Mathematics Tes...

A \(1 \mathrm{~kg}\) block is resting on a surface with coefficient of friction \(0.1\). A force of \(0.8 \mathrm{~N}\) is applied to the block as shown in figure. The friction force is:

A force F is acting on a bent bar that is clamped at one end as shown in the figure.

Two like parallel forces are acting at a distance of \(30 \mathrm{~mm}\) apart and their resultant is \(60 \mathrm{~N}\), if the line of action of the resultant is \(10 \mathrm{~mm}\) from one of the forces, the two forces are:

If x, y, z are three consecutive positive integers, then log (1+x z) is:

What is the value of \(\lambda\) for which the vectors \(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(-\hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) are perpendicular?

A man can swim with a speed of \(4.0 \mathrm{~km/h}\) in still water. How long does he take to cross a river \(1.0 \mathrm{~km}\) wide if the river flows steadily at \(3 \mathrm{~km/h}\) and he makes his strokes normal to the river current? How far does he go in the river when he reaches the other bank of the river?

In a GP consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the GP is:

Find the equation of the tangent to the ellipse x² + 2y² = 4 at the point where ordinate is 1 such that point lies in the first quadrant?

If \(y=x^{\frac{1}{ 3}}\) then \(\frac{d y}{d x}=?\)