If the term without \(x\) in the expansion of \(\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}\)is 7315 , then \(|\alpha|\) is equal to ___
The sum of the common terms of the following three arithmetic progressions\(3,7,11,15, \ldots , 399\), \(2,5,8,11, \ldots , 359\)and \(2,7,12,17, \ldots , 197,\) is equal to _____
Number of integral solutions to the equation \(x+y+z=21\), where \(x \geq 1\), \(y \geq 3\), \(z \geq 4\), is equal to ___
If the x-intercept of a focal chord of the parabola \(y^2=8 x+4 y+4\) is 3 , then the length of this chord is equal to ___
The point of intersection \(C\) of the plane \(8 x+y+2 z=0\) and the line joining the points \(A (-3,-6,1)\) and \(B (2,4,-3)\)divides the line segment \(AB\) internally in the ratio\(k : 1 \ If a , b , c (| a |,| b |, | c |\)are coprime) are the direction ratios of the perpendicular from the point \(C\)on the line \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\), then \(| a + b + c |\)is equal to ___
The number of integral values of \(k\), for which one root of the equation \[2x^2 - 8x + k = 0\] lies in the interval \((1, 2)\) and its other root lies in the interval \((2, 3)\), is:
Benzyl isocyanide can be obtained by:Choose the correct answer from the options given below:
In the wet tests for identification of various cations by precipitation, which transition element cation doesn’t belong to group IV in qualitative inorganic analysis?
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A): In expensive scientific instruments, silica gel is kept in watch-glasses or in semipermeable membrane bags.Reason (R): Silica gel adsorbs moisture from air via adsorption, thus protects the instrument from water corrosion (rusting) and/or prevents malfunctioning.In the light of the above statements, choose the correct answer from the options given below:
Which of the following compounds would give the following set of qualitative analysis?• (i) Fehling’s Test: Positive• (ii) Na fusion extract upon treatment with sodium nitroprusside gives a blood red colour but not
For \(\text{OF}_2\) molecule consider the following:[(A)] Number of lone pairs on oxygen is 2.[(B)] F--O--F angle is less than \(104.5^\circ\).[(C)] Oxidation state of O is \(-2\).[(D)] Molecule is bent ‘V’-shaped.[(E)] Molecular geometry is linear.Correct options are:
To inhibit the growth of tumours, identify the compounds used from the following:(A) EDTA(B) Coordination Compounds of Pt(C) D – Penicillamine(D) Cis – PlatinChoose the correct answer from the options given below:
What is the correct order of acidity of the protons marked A-D in the given compounds?
Formation of photochemical smog involves the following reaction in which A, B, and C are respectively:\(\text{NO}_2 \xrightarrow{h\nu} \text{A} + \text{B}\)\(\text{B} + \text{O}_2 \rightarrow \text{C}\)\(\text{A} + \text{C} \rightarrow \text{NO}_2 + \text{O}_2\)Choose the correct answer from the options given below:
Figures (a), (b), (c) and (d) show variation of force with time The impulse is highest in figure
The alkaline earth metal sulphate(s) which are readily soluble in water is/are:(a) BeSO4(b) MgSO4(c) CaSO4(d) SrSO4(e) BaSO4Choose the correct answer from the options given below:
Consider the following reaction approaching equilibrium at \(27^\circ \text{C}\) and 1 atm pressure:\[\text{A + B} \rightleftharpoons \text{C + D}\]\[K_f = 10^3, \quad K_r = 10^2\]The standard Gibbs energy change (\(\Delta_r G^\circ\)) at \(27^\circ \text{C}\) is — kJ mol\(^{-1}\) (Nearest integer).
Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is_____ \(\times 10^{–1}\).
Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is \(x \times 10^{-1}\). The value of \(x\) is — (Nearest integer).
Water decomposes at 2300 K:\[2\text{H}_2\text{O}(g) \rightleftharpoons 2\text{H}_2(g) + \text{O}_2(g).\]The percent of water decomposing at 2300 K and 1 bar is — (Nearest integer).Equilibrium constant for the reaction is \(2 \times 10^{-3}\) at 2300 K.
Following figure shows dependence of molar conductance of two electrolytes on concentration. Λo m is the limiting molar conductivity. The number of incorrect statement(s) from the following is ________ (A) \(\Lambda \text{o m}\) for electrolyte A is obtained by extrapolation. (B) For electrolyte B, \(\Lambda \text{m}\) vs \(\sqrt c\) graph is a straight line with intercept equal to o \(\Lambda \text{m}\)(C) At infinite dilution, the value of degree of dissociation approaches zero for electrolyte B. (D) Λo m for any electrolyte A or B can be calculated using \(\lambda0\) for individual ions.
