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IIT JEE 1981
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47
Duration
180 mins
Package
IIT-JEE Advance - Previous Year Papers
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47questions
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25
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19
40.4%
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3
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47questions
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PYP
IIT JEE 1981
When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the direction of his motion.
PYP
IIT JEE 1981
For every integer n > 1, the inequality $${(n!)^{1/n}} < {{n + 1} \over 2}$$ holds.
PYP
IIT JEE 1981
Let $$\overrightarrow A ,\overrightarrow B $$ and $${\overrightarrow C }$$ be unit vectors suppose that $$\overrightarrow A .\overrightarrow B = \overrightarrow A .\overrightarrow C = 0,$$ and thatthe angle between $${\overrightarrow B }$$ and $${\overrightarrow C }$$ is $$\pi /6.$$ Then $$\overrightarrow A = \pm 2\left( {\overrightarrow B \times \overrightarrow C } \right).$$
PYP
IIT JEE 1981
For complex number $${z_1} = {x_1} + i{y_1}$$ and $${z_2} = {x_2} + i{y_2},$$ we write $${z_1} \cap {z_2},\,\,if\,\,{x_1} \le {x_2}\,\,and\,\,{y_1} \le {y_2}.$$
Then for all complex numbers $$z\,\,with\,\,1 \cap z,$$ we have $${{1 - z} \over {1 + z}} \cap 0.$$
Then for all complex numbers $$z\,\,with\,\,1 \cap z,$$ we have $${{1 - z} \over {1 + z}} \cap 0.$$
PYP
IIT JEE 1981
Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the points B (1, 7) and D (4. - 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.
PYP
IIT JEE 1981
If 0.50 mol of BaCl2 is mixed with 0.20 mol of Na3PO4, the maximum amount of Ba3(PO4)2 that can be formed is
PYP
IIT JEE 1981
Equal weights of methane and oxygen are mixed in an empty container at 25oC. The fraction of the total pressure exerted by oxygen is
PYP
IIT JEE 1981
A 1.00 gm sample of H2O2 solution containing X percent H2O2 by weight requires X ml of a KMnO4 solution for complete oxidation under acidic conditions. Calculate the normality of the KMnO4 solution.
PYP
IIT JEE 1981
The energy of the electron in the second and the third Bohr's orbits of the hydrogen atom is -5.42 $$\times$$ 10-12 erg and -2.41 $$\times$$ 10-12 erg respectively. Calculate the wavelength (in Å) of the emitted radiation when the electron drops from the third to second orbit.
PYP
IIT JEE 1981
The vapour pressure of pure benzene is 639.7 mm of mercury and the vapour of a solution of a solute in benzene at the same temperature is 631.9 mm of mercury. Calculate this molality of the solution.
PYP
IIT JEE 1981
Give reasons of the following:
Sodium carbonate is made by Solvay process but the same process is not extended to the manufacture of potassium carbonate.
Sodium carbonate is made by Solvay process but the same process is not extended to the manufacture of potassium carbonate.
PYP
IIT JEE 1981
Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place the balls so that no box remains emply?
PYP
IIT JEE 1981
An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are $$0.4, 0.3, 0.2$$ and $$0.1$$ respectively. What is the probability that the gun hits the plane?
PYP
IIT JEE 1981
Let the complex number $${{z_1}}$$, $${{z_2}}$$ and $${{z_3}}$$ be the vertices of an equilateral triangle. Let $${{z_0}}$$ be the circumcentre of the triangle. Then prove that $$z_1^2 + z_2^2 + z_3^2 = 3z_0^2$$.
PYP
IIT JEE 1981
Suppose that the normals drawn at three different points on the parabola $${y^2} = 4x$$ pass through the point $$(h, k)$$. Show that $$h>2$$.
PYP
IIT JEE 1981
For all $$x$$ in $$\left[ {0,1} \right]$$, let the second derivative $$f''(x)$$ of a function $$f(x)$$ exist and satisfy $$\left| {f''\left( x \right)} \right| < 1.$$ If $$f(0)=f(1)$$, then show that $$\left| {f\left( x \right)} \right| < 1$$ for all $$x$$ in $$\left[ {0,1} \right]$$.
PYP
IIT JEE 1981
Let $$x$$ and $$y$$ be two real variables such that $$x>0$$ and $$xy=1$$. Find the minimum value of $$x+y$$.
PYP
IIT JEE 1981
Use the function $$f\left( x \right) = {x^{1/x}},x > 0$$. to determine the bigger of the two numbers $${e^\pi }$$ and $${\pi ^e}$$
PYP
IIT JEE 1981
The angle between two convalent bonds is maximum in ________. (CH4, H2O, CO2)
PYP
IIT JEE 1981
Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n}}} \right) = \log 6$$
PYP
IIT JEE 1981
Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ be vectors of length $$3, 4, 5$$ respectively. Let $$\overrightarrow A $$ be perpendicular to $$\overrightarrow B + \overrightarrow C ,\overrightarrow B $$ to $$\overrightarrow C + \overrightarrow A $$ to $$\overrightarrow A + \overrightarrow B .$$ Then the length of vector $$\overrightarrow A + \overrightarrow B + \overrightarrow C $$ is ..........
PYP
IIT JEE 1981
Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C0, C1 ,....Cn are constants, and $${C_n} \ne 0$$ , then the value of n is _____.
PYP
IIT JEE 1981
The temperature at which a real gas obeys the ideal gas aws over a wide range of pressure is
PYP
IIT JEE 1981
The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................
PYP
IIT JEE 1981
Let $$a, b, c$$ be positive real numbers Let
$$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}}} + {\tan ^{ - 1}}\sqrt {{{b\left( {a + b + c} \right)} \over {ca}}} $$ $$ + {\,\,\tan ^{ - 1}}\sqrt {{{c\left( {a + b + c} \right)} \over {ab}}} $$
$$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}}} + {\tan ^{ - 1}}\sqrt {{{b\left( {a + b + c} \right)} \over {ca}}} $$ $$ + {\,\,\tan ^{ - 1}}\sqrt {{{c\left( {a + b + c} \right)} \over {ab}}} $$
Then $$\tan \theta = $$ ____________
PYP
IIT JEE 1981
1 mole of N2H4 loses 10 moles of electrons to form a new compound Y. assuming that all nitrogen appears in the new compound , what is the oxidation state of nitrogen in Y ? (there is no change in the oxidation state of hydrogen)
PYP
IIT JEE 1981
The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is
PYP
IIT JEE 1981
Rutherford's experiment on scattering of $$\alpha-particles$$ showed for the first time that the atom has
PYP
IIT JEE 1981
A solution of sodium metal in liquid ammonia is strongly reducing due to the presence of
PYP
IIT JEE 1981
The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie on
PYP
IIT JEE 1981
The correct order of second ionisation potential of carbon, nitrogen, oxygen and fluorine is
PYP
IIT JEE 1981
The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow A + \overrightarrow B + \overrightarrow C } \right)$$ equals :
PYP
IIT JEE 1981
If a molecule MX3 has zero dipole moment, the sigma bonding orbitals used by M (atomic number < 21) are
PYP
IIT JEE 1981
The general solution of the trigonometric equation sin x+cos x=1 is given by:
PYP
IIT JEE 1981
Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have the following property. For any two points $$\left( {{x_1},{y_1}} \right)$$ and $$\left( {{x_2},{y_2}} \right)$$ in the region, the point $$\left( {{{{x_1} + {x_2}} \over 2},{{{y_1} + {y_2}} \over 2}} \right)$$ is also in the region. The inequality defining this region is
PYP
IIT JEE 1981
Let $$a, b, c$$ be non-zero real numbers such that
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx = \int\limits_0^2 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx.} } $$
Then the quadratic equation $$a{x^2} + bx + c = 0$$ has
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx = \int\limits_0^2 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx.} } $$
Then the quadratic equation $$a{x^2} + bx + c = 0$$ has
PYP
IIT JEE 1981
The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx$$
PYP
IIT JEE 1981
The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents
PYP
IIT JEE 1981
A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static pressure, 'd' is the density of water and 'E' is the total energy of the explosion. Find the value of a, b and c.
PYP
IIT JEE 1981
Balance the following Equations:
(i) Cu2O + H+ + $$NO_3^ - \to $$ Cu2+ + NO + H2O
(ii) K4[Fe(CN)6] + H2SO4 + H2O $$\to$$ K2SO4 + FeSO4 + (NH4)2SO4 + CO
(iii) C2H5OH + I2 + OH- $$\to$$ CHI3 + $$HCO_3^-$$ + I- + 4H2O
(i) Cu2O + H+ + $$NO_3^ - \to $$ Cu2+ + NO + H2O
(ii) K4[Fe(CN)6] + H2SO4 + H2O $$\to$$ K2SO4 + FeSO4 + (NH4)2SO4 + CO
(iii) C2H5OH + I2 + OH- $$\to$$ CHI3 + $$HCO_3^-$$ + I- + 4H2O
PYP
IIT JEE 1981
For a biased die the probabilities for the different faces to turn up are given below :
This die tossed and you are told that either face $$1$$ or face $$2$$ has turned up. Then the probability that it is face $$1$$ is ...............
PYP
IIT JEE 1981
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where
$$0 \le {\cos ^{ - 1}}x \le \pi $$ and $$ - \pi /2 \le {\sin ^{ - 1}}x \le \pi /2$$.
$$0 \le {\cos ^{ - 1}}x \le \pi $$ and $$ - \pi /2 \le {\sin ^{ - 1}}x \le \pi /2$$.
PYP
IIT JEE 1981
Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqrt 3 :\sqrt 2 $$. Find the angle $$A$$.
PYP
IIT JEE 1981
Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.
PYP
IIT JEE 1981
Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$
PYP
IIT JEE 1981
Evaluate $$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$
PYP
IIT JEE 1981
Find the area bounded by the curve $${x^2} = 4y$$ and the straight
Showing 5 of 47 questions