Class 12th

Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral ${\displaystyle \underset{0}{\overset{1}{\int }}\left[-8x^2+6x-1\right]dx}$  is equal to

The magnetic field at the centre of current carrying circular loop is B₁. The magnetic field at a distance of $\sqrt[]{3}$ times radius of the given circular loop from the center on its axis is B₂. The value of B₁/B₂ will be

Blocks of masses $m,2m$ and $8m$ are arranged in a line on a frictionless floor. Another block of mass $m$ , moving with speed $v$ along the same line (see figure) collides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8\mathrm{m}$ starts moving the total energy loss is $\mathrm{p}\mathrm{\%}$ of the original energy. Value of ' $p$ ' is close to:

Let A₁, A₂, A₃,…. be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = $\frac{1}{1296}$  and A₂ + A₄ = $\frac{7}{36},$  then, the value of A₆ + A₈ + A₁₀ is equal to

A triangular shaped wire carrying 10 A current is a uniform magnetic field of 0.5T, as shown in figure.

The magnetic force on segment CD is (Given BC = CD = BD = 5cm).

Given below are two statements:

Statement I : A uniform wire of resistance 80 $\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5 $\Omega .$

Statement II : Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3 : 2.

In the light of the above statements, choose the most appropriate answer from the option given below

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Starting from the origin at time $t=0$ , with initial velocity $5\hat{j}{\mathrm{m}\mathrm{s}}^{-1}$ , a particle moves in the $x$$-y$ plane with a constant acceleration of $(10\hat{i}+4\hat{j}){\mathrm{m}\mathrm{s}}^{-2}$ . At time $t$ , its coordinates are $(20$ $\left.m,y_{0}m\right)$ . The values of $t$ and $y_0$ are, respectively:

A uniform electric field E = (8m/e) V/m is created between two parallel plate of length 1m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation ( θ) of the path of the electron as it comes out of the field will be________.

Let A be matrix of order 3 * 3 and det(A) = 2. Then $det\left(det\left(A\right)adj\left(5adj\left(A^3\right)\right)\right)$ is equal to