List of practice Questions

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x² – 2x and g(f(x)) = 4x² + 6x + 1, then the value of f(2) + g(2) is ____________ .

Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 3, 4, 5}. If the sum of all the entries of A is a prime number p, \(2 < p < 8\), then the number of such matrices A is ___________.

A chemical which stimulates the secretion of pepsin is

Let
\(f(x) = \begin{vmatrix} a & -1 & 0\\ ax & a & -1\\ ax^2 & ax & a \end{vmatrix}\)
a ∈ R. Then the sum of the square of all the values of a, for which 2f′(10) –f′(5) + 100 = 0, is

Match List-I with List-II :

List-I	List-II
(A) Negatively charged sol	(I) Fe₂O₃.xH_2O
(B) Macromolecular colloid	(II) CdS sol
(C) Positively charged sol	(III) Starch
(D) Cheese	(IV) a gel

Choose the correct answer from the options given below:

Among the following, basic oxide is:

The activation energy of one of the reactions in a biochemical process is 532611 J mol^–1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k₃₀₀ = x × 10^–3 k₃₁₀. The value of x is ______.

[Given: ln10 = 2.3, R = 8.3 JK^–1 mol^–1]

The area enclosed by the curves

\(\begin{array}{l} y=\text{log}_e\left(x+e^2\right),\ x=\text{log}_e\left(\frac{2}{y}\right)\text{ and }x=\text{ log }_e\ 2,\end{array}\)

above the line y = 1 is

An element A of group1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is:

Amongst the following, the major product of the given chemical reaction is

Amongst the following, the major product of

An antiseptic Dettol is a mixture of two compounds ‘A’ and ‘B’ where A has 6π electrons and B has 2π electrons. What is ‘B’?

Which of the following reagents/reactions will convert ‘A’ to ‘B’?

s-block element which cannot be qualitatively confirmed by the flame test is

Let ƒ R ⇒ R be a function defined by

Let ƒ : R ⇒ R be a function defined by

where [t] is the greatest integer less than or equal to t. Let m be the number of points where ƒ is not differentiable and

Then the ordered pair (m, I) is equal to :

The intermediate X, in the reaction is:

The boolean expression (~(p ∧q)) ∨q is equivalent to:

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

A pressure-pump has a horizontal tube of cross sectional area \(10 cm^2 \) for the outflow of water at a speed of \(20 m/s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is

[given: density of water = \(1000 kg/m^3\)].

Let \([t]\) denote the greatest integer less than or equal to \(t\). Then, the value of the integral \(∫_0^1 [ -8x^2 + 6x - 1] dx\) is equal to

In the following nuclear reaction,
\(D \stackrel{α}{⟶} D1 \stackrel{β^-}{⟶} D2 \stackrel{α}{⟶} D3 \stackrel{γ}{⟶} D4\)
Mass number of D is 182 and atomic number is 74. Mass number and atomic number
of D_4, respectively, will be _____.

The positive value of the determinant of the matrix A, whose
\(\text{Adj}(\text{Adj}(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}\)
is ___.

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.

We do not transmit low frequency signal to long distance because-
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength
(b) Effective power radiated by a long wavelength baseband signal would be high
(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously
(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well
Therefore, the most suitable option will be

A rolling wheel of \(12\) kg is on an inclined plane at position P and connected to a mass of \(3\) kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.
The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be \(\frac{1}{2}\sqrt{ xgh}\) \(m/s\). The value of x is _________.

The integral \(∫_0^ 1 \frac{ 1}{7^{[\frac{1}{z}}]}dx\) where [⋅] denotes the greatest integer function, is equal to