List of top Questions asked in MET- 2022

If the lines \( \frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k} \) and \( \frac{x-1}{2k} = \frac{y-3}{2} = \frac{z-5}{1} \) are coplanar, then \( k \) can have

If \[ \begin{vmatrix} a & a^2 & 1+a^3 b & b^2 & 1+b^3 c & c^2 & 1+c^3 \end{vmatrix} = 0 \] and vectors \( (1,a,a^2), (1,b,b^2), (1,c,c^2) \) are non-coplanar, then the product \( abc \) is ___.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is \( p \), then \( 96p \) is equal to ___.

A multiple choice examination has 5 questions. Each question has 4 alternatives of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is

If the foot of the perpendicular drawn from the point \( (0,2,1) \) on a line passing through \( (a,5,1) \) is \( \left(\frac{5}{3}, \frac{7}{3}, \frac{15}{3}\right) \), then \( a \) is equal to ___.

The area of the region described by \( A = \{(x,y) : x^2 + y^2 \le 1 \text{ and } y^2 \le 1 - x \} \) is

The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and the x-axis is

If \( \int f(x)\,dx = g(x) \), then \( \int x^9 f(x^5)\,dx \) is equal to

For what value of \( \theta \) lying between \(0\) and \( \pi \) which satisfy inequality \( \sin\theta \cos^3\theta>\sin^3\theta \cos\theta \)

Let \( f(x) = \sqrt{1 + x^2} \), then

If \( A \) is an \( n \times n \) non-singular matrix such that \( AA^T = A^{-1}A \) and \( B = A^{-1}A^T \), then \( BB' \) is equal to

If \( A = \{1,2\}, B = \{1,2,3,4\}, C = \{5,6\}, D = \{5,6,7,8\} \), then state which of the following is true?

If \( \sum_{i=1}^{10} (x_i - 3) = 7 \) and \( \sum_{i=1}^{10} (x_i - 3)^2 = 27 \), then the standard deviation of the 10 items is

\( \lim_{x \to 2} \frac{x^2 + 2^2 - 5}{2^{x-2} - 2} \) is equal to ____

The value of \( \lim_{x \to 0} \frac{\int_0^{x^2} \sec^2 t \, dt}{x \sin x} \) is

The differential equation of all circles passing through the origin and having their centre on the X-axis is

The coefficient of the middle term in the binomial expansion in powers of \( x \) of \( (1 + \alpha x)^4 \) and \( (1 - \alpha x)^6 \) is the same, if \( \alpha \) is equal to

If \( \alpha, \beta, \gamma \) are in AP and \( \tan^{-1}\alpha, \tan^{-1}\beta, \tan^{-1}\gamma \) are also in AP, then

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is

If \( \left| z + \frac{2}{z} \right| = 2 \), then the minimum value of \( |z| \) is

Polystyrene is a ___ polymer whereas dacron is a ___ polymer.

In the following sequence of reactions, the compound \( C \) formed would be \[ CH_3CH_2CONH_2 \xrightarrow{LiAlH_4} A \xrightarrow{HNO_2} B \xrightarrow{CrO_3} C \]

Out of the given compounds, the number of compounds which are weaker acids than benzoic acid are

Alcoholic group of which position in the given molecule reacts fastest with Lucas' reagent?

Select the correct statement.