List of practice Questions

The radical axis of the circles \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] and \[ 2x^2 + 2y^2 + 3x + 8y + 2c = 0 \] touches the circle \[ x^2 + y^2 + 2x + 2y + 1 = 0. \] Then:
The equation of a circle which touches the straight lines \[ x + y = 2, \quad x - y = 2 \] and also touches the circle \[ x^2 + y^2 = 1 \] is:
The plane 𝑧=0 separates two linear dielectric media with relative permittivities 𝜀𝑟1=4 and 𝜀𝑟2=3, respectively. There is no free charge at the interface. If the electric field in the medium 1 is 𝐸⃗ 1=3𝑥̂+2𝑦̂ +4𝑧̂, then the displacement vector \(\overrightarrow{D_2}\) in medium 2 is: (𝜀0 is the permittivity of free space)
The number of cytosine molecules in a typical ds DNA molecule which is having 20 coils with 480 Hydrogen bonds.
If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are position vectors of 4 points such that \( 2\vec{a} + 3\vec{b} + 5\vec{c} - 10\vec{d} = 0 \), then the ratio in which the line joining \( \vec{c} \) divides the line segment joining \( \vec{a} \) and \( \vec{b} \) is:
A square shaped aluminium coin weighs 0.75 g and its diagonal measures 14 mm. It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges (+Q and -Q) that are separated by a distance equal to the side of the coin, the dipole moment of the dipole is:
The electrostatic potential energy of the electron in an orbit of hydrogen is \( -6.8 \) eV. The speed of the electron in this orbit is (C is the speed of light in vacuum):
Which one of the following corresponds to the wavelength of line spectrum of H atom in its Balmer series? (R = Rydberg constant)
The current passing through a coil of 120 turns and inductance \( 40 \) mH is \( 30 \) mA. The magnetic flux linked with the coil is:
A flask contains 98 mg of H₂SO₄. If \( 3.01 \times 10^{20} \) molecules of H₂SO₄ are removed from the flask, the number of moles of H₂SO₄ remaining in the flask is (\( N = 6.02 \times 10^{23} \)):
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange’s Mean Value Theorem is not applicable.
P is a point on \( x + y + 5 = 0 \), whose perpendicular distance from \( 2x + 3y + 3 = 0 \) is \( \sqrt{13} \), then the coordinates of P are:
A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.
Alternative_Text
The final compound formed when methane reacts with chlorine in the presence of sunlight is
If \( O(0, 0, 0), A(3, 0, 0), B(0, 4, 0) \) form a triangle then the incenter of triangle OAB is:
The capacitance of a parallel plate capacitor is 400 pF. It is connected to an ac source of 100 V having an angular frequency 100 rad s$^{-1}$. If the rms value of the current is 4 μA, the displacement current is:
What will come in place of the question mark (?) in the equation \( 38^2 + 63^2 + (?)^2 = 6089 \) ?
In Kolbe's electrolysis of sodium propanoate, products formed at anode and cathode are respectively:
Suppose the axes are to be rotated through an angle \( \theta \) so as to remove the \( xy \) term from the equation \(3 x^2 + 2\sqrt{3}xy + y^2 = 0 \). Then in the new coordinate system, the equation \( x^2 + y^2 + 2xy = 2 \) is transformed to:
A 4 kg stone is attached to a steel wire being whirled at a constant speed of \( 12 \) m/s in a horizontal circle. The wire is 4 m long with a diameter of 2 mm, and Young’s modulus is \( 2 \times 10^{11} \) Nm\(^2\). The strain in the wire is:
Polar covalent bond present in
For a $30^\circ$ prism, when a ray of light is incident at an angle $60^\circ$ on one of its faces, the emergent ray passes normal to the other surface. Then the refractive index of the prism is:
If \(540^\circ<A<630^\circ\) and \(|\cos A| = \frac{5}{13}\), then \( \tan\frac{A}{2} \tan A =\)
Match the transport infrastructure described in Column I, with their names and locations in Column II.
transport infrastructure described

Which of the following tasks is NOT a part of the job of an architect?