List of practice Questions

If \(y = (1+x^2) \tan^{-1}(x) - x\). Then \(\frac{dy}{dx}\) is

If the vertices of triangle are (-2,6), (3,-6) and (1,5), then the area of the triangle is

If there are two values of ‘a’ which makes determinant
\(\Delta=\begin{bmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \\ \end{bmatrix}=86\)
Then the sum of these numbers

If A is a 3x3 Matrix such that \(|5 \cdot \text{adj}(A)| = 5, \text{ then } |A|\) is equal to

If A = \(\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}\) then \((aI + bA)^n\) is (where I is the identity matrix of order 2)

If A=\([\begin{smallmatrix} 2 & -1 \\ 3 & -2 \end{smallmatrix}]\) ,then the inverse of the matrix A³ is

If A is matrix of order 3x3, then \((A^2)^{-1}\) is equal to

\(\lim_{{y \to 0}} \frac{\sqrt{3} + y^3 - \sqrt{3}}{y^3}\)

If \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x) = \begin{cases}  2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases}\). Then \(f(-1) + f (2) + f(4)\) is

If the set x contains 7 elements and set y contains 8 elements, then the number of bijections from x to y is

If the standard deviations of the numbers - 1, 0, 1, K is \(\sqrt5\), where \(k>0\), then k is equal to

If 3x + i(4x-y) = 6-i, where x and y are real numbers, then the value of x and y are respectively

The octant in which the point (2,-4,-7) lies is

If the straight line 2x-3y+17 = 0 is perpendicular to the line passing through the points (7,17) and (15,β), then β equals

If \(a_1, a_2, a_3, \ldots, a_{10}\) is a geometric progression and \(\frac{a_3}{a_1} = 25\) then \(\frac{a_9}{a_5}\) equals

If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning, which one of the following is 19th word ?

In Kolbe's reaction the reacting substances are

An organic compound with molecular formula C₇H₈O dissolves in NaOH and gives a characteristic colour with FeCl₃. On treatment with bromine, it gives a tribromo derivative C₇H₅OBr₃. The compound is

Identify the products A and B in the reactions: \(R-X + AgCN \longrightarrow A + AgX\)  \(R-X + KCN \longrightarrow B+ KX\)

Among the following product the products formed by the reaction of anisole with HI are

The major product obtained when ethanol is heated with excess of conc. \(H_2SO_4\) at 443 K is

All Cu(II) halides are known, except ithe iodide, the reason for it is that

In the following pairs of halogen compounds, which compound undergoes SN¹ reaction?

The Complex hexamine platinum (IV) chloride will give ___ number of ions on ionization

\((NH_4)_2Cr_2O_7\) on heating liberates a gas. The same gas will be obtained by