List of practice Questions

If the length of the latus rectum of the ellipse x² + 4y² + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, 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 _________.

A metallic rod of length \(20\) cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth’s magnetic field at that place is \(4 × 10^{–3}\) T and the angle of dip is \(45º\). The emf induced in the rod is __________mV.

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

Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: \(Mn = 25; Fe = 26\))
(1) \([FeF_6]^{3–}\)
(2) \([Fe(CN)_6]^{3–}\)
(3) \([MnCl_6]^{3–}\)(high spin)
(4) \([Mn(CN)_6]^{3–}\)

Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is,
Given : Atomic masses of C, H and N are 12, 1 and 14 amu, respectively.
The molar mass of the compound A is 162g mol^–1.

17.0 g of NH₃ completely vapourises at – 33.42°C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol^–1. The enthalpy change for the vapourisation of 85 g of NH₃under the same conditions is ____ kJ.

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

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 :