List of practice Questions

The structure shown below is of which well-known drug molecule?

In the flame test of a mixture of salts, a green flame with blue centre was observed. Which one of the following cations may be present?

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for the coefficient of viscosity is

The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, is

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:
(Given : relative permeability of medium μ_r= 1)

The ratio for the speed of the electron in the 3^rd orbit of He⁺ to the speed of the electron in the 3^rd orbit of hydrogen atom will be :

Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is

The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because:

The difference of speed of light in the two media A and B(υ_A – υ_B) is 2.6 × 10⁷ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: speed of light in vacuum C = 3 × 10⁸ms^–1)

\(f(x) = \begin{cases} \frac{sin(x-|x|)}{x-|x|} & \quad {x \in(-2,-1) } \\ max{2x,3[|x|]}, & \quad \text{|x|<1}\\1 & \quad \text{,otherwise} \end{cases}\) Where [t] denotes greatest integer t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is

A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for \(\frac 13\) deflection in the galvanometer. Which of the below is true for measuring value of G?

Let a circle C touch the lines L₁ : 4x – 3y +K₁ = 0 and L₂ : 4x – 3y + K₂ = 0, K₁, K₂∈R. If a line passing through the centre of the circle C intersects L₁ at (–1, 2) and L₂ at (3, –6), then the equation of the circle C is :

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P(–2, 0) and cuts the y-axis at the point Q, where y′ is equal to 3. Then the local maximum value of y(x) is

The area of the region given by A={(x,y); \(x^2\)≤y≤min{x+2,4−3x}} is

Let \(ƒ : R→R\) be defined as \(ƒ(x) = x^3 + x – 5\) . If g(x) is a function such that \(ƒ(g(x)) = x\), ∀‘x‘∈R. Then \(g^′(63)\) is equal to_____.

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is –

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below

If ρ is the density and η is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R_e is:

The slope of the tangent to a curve C: y = y(x) at any point (x, y) on it is \(\frac{2e^{2x}-6e^{-x}+9}{2+9e^{-2x}}\).If C passes through the points (0,\(\frac{1}{2}\)+\(\frac{\pi}{2\sqrt2}\)) and (α,\(\frac{1}{2e^{2\alpha}}\)), then e^α is equal to

A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as \(v_2\)=\(\frac {n}{m^2}\)\(v_1\) and \(a_2\)= \(\frac {a1}{mn}\) respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

Let the locus of the centre (α, β), β> 0, of the circle which touches the circle x² +(y – 1)² = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:

If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:

Let \(ƒ(x)\) be a polynomial function such that \(ƒ(x) + ƒ^′(x) + ƒ^{′′}(x) = x^5 + 64\). Then, the value of \(\lim\limits_{x \to 1}\frac {f(x)}{x−1}\) is equal to :