IIT-JEE 1994

The IUPAC name of succinic acid is _______.

Using the VSEPR theory, identify the type of hybridization and draw the structure of OF2. What are the oxidation states of O and F?

The two types of bond present in B2H6 are covalent and _______.

The standard reduction potential of the Ag+/Ag electrode at 298 K is 0.799V. Given that for AgI, Ksp = 8.7 \(\times\) 10-17, evaluate the potential of the Ag+/Ag electrode in a saturated solution of AgI. Also calculate the standard reductio...

The Edison storage cells is represented as
Fe(s) | FeO(s) | KOH (aq) | Ni2O3(s) | Ni(s)
The half-cell reactions are:
Ni2O3 + H2O (l) + 2e- \(\leftrightharpoons\) 2NiO(s) + 2OH-; Eo = +0.40V
FeO(s) + H2O(l) + 2e- \(\leftrightharpoons\) Fe(s)...

An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg and shows a pressure of 2.5 atm. In the course of use at 27o C, the weight of the full cylinder reduces to 23.2 kg. Find out the volume of the...

A 4 : 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out initially?

Statement (S) The alkali metals can form ionic hydrides which contain the hydride ion H-.
Explanation (E) The alkali metals have low electronegativity; their hydrides conduct electricity when fused and liberate hydrogen at the anode.

Complete and balance the following reactions:
Ca5(PO4)3F + H2SO4 + H2O \(\buildrel {Heat} \over \longrightarrow\) ........ + 5CaSO4.2H2O + ........

A is binary compound of a univalent metal. 1.422 g of A
reacts completely with 0.321 g of sulphur in an evacuated
and sealed tube to give 1.743 g of a white crystalline solid
B, that forms a hydrated double salt, C with Al2
(SO4)3
.
Identif...

8.0575 \(\times\) 10-2 kg of Glauber's salt is dissolved in water to obtain 1 dm3 of a solution of density 1077.2 kg.m-3. Calculate the molarity, molality and mole fraction Na2SO4 in the solution.

The composition of a sample of Wustite is Fe0.93O1.00 what percentage of the iron is present in the form of Fe(III)?

The compound YBa2Cu3O7, which shows superconductivity, has copper in oxidation state ______ assume that the rare earth element yttrium is in its usual +3 oxidation state.

Find out the number of waves made by a Bohr electron in once complete revolution in its 3rd orbit?

The outermost electronic configuration of Cr is _______.

Let \(\alpha ,\beta ,\gamma\) be distinct real numbers. The points with position
vectors $$\alpha \widehat i + \beta \widehat j + \gamma \widehat k,\,\,\beta \widehat i + \gamma \widehat j + \alpha \widehat k,\,\,\gamma \widehat i + \alph...

Let \(\overrightarrow p\) and \(\overrightarrow q\) be the position vectors of \(P\) and \(Q\) respectively, with respect to \(O\) and \(\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.\) The points \(R\) a...

A unit vector perpendicular to the plane determined by the points \(P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)\) and \(R\left( {0,2,1} \right)\) is ............

The circle \({x^2} + {y^2} = 1\) cuts the \(x\)-axis at \(P\) and \(Q\). Another circle with centre at \(Q\) and variable radius intersects the first circle at \(R\) above the \(x\)-axis and the line segment \(PQ\) at \(S\). Find the maximu...

The function defined by \(f\left( x \right) = \left( {x + 2} \right){e^{ - x}}\)

Let \(P\) be a variable point on the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) with foci \({F_1}\) and \({F_2}\). If \(A\) is the area of the triangle \(P{F_1}{F_2}\) then the maximum value of \(A\) is ..........

Which one of the following curves cut the parabola \({y^2} = 4ax\) at right angles?

The curve \(y = a{x^3} + b{x^2} + cx + 5\), touches the \(x\)-axis at \(P(-2, 0)\) and cuts the \(y\) axis at a point \(Q\), where its gradient is \(3\). Find \(a, b, c\).

Let \(C\) be the curve \({y^3} - 3xy + 2 = 0\). If \(H\) is the set of points on the curve \(C\) where the tangent is horizontal and \(V\) is the set of the point on the curve \(C\) where the tangent is vertical then \(H=\).............. an...

In what ratio does the \(x\)-axis divide the area of the region
bounded by the parabolas \(y = 4x - {x^2}\) and \(y = {x^2} - x?\)

The circles \({x^2} + {y^2} - 10x + 16 = 0\) and \({x^2} + {y^2} = {r^2}\) intersect each other in two distinct points if

Suppose Z1, Z2, Z3 are the vertices of an equilateral triangle inscribed in the circle \(\left| Z \right| = 2.\) If Z1 = \(1 + i\sqrt 3\) then Z2 = ......., Z3 =..............

Show that \(\int\limits_0^{n\pi + v} {\left| {\sin x} \right|dx = 2n + 1 - \cos \,v}\) where \(n\) is a positive integer and \(\,0 \le v < \pi .\)

The value of \(\int\limits_2^3 {{{\sqrt x } \over {\sqrt {3 - x} + \sqrt x }}} dx\) is ...........

A normal is drawn at a point \(P(x,y)\) of a curve. It meets the \(x\)-axis at \(Q.\) If \(PQ\) is of constant length \(k,\) then show that the differential equation describing such curves is $$y = {{dy} \over {dx}} = \pm \sqrt {{k^2} - {y...

If \(y = {\left( {\sin x} \right)^{\tan x}},\) then \({{dy} \over {dx}}\) is equal to

Let \(E\) be the ellipse \({{{x^2}} \over 9} + {{{y^2}} \over 4} = 1\) and \(C\) be the circle \({x^2} + {y^2} = 9\). Let \(P\) and \(Q\) be the points \((1, 2)\) and \((2, 1)\) respectively. Then

The equation \(2{x^2} + 3{y^2} - 8x - 18y + 35 = k\) represents

Find the indefinite integral \(\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta\)

If we consider only the principle values of the inverse trigonometric functions then the value of
\(\tan \left( {{{\cos }^{ - 1}}{1 \over {5\sqrt 2 }} - {{\sin }^{ - 1}}{4 \over {\sqrt {17} }}} \right)\) is

If \(x\) is not an integral multiple of \(2\pi\) use mathematical induction to prove that :
\($\cos x + \cos 2x + .......... + \cos nx = \cos {{n + 1} \over 2}x\sin {{nx} \over 2}\cos ec{x \over 2}\)$

Let \(n\) be a positive integer and \({\left( {1 + x + {x^2}} \right)^n} = {a_0} + {a_1}x + ............ + {a_{2n}}{x^{2n}}\)
Show that \(a_0^2 - a_1^2 + a_2^2...... + {a_{2n}}{}^2 = {a_n}\)

Let \(n\) be positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of \({\left( {1 + x} \right)^n}\) are in A.P., then the value of \(n\) is ................

The point of intersection of the tangents at the ends of the latus rectum of the parabola \({y^2} = 4x\) is ...... .

Through the vertex \(O\) of parabola \({y^2} = 4x\), chords \(OP\) and \(OQ\) are drawn at right angles to one another . Show that for all positions of \(P\), \(PQ\) cuts the axis of the parabola at a fixed point. Also find the locus of the...

A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In how many of these committees? In how may of these committees
(a) The women are in majo...

If two events \(A\) and \(B\) are such that \(P\,\,\left( {{A^c}} \right)\,\, = \,\,0.3,\,\,P\left( B \right) = 0.4\) and \(P\left( {A \cap {B^c}} \right) = 0.5,\) then \(P\left( {B/\left( {A \cup {B^c}} \right)} \right.\)$$\left. \, \righ...

An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards number...

Let \(A, B, C\) be three mutually independent events. Consider the two statements \({S_1}\) and \({S_2}\)
\({S_1}\,:\,A\) and \(B \cup C\) are independent
\({S_2}\,:\,A\) and \(B \cap C\) are independent
Then,

In a triangle \(ABC\), \(AD\) is the altitude from \(A\). Given \(b>c\), \(\angle C = {23^ \circ }\) and \(AD = {{abc} \over {{b^2} - {c^2}}}\) then \(\angle B =\).................

Let \({A_1},{A_2},........,{A_n}\) be the vertices of an \(n\)-sided regular polygon such that \({1 \over {{A_1}{A_2}}} = {1 \over {{A_1}{A_3}}} + {1 \over {{A_1}{A_4}}}\), Find the value of \(n\).

Consider the following statements connecting a triangle \(ABC\)
(i) The sides \(a, b, c\) and area \(\Delta\) are rational.
(ii) \(a,\tan {B \over 2},\tan {c \over 2}\) are rational.
(iii) \(a,\sin A,\sin B,\sin C\) are rational.
Prove th...

A circle is inscribed in an equilateral triangle of side \(a\). The area of any square inscribed in this circle is ..............

A tower \(AB\) leans towards west making an angle \(\alpha\) with the vertical. The angular elevation of \(B\), the topmost point of the tower is \(\beta\) as observed from a point \(C\) due west of \(A\) at a distance \(d\) from \(A\). I...

If the lengths of the sides of triangle are \(3, 5, 7\) then the largest angle of the triangle is