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Algebra — JEE Mathematics MCQs

Master Algebra for JEE Main with free mathematics MCQs. Each question includes a detailed solution and instant feedback — practice at easy, medium, and hard difficulty levels to build exam-ready confidence.

2 practice questions with instant feedback and solutions.

Hard•Algebra

Let

P=\left[\begin{array}{ccc}1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1\end{array}\right]

and

I

be the identity matrix of order 3. If

Q=\left[q_{i j}\right]

is a matrix such that

P^{50}-Q=I

, then

\frac{q_{31}+q_{32}}{q_{21}}

equals

Hard•Algebra

Let

M=\left[\begin{array}{cc} \sin ^{4} \theta & -1-\sin ^{2} \theta \\ 1+\cos ^{2} \theta & \cos ^{4} \theta \end{array}\right]=\alpha I+\beta M^{-1}

where

\alpha=\alpha(\theta)

and

\beta=\beta(\theta)

are real numbers, and

I

is the

2 \times 2

identity matrix. If

\alpha^{*}

is the minimum of the set

\{\alpha(\theta): \theta \in[0,2 \pi)\}

and

\beta^{*}

is the minimum of the set

\{\beta(\theta): \theta \in[0,2 \pi)\}

then the value of

\alpha^{*}+\beta^{*}