List of top Questions asked in GUJCET- 2026

The nuclides of $^{197}_{79}\mathrm{Au}$ and $^{196}_{80}\mathrm{Hg}$ are called ______ of each other
If $\tan \theta = 1$, then $\theta = $:
Value of $\sin^2\theta + \cos^2\theta$:
Mean of first 5 natural numbers:
Probability of getting a head in a fair coin toss:
Direction ratios of x-axis are:
Equation of line with slope 2 passing through origin:
Distance between points (1,2) and (4,6) is:
Number of permutations of 5 distinct objects is:
If $\log_a b = 2$, then $b = ?$
The value of the determinant $\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$ is:
If $a + b = 5$ and $ab = 6$, find $a^2 + b^2$:
If a function is increasing, then its derivative is:
Evaluate: $\int x \, dx$
The derivative of $\sin x$ is:
If $f(x) = x^2 + 3x$, then $f'(x)$ is:
The interval in which \( y = x^2 e^x \) is decreasing is _____
The maximum value of the function \( f(x) = -|x+1| + 3, \; x \in \mathbb{R} \) is _____
The total revenue in Rupees received from the sale of \( x \) units of a product is given by \( R(x) = 3x^2 + 36x + 5 \). The marginal revenue, when \( x = 15 \), is _____

If $e^y (x+1) = 1$, then find the value of $$ \frac{d^2 y}{dx^2} - \left(\frac{dy}{dx}\right)^2. $$ 

If \( y = \log_{2026}(\log_{2025} x) \), then \( \frac{dy}{dx} \)= _____
If \( x = a t^2, \; y = 2at \), then \( \frac{d^2 y}{dx^2} =\) _____
If function \( f \) is continuous at point \( x = \pi \) and \[ f(x) = \begin{cases} kx + 1, & x \le \pi \\ \cos x, & x>\pi \end{cases} \] then the value of \( k \) is ______
If inverse matrix of \( A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix} \) is \( A^{-1} = \begin{bmatrix} a & \frac{3}{11} \\ \frac{1}{11} & b \end{bmatrix} \), then a + b = _____
If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix} \] then \( A^2 + B^2 = \underline{\hspace{2cm}} \)