JEE Advanced 1978 Question Paper with Solutions

A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. What is the tension in the rope at a distance l from the end where the force is applied?

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time lapse is t seconds, evaluate. (i) maximum velocity reached, and (ii) the total distance travelled.

One gram of an alloy of aluminium and magnetism when treated with excess of dil. HCl forms magnesium chloride, aluminium chloride and hydrogen. The evolved hydrogen, collected over mercury at 0 o C has a volume of 1.20 litres at 0.92 atm. pressure. Calculate the composition of the alloy. [H = 1, Mg = 24, Al = 27]

A compound was found to contain nitrogen and oxygen in the ratio 28 gm and 80 gm respectively. The formula of compound is

27 g of Al will react completely with how many grams if oxygen?

What weight of AgCl will be precipitated when a solution containing 4.77 g of NaCl is added to a solution of 5.77g of AgNO 3 ?

Igniting MnO 2 converts it quantitatively to Mn 3 O 4 . A sample of pyrolusite is of the following composition : MnO 2 80%, SiO 2 and other inert constituents 15%, rest being water. The sample is ignited in air to constant weight. What is the percentage of Mn in the ignited sample? [O = 16, Mn = 54.9]

One side of rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1).$ Find the equations of the other three sides.

Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.

Show that the square of $\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}$ is a rational number.

Solve the following equation for $x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$

If $\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n + 1}}} \right)} \over {\left( {1 - x} \right)\left( {1 - {x^2}} \right).........\left( {1 - {x^n}} \right)}}$ where $m$ and $n$ are positive integers $\left( {n \le m} \right),$ show that $\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$

From a point $O$ inside a triangle $ABC,$ perpendiculars $OD$ , $OE, OF$ are drawn to the sides $BC, CA, AB$ respectively. Prove that the perpendiculars from $A, B, C$ to the sides $EF, FD, DE$ are concurrent.

Balls are drawn one-by-one without replacement from a box containing $2$ black, $4$ white and $3$ red balls till all the balls are drawn. Find the probability that the balls drawn are in the order $2$ black, $4$ white and $3$ red.

Find the derivative of $\sin \left( {{x^2} + 1} \right)$ with respect to $x$ first principle.

Evaluate $\int {{{\sin x} \over {\sin x - \cos x}}dx}$