List of practice Questions

In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
If 35 is removed from the data 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by
In which of the following species, the ratio of s-electrons to p-electrons is the same?
If \(\cos x + \cos y = \tfrac{2}{3}\) and \(\sin x - \sin y = \tfrac{3}{4}\), then \[ \sin(x - y) \;+\; \cos(x - y) \;=\;? \]
If R is the resistance of a conductor of length l, then
Among the oxides SiO\(_2\), SO\(_2\), Al\(_2\)O\(_3\), and P\(_2\)O\(_5\), the correct order of acidic strength is:
The power of a lens of focal length 20 cm is
Given below are two statements
Statement - I: For isothermal irreversible change of an ideal gas, \[ q = -w = P_{\text{ext}}(V_{\text{final}} - V_{\text{initial}}) \] Statement - II: For adiabatic change, \[ \Delta U = W_{\text{adiabatic}} \] The correct answer is:
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:
If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:

The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:

Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively

If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is: 

An ink mark is made on a piece of paper and a glass slab of thickness $t$ and refractive index $\mu$ is placed on it. If the image of the ink mark appears to be at a distance of $x$ from the top surface of the slab, then the value of $x$ is
Which of the following statements is correct for a spontaneous polymerization reaction?
If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?
The symmetric equation of the straight line passing through the points \( (-1, 4, 2) \) and \( (-3, 0, 5) \) is
The position vector of a particle of mass \(m\) moving with a constant velocity \(\mathbf{u}\) is given by \(\mathbf{r} = x(t)\hat{i} + b\hat{j}\), where \(b\) is a constant. At an instant, \(\mathbf{r}\) makes an angle \(\theta\) with the x-axis as shown in the figure. The variation of the angular momentum of the particle about the origin with \(\theta\) will be:
Ques Fig
A rectangular tank of depth 4 m is full of water of refractive index \(\frac 43\). When viewed from the top, the bottom of the tank is seen at a depth of
If \(v_1\) and \(v_2\) are the speeds of light in the two media of refractive indices \(n_1\) and \(n_2\) respectively, then
Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:
The pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) has a unique solution, then
On disSolution of a partnership firm, if realisation expenses are paid by the firm on behalf of a partner, then such expenses are debited to which of the following account:
The correct IUPAC name of the compound
IUP
is:
If a body is taken above the surface of the Earth, it loses its weight by 20% at a height of \( h = \frac{\sqrt{5}}{2} R \), where \( R \) is the radius of the Earth, then: