List of top Questions asked in UP Board XII

What is antitoxin?
Describe exponential growth.

कालिदास का संक्षिप्त जीवन परिचय देते हुए कालिदास की काव्यशैली की विवेचना कीजिए।

The voltage and current of an ac circuit are represented as \( V = 100 \sin(100t) \) volt and \( i = 100 \sin(100t + \frac{\pi}{3}) \) mA respectively. The power dissipated in the circuit is:
Answer the following questions in about 40 words each:
b.What complaint did Rajkumar Shukla file when he came to the Congress Session?
Mention any two causes of Globalization.
Equation of electric field of a plane electromagnetic wave is given as:
\[ E_z = 60 \sin(500x + 1.5 \times 10^{11} t) \, \text{V/m}. \] Write the equation for the magnetic field of the wave.
Find the Cartesian equation of a line which passes through point (3, -2, -5) and is parallel to the vector \( (3\hat{i} + 2\hat{j} - 2\hat{k}) \).
Magnetic moment of a bivalent ion in aqueous solution will be, if its atomic number is 25:
Suppose you are Amit and while playing you used abusive terms to your friend, Vikas. Now, write a letter of apology to him assuring that you will never do it again.
Who guided the model of shock therapy?
The probability of solving a question by the three students A, B, C are respectively \( \frac{3}{10}, \frac{1}{5} \) and \( \frac{1}{10} \). Find the probability of solving the question.
Explain the following:
(i) Lanthanoid contraction
(ii) Oxidation states in Lanthanoids and Actinoids
Find the unit vector perpendicular to each of the vectors \( (\vec{a} + \vec{b}) \) and \( (\vec{a} - \vec{b}) \) where \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} \).
(a) A person with narrow religious views is called
The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left(\frac{dy}{dx}\right)^2 \right\}^{\tfrac{3}{2}} \] is
If \( y = x^{x^{x^{.... \text{ad inf}}}} \), then prove that \( x\frac{dy}{dx} = \frac{y^2}{1 - y \log x} \).
Integrate: \( \int \left(\frac{2 + \sin 2x}{1 + \cos 2x}\right) e^x dx \)
If \( y = e^{\tan^{-1}x} \), prove that \( (1 + x^2)\frac{d^2y}{dx^2} + (2x - 1)\frac{dy}{dx} = 0 \).
The value of expression \( \hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} + \hat{k} \times \hat{k} \) is
100 ml of 10 M HCl is mixed with 75 ml of 10 M Na$_2$CO$_3$. The resulting solution would be –
Find the principal value of \( \sec^{-1}(-\sqrt{2}) \).
Answer the following questions in about 40 words each:
(a) Where did the squatters living in the periphery of Delhi come from?
Write IUPAC names of the following compounds:
(i)\; \includegraphics[height=10pt]{dummy} (ring with –CHO and adjacent –CH$_3$)
(ii)\; (CH$_3$)$_2$CHCOCH(CH$_3$)$_2$
(iii)\; CH$_3$CH(OCH$_3$)CHO
(iv)\; HOOC–(CH$_2$)$_4$–COOH
(v)\; \includegraphics[height=10pt]{dummy} (benzene–CH$_2$COOH)
Differentiate \( \tan^{-1}\left(\frac{\sin x}{1 + \cos x}\right) \) with respect to x.