List of practice Questions

If the vectors $ \overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k} $ and $ \overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k} $ are coplanar, then the value of $\lambda$ is equal to

$ \int{({{\sin }^{6}}x+{{\cos }^{6}}x+3{{\sin }^{2}}x \,{{\cos }^{2}}x)}dx $ is equal to

Let $a, a + r$ and $a + 2r$ be positive real numbers such that their product is $64$. Then the minimum value of $a + 2r$ is equal to

The derivative of $ {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) $ with respect to $ {{\sin }^{-1}}(3x-4{{x}^{3}}) $ is

$ \int{\frac{{{x}^{3}}\sin [{{\tan }^{-1}}{{(x)}^{4}}]}{1+{{x}^{8}}}}dx $ is equal to:

If $x_1$ and $x_2$ are the roots of $3x^2 - 2x - 6 = 0$, then $x_1^2 + x_2^2$ is equal to

Amitosis usually occurs in

The magnetic field of earth at the equator is approximately $4 \times 10^{-5} \, T$. The radius of earth is $6.4 \times 10^6 \, m$. Then the dipole moment of the earth will be nearly of the order of:

The vapour pressure of a solvent at 293 K is 100 mm Hg. Then the vapour pressure of a solution containing 1 mole of a strong electrolyte $(AB_2)$ in 99 moles of the solvent at 293 K is (assume complete dissociation of solute)

For a particle, acceleration-time graph gives the velocity. Rate of change of velocity is acceleration.

If $x=exp\left\{tan^{-1}\left(\frac{y-x^{2}}{x^{2}}\right)\right\}$, then $\frac{dy}{dx}$ equals

If A and B are square matrices of the same order such that \(AB=BA\),then prove by induction that \(AB^n=B^nA\).Further, prove that \((AB)^n=A^nB^n\) for all \(n∈N\)

Water is flowing through a horizontal pipe in stream line flow at the narrowest part of the pipe?

The height from earth's surface at which acceleration due to gravity becomes g/ where g is acceleration due to gravity on the surface of earth and R is radius of earth?

$ \displaystyle\lim_{x \to 1} [x -1]$, where [.] is greatest integer function, is equal to

Express the following as the sum of two odd primes.

1. 44
2. 36
3. 24
4. 18

The mass of 112 $cm^3$ of $CH_4$ gas at STP is

If p is the hole concentration, n is the electron concentration and ni is the intrinsic concentration then at thermal equilibrium, then the mass action in semiconductors states that

Boolean Identity (A→ + B→).(A +B) is equal to

If a x b and c x d are perpendicular satisfying a.c = λ, b.d = λ (λ>0) and a.d = 4, b.c = 9, then λ is equal to:

Who has zero dipole moment?

atomic mass unit is____.

Two identical metal block with charges +2Q and -Q are separated by some distance, and exert a force F on each other. The force between them then will be.

Products when H₂SO₄ is reacted with sucrose