PYQs Based Test - 17 : Engineering Mathematics

Topics Covered

Sample Questions from this Test

1. A real (4 × 4) matrix A satisfies the equation A² = I, where I is a (4 × 4) identity matrix. The positive eigenvalue of A is ________.
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2. Let α, β be two non-zero real numbers and v₁, v₂ be two non-zero real vectors of size 3 × 1. Suppose that v₁ and v₂ satisfy $v_1^T{v}_2=0,v_1^T{v}_1=1$, and $v_2^T{v}_2=1$. Let A be the 3 × 3 matrix given by:
   
   $\mathrm{A}=\alpha {\mathrm{v}}_1{\mathrm{v}}_1^{\mathrm{T}}+\beta {\mathrm{v}}_2{\mathrm{v}}_2^{\mathrm{T}}$
   
   The eigenvalues of A are _______
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3. The integral $\underset{0}{\overset{1}{\int }}\frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}}}$ is equal to _______

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Test Instructions

• The test contains 20 questions and a total of 32 marks.
• You will have 180 minutes to complete the test. The timer cannot be paused once started.
• Negative marking: 0.25 mark(s) deducted per wrong answer.
• Use the question palette to mark questions for review and navigate freely.
• Detailed solutions and analytics are available immediately after submission.
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