2023 May 16 EAPCET Engineering Afternoon Practice Test

Test Description

This EAMCET Engineering Practice Test was a previous year EAMCET exam conducted on 2023 May 16th Shift 2. This test consists of 160 objective type questions from both Intermediate First Year and Intermediate Second Year Mathematics (80), Physics (40) and Chemistry (40). 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 160 multiple-choice questions.
Total time for the test is 3h 00m.
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 160) Let

A \subseteq ℝ

B \subseteq ℝ

and

f : A \to B

be defined by

f (x) = x^{2} - 3 x + 2

. If f is a bijection, then

$A = (- \infty, 0], B = (- \infty, \frac{- 1}{4}]$
$A = (- \infty, \frac{3}{2}], B = [\frac{- 1}{4}, \infty)$
$A = [\frac{3}{2}, \infty), B = (- \infty, \frac{- 1}{4}]$
$A = (- \infty, \infty), B = [\frac{- 1}{4}, \infty)$

(2 of 160) If

f : ℝ \to ℝ

is defined by f(x+y) = f(x) + f(y)

\forall x, y \in ℝ

and f(1) = 7, then

Σ_{r = 1}^{n} f (r) =

$\frac{3 n (n + 2)}{4}$
$\frac{n (n - 1)}{2}$
$\frac{7 n (n + 1)}{2}$
$\frac{(n + 1) (n + 2)}{4}$

(3 of 160) Let

A = (\begin{matrix} - \cot θ & cosec θ \\ cosec θ & - \cot θ \end{matrix})

. If

A^{- 1} = A

θ = θ_{1}

and

A^{- 1} + A = O

θ = θ_{2}

, then which one of the following is true

$θ_{1} = \frac{π}{2}, θ_{2} = π$
$θ_{1} = \frac{π}{2}$ , such $θ_{2}$ does not exist
$θ_{1} = \frac{π}{4}, θ_{2} = \frac{π}{2}$
such $θ_{1}$ does not exist, $θ_{2} = π$

(4 of 160) A matrix whose elements

a_{ij}

are defined by

a_{ij} = \frac{1}{3} |i - 5 j|

, i, j = 1,2,3 is

$[\begin{matrix} 4 & 3 & \frac{14}{3} \\ 1 & \frac{8}{3} & 13 \\ \frac{2}{3} & \frac{7}{3} & 4 \end{matrix}]$
$[\begin{matrix} \frac{4}{3} & 3 & \frac{14}{3} \\ 1 & \frac{8}{3} & \frac{13}{3} \\ \frac{2}{3} & \frac{7}{3} & 4 \end{matrix}]$
$[\begin{matrix} \frac{4}{3} & 3 & \frac{10}{3} \\ 1 & \frac{8}{3} & \frac{13}{3} \\ 2 & 7 & 4 \end{matrix}]$
$[\begin{matrix} 4 & 3 & 10 \\ 1 & 8 & 13 \\ 2 & 7 & 4 \end{matrix}]$

(5 of 160) If P, Q and R are

3 \times 3

matrices such that

$[\begin{matrix} 3 x^{2} + x + 3 & 2 x^{2} - x + 4 & 7 x^{2} + 8 x + 5 \\ 5 x^{2} + 3 x + 2 & 4 x^{2} - 2 x - 1 & 7 x^{2} + 5 x + 8 \\ 3 x^{2} + 2 x + 5 & 4 x^{2} - x - 2 & 3 x^{2} + 8 x + 7 \end{matrix}] = {Px}^{2} + Qx + R$ , then det R=