List of practice Questions

If one of the roots of the quadratic equation $ax^2 - bx + a = 0$ is $6$, then value of $\frac{ b}{ a}$ is equal to

If $ {{x}^{2}}-px+q=0 $ has the roots $ \alpha $ and $ \beta $ then the value of $ {{(\alpha -\beta )}^{2}} $ is equal to

If $a + 1, 2a + 1, 4a - 1$ are in arithmetic progression, then the value of $a$ is

Which of the following statement is INCORRECT

A metallic rod of length 4 m is rotating about perpendicular bisector of the rod with angular velocity of 2 rad/s in presence of transverse magnetic field of 0.5 T. Potential difference developed across ends of rod is

Two tangent galvanometers $A$ and $B$ have coils of radii $8 \,cm$ and $16\, cm$ respectively and resistance $ 8\,\Omega $ , each. They are connected in parallel with a cell of emf $4\, V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $ 30{}^\circ $ and $ 60{}^\circ $ respectively. If $A$ has $2$ turns, then $B$ must have

In the Wheatstone's network given, $ P=10\,\Omega , Q=20\,\Omega ,\,R=15\,\Omega , S=30\,\Omega , $ the current passing through the battery (of negligible internal resistance) is

A uniform heavy rod of length L and area of cross section 'A' is hanging from a fixed support. It young's modulus of the material of the rod is Y, the increase the length of rod is ( p is density of the mateiral of the rod)

Instantaneous current in a circuit is \(i(t)=[6+\sqrt54sin(2\pi + \pi/3)]\) A RMS value of current is

A research satellite of mass 200 kg circles the earth in an orbit of average radius $\frac{3R}{2}$ where R is the radius of earth. Assuming the gravitatioaal pull on a mass of 1 kg on the earth's surface to be 10 N, the puII on the sateIlite will be

A bullet is fired from a gun. The force on the bullet is given by $ F=600-2\times {{10}^{5}}t, $ where F is in newton and t is in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

The number of real solution x|x + 5| + 2|x + 7| - 2 = 0 is

A fighter aircraft is looping in a vertical plane. The minimum velocity at the highest point is (Given, r = radius of the loop)

How many of the following have zero dipole moment $H_2S, CH_4, NH_3, BF_3, SO_2, NF_3$

In an atom, how many electrons can have
(i) n = 4 (ii) m1 =1 (iii) ms = ½

Equanil drug is used for which disease?

Shortest wavelength in Lyman series has wavelength of 915 À. Longest wavelength of Balmer series has a value of ?

A truck is moving from rest with constant power P. if the displacement of the truck is proportional to t", where t is time, find n.

Which postulate of Dalton's theory is wrong

Arrange the following carbocations in increasing order of their stability.
I) \((CH_3)_3C^{\oplus}\)
II) \((CH_3)_2\overset{{\oplus}}{C}H\)
III) \(\overset{{\oplus}}{C}H_3\)
IV) \(CH_3\overset{{\oplus}}{C}H_2\)

Sum of O atoms in A and B is ?

In sonometer, fundamental frequency changes from 400 Hz to 500 Hz keeping same tension. Find percentage change in length.

For what boolean values of A, B & C the given logic gate gives output of zero?

In group A there are 4 men and 5 women and in group B there are 5 men and 4 women, if 4 people are selected from each group. Find a number of ways to select 4 men and 4 women.

If $f(x)= x^5 + 2x^3 + 3x + 1$ and $g(f(x)) = x,$ then $\frac{g(1)}{g’(1)}$ is equal to