List of top Questions asked in GUJCET

Global maximum value of the function \( f(x) = \sin x + \cos x, \quad x \in [0, \pi] \) is: ...

If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]

If \( A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{pmatrix} \), find \( I + A^2 \), where \( I \) is the identity matrix.

If \[ \left| \begin{pmatrix} 2017 & 2018 \\ 2019 & 2020 \end{pmatrix} \right| + \left| \begin{pmatrix} 2021 & 2022 \\ 2023 & 2024 \end{pmatrix} \right| = 2k \] find \( k^3 \).

Evaluate the integral \( \int \frac{1}{\sqrt{4x - x^2}} \, dx \).

Evaluate the integral \( \int e^x \left( \frac{1 + \sin x}{1 - \sin x} \right) \, dx \).

If \( x = a(1 - \cos\theta) \), \( y = a(\theta + \sin\theta) \), then \( \frac{dy}{dx} \) is: ...

Evaluate \( \int \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \).

Lactose is a compound of which units?

Which diazonium salt is water insoluble and stable at room temperature?

Which is the correct order of the basic strength of given amines?

Which of the following carboxylic acid has the least pKa value among all?

'R' + CH₃-CO-CH₃ → Schiff's base. What is 'R' in this reaction?

Identify the optically active compound from the following.

Which one of the correct formula for the coordination compound tris[ethane-1,2-diamine] cobalt (III) sulfate?

Hybridizations of Ni(CO)_4 and \([{Ni(CN)}_4]^{3-}\) are respectively.}

In the complex K[Cr(H₂O)₂(C₂O₄)₂], Central metal ion is and .

Which reagent will be used for the following reaction?
CH₃CH₂CH₂CH₃ →

Name the member of the lanthanide series which is well known to exhibit a \( +4 \) oxidation state.

If \( A \) is a square matrix such that \( A^2 = A \), then \( (I - A)^3 - (I + A)^2 = \) __________.

Find \( \sin^{-1} \left( \sin \frac{23\pi}{6} \right) = \) __________.

Which one of the following is an amphoteric oxide?

Which of the following ions shows the highest spin-only magnetic moment value?

Reaction \( 2A \rightarrow B + 3C \) is a zero-order reaction. What will be the rate of production for "C"?

A radius of a spherical charged shell is 10 cm, and the electric potential on its surface is 100 V. Then, the potential at 2 cm from the center of the shell will be