was a previous year EAPCET exam conducted on 2023 May 16 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) Let

f : ℝ \to ℝ

be a function defined by

f (x) = \frac{2 x + 1}{3}

. If

α

is an element in the domain of f whose image is

\frac{1}{α}

, then the sum of all possible values of such

α

$\frac{- 1}{2}$
$\frac{1}{2}$
$\frac{5}{2}$
$0$

(2 of 80) Let

f (x) = |x|

and

g (x) = |x| + a

(a > o)

. For

0 \leq x \leq b

\{(x, y) / g (x) \leq y \leq f (x)\}

represents all the points in the interior of

a parallelogram
a triangle
a square
a circle

(3 of 80) If there exists a

k^{th}

order non-singular sub matrix in a matrix P of order

m \times n

, then the rank

(ρ)

of P

satisfies $k \leq ρ \leq m$
satisfies $k < ρ < n$
satisfies $k \leq ρ \leq \min \{m, n\}$
is equal to $k + 1$

(4 of 80) If

A = [\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{matrix}]

and

B = [\begin{matrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{matrix}]

, then which one of the following is true?

$A^{T} {BB}^{T} A = B^{T} {AA}^{T} B$
The orders of $A^{T} {BB}^{T} A$ and $B^{T} {AA}^{T} B$ are equal
The orders of $A + B$ , $A^{T} B$ , ${BA}^{T}$ are equal
Rank of A and B are equal

(5 of 80) In a matrix A, if all the sub matrices of

k^{th}

order are singular and there is one non-singular sub matrix of order r (r < k), then the rank (

ρ

) of the matrix A

satisfies $r \leq ρ < k$
is equal to r
is equal to (k-1)
is equal to (k+1)

(6 of 80) If

\sqrt{- 3 - 4 i} = {re}^{iθ}

, then

r^{2} \tan θ =

-5
5
10
-10

(7 of 80) If

z_{1} = 2 - 3 i

and the roots of the equation

z^{3} + {bz}^{2} + cz + d = 0

are

i, z_{1}

and

z_{1}

, then b+c+d=

13
7
9 - 10i
10 - 10i

(8 of 80) If

ω

is a complex cube root of unity, then

\cos (Σ_{k = 1}^{7} (k - ω) (k - ω^{2}) \frac{π}{175}) =

-1
0
1
5

(9 of 80) Let the two values of

z = \sqrt{\frac{1 - i}{1 + i}}

z_{1}

and

z_{2}

. If

- \frac{π}{2} < Arg (z_{1}) < Arg (z_{2}) < π

, then

\arg (z_{1}) + \arg (z_{2}) =

$\frac{π}{4}$
$\frac{3 π}{2}$
$\frac{π}{3}$
$\frac{π}{2}$

(10 of 80) If

α

and

β

are the roots of the equation

x^{2} + x + 1 = 0

, then the quadratic equation whose roots are

α^{2023}

and

β^{1012}

$x^{2} + x + 1 = 0$
$x^{2} - x + 1 = 0$
$x^{2} - x + 2 = 0$
$x^{2} + x + 2 = 0$

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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