List of top Questions asked in MET- 2014

The distance of the point (3, 5) from $2x + 3y -14 = 0$ measured parallel to $x - 2y = 1$ is
In a triangle, the lengths of two larger sides are 10 cm and 9 cm. If the angles are in AP, then the third side is
If \( a\cos^3\alpha + 3a\cos\alpha\sin^2\alpha = m \) and \( a\sin^3\alpha + 3a\cos^2\alpha\sin\alpha = n \), then \( (m+n)^{2/3} + (m-n)^{2/3} \) is equal to
If \( \tan \frac{\alpha}{2} \) and \( \tan \frac{\beta}{2} \) are the roots of \( 8x^2 - 26x + 15 = 0 \), then \( \cos(\alpha + \beta) \) is
If the term free from \( x \) in the expansion of \( \left(\sqrt{x} - \frac{k}{x^2}\right)^{10} \) is 405, then the value of \( k \) is
Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is
\( S = \{1,2,3,\dots,20\} \) is to be partitioned into four sets \( A, B, C, D \) of equal size. The number of ways is
A circle of radius 2 is touching both the axes and a circle with centre (6, 5). The distance between their centres is
The variance of first $n$ natural numbers is
10 different toys are to be distributed among 10 children such that exactly two children do not get any toy. Total number of ways is
The common tangent of the parabolas $y^2 = 4x$ and $x^2 = -8y$ is
Middle term in the expansion of $\left(x^2 + \frac{1}{x^2} + 2\right)^n$ is
If \( 1, \omega, \omega^2, \ldots, \omega^{n-1} \) are \( n \)th roots of unity, then the value of \( (9-\omega)(9-\omega^2)\cdots(9-\omega^{n-1}) \) is
If \( a = \cos \frac{2\pi}{7} + i \sin \frac{2\pi}{7} \), then the quadratic equation whose roots are \( \alpha = a + a^2 + a^4 \) and \( \beta = a^3 + a^5 + a^6 \) is
Which of the following best define the term hyperconjugation?
Which of the following is the strongest base?
Valence electrons in the element A are 3 and that in element B are 6. Most probable compound formed from A and B is
The dominant factor in determining the IE of the elements on moving down the groups is
Which pair is different from the others?
The complex [Fe(H\(_2\)O)\(_5\)NO]\(^{2+}\) is formed in the ring test for nitrate ion. This complex is formed by charge transfer in which
Out of the following redox reactions, \[ \text{I. NH}_4\text{NO}_3 \xrightarrow{\Delta} \text{N}_2\text{O} + 2\text{H}_2\text{O} \] \[ \text{II. NH}_4\text{NO}_2 \xrightarrow{\Delta} \text{N}_2 + 2\text{H}_2\text{O} \] \[ \text{III. PCl}_5 \xrightarrow{\Delta} \text{PCl}_3 + \text{Cl}_2 \] Disproportionation is not shown in
Strongest conjugate base is
Baking powder is more commonly used to make cakes or bread “rise”. Filler in baking powder is
The activity of alkaline earth metals as reducing agent
Which of the following phosphorus is the most reactive?