List of top Questions asked in CBSE CLASS XII

Identify the correct labellings in the figure of a fertilised embryo sac of an angiosperm given below:
Study the pedigree chart of a family showing the inheritance pattern of a certain disorder. Select the option that correctly identifies the nature of the trait depicted in the pedigree chart.
Match the following genes of the lac operon listed in column ‘A’ with their respective products listed in column ‘B’: \begin{center} \begin{tabular}{|c|c|} \hline Column A (Gene) & Column B (Product)
\hline a. ‘i’ gene & (i) \(\beta\)-galactosidase
b. ‘z’ gene & (ii) Lac permease
c. ‘a’ gene & (iii) Repressor
d. ‘y’ gene & (iv) Transacetylase
\hline \end{tabular} \end{center} Select the correct option:
If both the parents are carriers for thalassaemia, the chances of an afflicted child to be born to them is:
If the sequence of nitrogen bases of the coding strand in a transcription unit is 5\(\prime\)–ATGAATG–3\(\prime\), the sequence of bases in its RNA transcript would be:
Observe the schematic representation of assisted reproductive technology given below:
Identify the most appropriate technique depicted in the above diagram.
Interferons are proteins secreted by:
During biological treatment of sewage, the masses of bacteria held together by fungal filaments to form mesh-like structures are called:
Which one of the following statements is correct in the context of observing DNA separation by agarose gel electrophoresis?
A single gene that controls the expression of more than one trait is said to show:
If \( a_{ij} \) and \( A_{ij} \) represent the \((i,j)^\text{th}\) element and its cofactor of the matrix: \[ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}, \] respectively, then the value of \( a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23} \) is:
A relation \( R \) defined on set \( A = \{x : x \in \mathbb{Z} \text{ and } 0 \leq x \leq 10\} \) as \( R = \{(x, y) : x = y\) is given to be an equivalence relation. The number of equivalence classes is:
If \(A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix}\), find \(A^{-1}\) and use it to solve the following system of equations: \[ x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7. \]
Find: \[ \int_{\pi/6}^{\pi/3} \frac{\sin x + \cos x}{\sqrt{\sin 2x}} \, dx. \]
(a) Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]
(b) Evaluate: \[ \int_{1}^{3} \left(|x - 1| + |x - 2| + |x - 3|\right) \, dx. \]
Find the general solution of the differential equation: \[ \frac{dy}{dx} = \frac{x^2 + y^2}{2xy}. \]
Solve the following linear programming problem graphically: \[ \text{Maximise } z = 5x + 4y \] subject to the constraints: \[ x + 2y \geq 4, \quad 3x + y \leq 6, \quad x + y \leq 4, \quad x, y \geq 0. \]
(a) If \(\sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y)\), prove that \(\frac{dy}{dx} = \sqrt{\frac{1 - y^2}{1 - x^2}}\).
(b) If \(y = (\tan x)^x\), then find \(\frac{dy}{dx}\).
(a) Evaluate: \[ \int_{0}^{\pi/2} e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx. \]
If \( \vec{a} \) and \( \vec{b} \) are two non-zero vectors such that \( (\vec{a} + \vec{b}) \perp \vec{a \) and \( (2\vec{a} + \vec{b}) \perp \vec{b} \), then prove that \( |\vec{b}| = \sqrt{2} |\vec{a}| \).}
(a) If \( y = \sqrt{\cos x + y} \), prove that \[ \frac{dy}{dx} = \frac{\sin x}{1 - 2y}. \]
(b) Show that the function \( f(x) = |x|^3 \) is differentiable at all points of its domain.
Find the absolute maximum and minimum values of the function: \[ f(x) = 12x^{4/3} - 6x^{1/3}, \quad x \in [0, 1]. \]