List of practice Questions

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 :

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 
Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :
s-block element which cannot be qualitatively confirmed by the flame test is
The boolean expression (~(p ∧q)) ∨q is equivalent to:
The conductivity of a solution of complex with formula CoCl3(NH3)4 corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is ______.
The integral \(∫_0^ 1 \frac{ 1}{7^{[\frac{1}{z}}]}dx\) where [⋅] denotes the greatest integer function, is equal to
The intermediate X, in the reaction is:
The intermediate X, in the reaction
The line y = x + 1 meets the ellipse \(\frac{x^2}{4}+\frac{y^2}{2}=1\) at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to

The major product of the following reaction contains ______ bromine atom(s).

Fig

The number of non-ionisable protons present in the product B obtained from the following reactions is__.
C2H5OH+PCl3→C2H5Cl+A
A+PCl3→B

The number of terminal oxygen atoms present in the product B obtained from the following reaction is ______.
FeCr2O4 + Na2CO3 + O2 → A + Fe2O3 + CO2
A + H+ → B + H2O + Na+
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.

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 ___.

The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF4, MnF3 and MnF2 is____ B.M. [nearest integer]

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

Vulcanization of rubber is carried out by heating a mixture of
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
Which of the following reagents/reactions will convert ‘A’ to ‘B’?
reagents/reactions
A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
A company dissolves \(‘X’\) amount of \(CO_2\) at \(298\ K\) in \(1\) litre of water to prepare soda water. \(X\) = _____ \(× 10^{–3}\) g. (nearest integer)
(Given: partial pressure of \(CO_2\) at \(298\ K = 0.835\) bar. Henry’s law constant for \(CO_2\) at \(298\ K = 1.67\) Kbar. Atomic mass of \(H\), \(C\) and \(O\) is \(1\), \(12\), and \(6\) g mol–1, respectively)
A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that\( \begin{array}{l}\angle PAO = \angle PBO = 15^\circ ~\text{and}~ \angle PCO = 45^\circ,\end{array}\)where C is the midpoint of AB. Then (OP)2 is equal to
A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s2 and then climbs up with an acceleration of 5 m/s2. Choose the correct option (g = 10 m/s2).
A small bulb is placed at the bottom of a tank containing water to a depth of √7 m. The refractive index of water is 4/3. The area of the surface of water through which light from the bulb can emerge out is xπ m2. The value of x is ________.
Amongst FeCl3.3H2O, K3[Fe(CN)6)] and [Co(NH3)6]Cl3, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is_______B.M. [nearest integer]