Two very long, straight and insulated wires are kept at \(90^o\) angle from each other In \(xy -\) plane as shown in the figure. These wires carry current of equal magnitude \(I\), whose directions are shown in the figure. The net magnetic field at point \(P\) will be

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :-

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).

A block of mass \(1.9\, kg\) is at rest at the edge of a table, of height \(1\, m\). A bullet of mass \(0.1\, kg\) collides with the block and sticks to it. If the velocity of the bullet is \(20\, m / s\) in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is \(....J\) [Take \(g =10\, m / s ^{2}\). Assume there is no rotational motion and loss of energy after the collision is negligable. \(]\)

If a wave gets refracted into a denser medium, then which of the following is true?

The logic operations performed by the given digital circuit is equivalent to:

A submarine \((A)\) travelling at \(18\, km/hr\) is being chased along the line of its velocity by another submarine \((B)\) travelling at \(27\, km/hr\). \(B\) sends a sonar signal of \(500\, Hz\) to detect \(A\) and receives a reflected sound of frequency \(v\). The value of \(v\) is close to ... \(Hz\) (Speed of sound in water \(= 1500\, ms^{-1}\))

The half-life of a radioactive substance is \(T\). The time taken, for disintegrating \(\frac{7}{8}\) th part of its original mass will be

If a curve \(y=y(x)\) passes through the point \(\left(1, \frac{\pi}{2}\right)\) and satisfies the differential equation \(\left(7 x^4 \cot y-e^x \operatorname{cosec} y\right) \frac{d x}{d y}=x^5, x \geq 1\), then at \(x=2\), the value of cosy is:

Two blocks (\(P\) and \(Q\)) with respectively masses \(2\) kg and \(1.5\) kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (\(S\)), as shown in the figure below. Block \(P\) is positioned on the top surface which has no friction and block \(Q\) is in contact with side-surface, having coefficient friction \(\mu\). The cube (\(S\)) moves towards the right with acceleration of \(\dfrac{g}{2}\), where \(g\) is gravitational acceleration. During this movement the block \(P\) and \(Q\) remain stationary. The value of \(\mu\) is _______. (take \(g = 10\) m/s\(^2\))

Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is \(0.7\; \mathrm{V} .\) For the input voltages shown in the figure, the voltage (in \(Volts\)) at point \(A\) is

If the functions are defined as \(f(x)=\sqrt{x}\) and \(g ( x )=\sqrt{1- x },\) then what is the common domain of the following functions: \(f+g, f-g, f / g, g / f, g-f\) where \((f \pm g)(x)=\) \(f(x) \pm g(x),(f / g)(x)=\frac{f(x)}{g(x)}\)

Let f: R→R be a twice differentiable function such that the quadratic equation \( f(x)m^{2}-2f^{\prime}(x)m+f^{\prime\prime}(x)=0 \) in m, has two equal roots for every \( x\in R \). If \( f(0)=1, f^{\prime}(0)=2 \) and \( (\alpha, \beta) \) is the largest interval in which the function \( f(\log_{e}x-x) \) is increasing, then \( \alpha+\beta \) is equal to: