List of practice Questions

A straight wire of resistance \(R\) is bent in the shape of a square. A cell of emf 12 V is connected between two adjacent corners of the square. The potential difference across any diagonal of the square is:
If \( 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots \) (n terms) = \( n(n + 1)f(n) - 3n \), then \( f(1) = \):
The equation of the circle touching the circle $$ x^2 + y^2 - 6x + 6y + 17 = 0 $$ externally and to which the lines $$ x^2 - 3xy - 3x + 9y = 0 $$ are normal is: 
If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
If \[ \cos x \frac{dy}{dx} - y \sin x = 6x, \quad (0<x<\frac{\pi}{2}) \quad {and} \quad y(\frac{\pi}{3}) = 0, \quad {then} \quad y(\frac{\pi}{6}) = \]
Identify the correct equation relating \( \Delta H \), \( \Delta U \), and \( \Delta T \) for 1 mole of an ideal gas (R = gas constant):
Given below are two statements: I. Cytosine and guanine are formed in equal quantities in DNA hydrolysis.
II. Adenine and uracil are formed in equal quantities in RNA hydrolysis. The correct answer is:
What are X and Y respectively in the following reactions? \includegraphics[]{159.png}
If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then \( f'(2) \) is:
When a wave enters into a rarer medium from a denser medium, the property of the wave which remains constant is:
The capacitance of an isolated sphere of radius \( r_1 \) is increased by 5 times when enclosed by an earthed concentric sphere of radius \( r_2 \). The ratio \( \frac{r_1}{r_2} \) is:
If \( A = (1,2,3), B = (3,4,7) \) and \( C = (-3,-2,-5) \) are three points then the ratio in which the point C divides AB externally is
Which physical quantity is measured in barn?
Let \( A \) be a \( 4 \times 4 \) matrix and \( P \) be its adjoint matrix. If \( |P| = \left| \frac{A}{2} \right| \), then \( |A^{-1}| = ? \)
If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):
0.1 mole of potassium permanganate was heated at 300°C. What is the weight (in g) of the residue?
In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, \( \Delta = \frac{\sqrt{3}}{2} \) and \( r_1 r_2 = r_3 r \), then \( R \) is:
The length of x-intercept made by the pair of lines \( 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 \) is:
Equation of the normal to the curve \( y = x^2 + x \) at the point \( (1,2) \) is:
Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]
Match the complexes in list-I with their hybridization in list-II.
complexes in list-I with their hybridization
Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots \text{n times}) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)

If the line segment joining the points \( (1,0) \) and \( (0,1) \) subtends an angle of \( 45^\circ \) at a variable point \( P \), then the equation of the locus of \( P \) is: 

The correct order of bond angles of the molecules \( SiCl_4 \), \( SO_3 \), \( NH_3 \), \( HgCl_2 \) is:

200 g of water is heated from 40°C to 60°C. The change in its internal energy [No expansion is taken place] specific heat of water is 4200 J kg⁻¹ K⁻¹