List of top Questions asked in MET- 2023

Light of wavelength \(2475\,\text{\AA}\) is incident on barium. Photoelectrons emitted describe a circle of radius \(100\,\text{cm}\) in a magnetic field of flux density \(\frac{1}{\sqrt{17}} \times 10^{-5}\) tesla. The value of work function of barium is _ _ _ _ _ eV. (Given \(e/m = 1.7 \times 10^{11}\))

The \(pK_a\) of acetic acid is \(4.74\). The concentration of \( \mathrm{CH_3COOH} \) is \(0.01\, M\). The pH of \( \mathrm{CH_3COOH} \) is _ _ _ _ _ .

Total number of \(2c-2e^{-}\) and \(3c-2e^{-}\) bonds present in diborane is _ _ _ _ _ .

A 5% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol\(^{-1}\)) in the same solvent. If densities of both solutions are \(1 \, \text{g cm}^{-3}\), the molar mass of the substance is _ _ _ _ _ .

Among \( \mathrm{Cu^{2+}}, \mathrm{Fe^{3+}}, \mathrm{Ti^{3+}} \) and \( \mathrm{Zn^{2+}} \) ions, the number of ions that impart colour is _ _ _ _ _ _ _

The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is _ _ _ _ _ .

Last two digits in \(9^{50}\) are _ _ _ _ _.

If \( A = \begin{bmatrix} 2 & -1 \\ -7 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 4 & 1 \\ 7 & 2 \end{bmatrix} \), then \( B^T A^T \) is:

If the vectors \( \vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k},\ \vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k} \) and \( \vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k} \) are coplanar, then the value of \(a\) is _ _ _ _.

If the foot of the perpendicular drawn from the point \((2,0,1)\) on a line passing through \((\alpha,5,1)\) is \(\left(\frac{7}{3}, \frac{5}{3}, \frac{11}{4}\right)\), then \(\alpha\) is equal to _ _ _ _ _ _

An unbiased coin is tossed \(n\) times. If the probability of getting 5 heads is equal to the probability of getting 6 heads, then the probability of getting 3 heads is:

If the lines \( \frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1} \) intersect, then \(k\) is equal to:

The area of the region bounded by the curves \( y = |5 - x| \), \( x = 1 \), \( x = 6 \) and the X-axis is:

The area bounded by the curves \( y = \tan x,\ -\frac{\pi}{3} \le x \le \frac{\pi}{3} \), \( y = \cot x,\ \frac{\pi}{6} \le x \le \frac{\pi}{2} \) and the X-axis is:

If \( \int f(x)\,dx = g(x) \), then \( \int \cos x \, f(\sin x)\,dx \) is equal to:

Set of values of \(x\) lying in \([0,2\pi]\) satisfying the inequality \( |\sin x|>2\sin^2 x \) contains:

If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \(x_1, x_2, \ldots, x_9\) is:

Let \(A = \{1,2,3,4,5,6,7\}\) and \(B = \{3,6,7,9\}\). Then, the number of elements in the set \(\{ C \subseteq A : C \cap B \neq \phi \}\) is:

The differential equation of all circles which pass through the origin and whose centres lie on Y-axis is:

If \( f : \mathbb{R} \to \mathbb{R} \) is a differentiable function and \( f(3) = 6 \), then \[ \lim_{x \to 3} \frac{\displaystyle \int_{6}^{f(x)} \frac{2t \, dt}{t - 2}}{x - 3} \text{ is equal to} \]

If \(a^2, b^2, c^2\) are in A.P., then \(b+c, c+a, a+b\) are in:

Which of the following reaction does not form benzaldehyde as product?