List of practice Questions

The maximum value of $z = 3x + 4y$ subject to the condition $x + y \le 40, x + 2y \le 60, x,y \ge 0$ is
The maximum value of $z = 5x + 3y$, subjected to the conditions $3x + 5y \le 15, 5x + 2y \le 10, x, y \ge 0$ is
A barbituric acid derivative drug Veronal is used as
Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat costs ? 4 per kg and rice ? 6. The minimum daily requirements of proteins and carbohydrates for an average child are 50 g and 200 g respectively. Then in what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirement of proteins and carbohydrates at minimum cost
A bar magnet of moment M is bent into are, its moment
A bar of cross-section area A is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane $BB'$ making an angle $\theta$ with the length.
The ratio of tensile stress to the shearing stress on the plane $BB'$ is
A bar magnet of magnetic moment 1.5 J/T is aligned with the direction of a uniform magnetic field of 0.22 T. The work done in turning the magnet so as to align its magnetic moment opposite to the field and the torque acting on it in this position are respectively.
A bandwidth of $5 \,MHz$ is available for AM transmission. If the maximum audio signal frequency used for modulating the carrier is not to exceed $5\, kHz$, how many stations can be broadcasted within this band simultaneously without interfering with each other?
A bar magnet is released from rest along the axis of a very long, vertical copper tube.After some time the magnet
A bar magnet of length 10cm and pole strength 2 Am makes an angle $60^{\circ}$ with a uniform malefic field of induction 50T . The couple acting on it is.
A ball $P$ is dropped vertically and another ball $Q$ is thrown horizontally with the same velocities from same height and at the same time. If an resistance is neglected, then
A ball is travelling with uniform translatory motion. This means that
A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$ . An elastic impact lasts for a time $\Delta t$ .
A ball is thrown from the top of a tower with an initial velocity of $10\,ms^{-1}$ at an angle of $30^?$ with the horizontal. If it hits the ground at a distance of $17.3\,m$ from the base of the tower, the height of the tower is (Take $g= 10\,m s^{-2}$)
A biconvexlens is cut intotwo equal parts by a plane perpendicular to the principal axis. If the power of the original lens is $4 D$, the power of a cut lens will be
In a laboratory four convex lenses $L_1 L_2, L_3$ and $L_4$ of focal lengths $2, 4, 6$ and $8$ cm, respectively are available. Two of these lenses from a telescope of length $10$ cm and magnifying power $4$. The objective and eye lenses are respectively
The refractive index of glass is $1.520$ for red light and $1.525$ for blue light. Let $D_1$, and $D_2$ be angles of minimum deviation for red and blue light respectively in a prism of this glass then,
A particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
Mercury boils at $367^{\circ}C$. However, mercury thermometers are made such that they can measure temperature upto $500^{\circ}C$. This is done by
A ball is dropped on to the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 seconds, what is the average acceleration during contact? (Take $g = 10\, m \,s^{-2}$ )
A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{ml^2}{3}$ the initial angular acceleration of the rod will be
A wheel has angular acceleration of $3.0 \,rad/s^2$ and an initial angular speed of $2.00 \,rad/s$. In a time of $2\, s$ it has rotated through an angle (in radian) of
A ball is dropped from height $10\, m$. It is embedded in sand $1m$ metre and stops.
A ball is dropped from a height of 20 cm. Ball rebounds to a height of 10 cm. What is the loss of energy?
A stone is dropped into a lake from a tower $500 \,m$ high. The sound of the splash will be heard by a man on the tower after: [Assume speed of sound $\left.=330\, m / s ; g =10 \,m / s ^{2}\right]$