List of practice Questions

The function \(f(x) = 4 \sin^3 x - 6 \sin^2 x + 12 \sin x + 100\) is strictly

The co-ordinates of the point on the \(\sqrt{x} + \sqrt{y} = 6\) at which the tangent is equally inclined to the axes is

The function \(f(x) = \log(1+x) - \frac{2x}{2+x}\) is increasing on

If A_n = \(\begin{bmatrix} 1-n & n \\ n & 1-n \\ \end{bmatrix}\) then | A₁ | + | A₂ | + ….. + | A₂₀₂₁ | =

If \(y = x^{\sin(x)} + (\sin(x))^x\), then \(\left. \frac{dy}{dx} \right|_{x = \frac{\pi}{2}}\) is

If \(f(1) = 1, \quad f'(1) = 3\) then the derivative of \(f(f(f(x))) + (f(x))^2\) at \(x= 1\) is

If \(y =\)\(e^{\sqrt{x\sqrt{x\sqrt{x\ldots}}}}\) \(x>1,\) then \(\left. \frac{{d^2y}}{{dx^2}} \right|_{x = \log_e 3}\) is

If \(x = e^\theta \sin \theta, \quad y = e^\theta \cos \theta\), where \(θ\) is a parameter , then \(\left. \frac{dy}{dx} \right|_{(1,1)}\) is equal to

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

Domain of \(cos^{-1} [x]\), where \([. ]\) denotes a greatest integer function

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 ?