Important Paper JEE Advanced

1. Let X and Y be two arbitrary, 3 x 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 x 3, non-zero, symmetric matrix. Then, which of the following matrices is/are skew-symmetric ?
(a) Y3Z4 – Z4Y3                                                    
(b) X44 + Y44
(c) X4Z3 – Z3X4                                                   
(d) X23 + Y23                                                                        
Ans (c,d)
2.  Let y(x) be a solution of the differential equation  (1 + ex)y’ + yex = 1. If y(0) = 2, then which of the following statement(s) is/are true ?
(a) y(-4) = 0
(b) y(-2) = 0
(c) y(x) has a critical point in the interval (-1, 0)
(d) y(x) has no critical point in the interval (-1, 0)                                                                                              
Ans (a,c)
3. The correct statement(s) about Cr2+ and Mn3+ is/are [atomic number of Cr = 24 and Mn = 25]
(a) Cr2+ is a reducing agent
(b) Mn3+ is an oxidizing agent
(c) both Cr2+ and Mn3+ exhibit d4 electronic configuration
(d) when Cr2+ is used as reducing agent, the chromium ionattains d5 electronic configuration                     
Ans (a,b,c)
4.   Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is/are
(a) impure Cu strip is used as cathode
(b) acidified aqueous CuSO4 is used as electrolyte
(c) pure Cu deposits at cathode
(d) impurities settle as anode-mud                                                                                                         
Ans (b,c,d)
5.   Fe3+ is reduced to Fe2+ by using
(a) H2O2 in presence of NaOH
(b) Na2O2 in water
(c) H2O2 in presence of H2SO4
(d) Na2O2 in presence of H2SO4                                                                                                                 
Ans (a,b)
6. Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both along positive y-directions. Then V1 and V2 are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct options is/are
(a) If B1 = B2 and n1 = 2n2, then V2 = 2V1
(b) If B1 = B2 and n1 = 2n2, then V2 = V1
(c) If B1 = 2B2 and n1 = n2, then V2 = 0.5V1
(d) If B1 = 2B2 and n1 = n2, then V2 = V1                                                                                                  
Ans (a,c)
7. Under hydrolysis conditions, the compounds used for preparation of linear polymer and for chain termination, respectively are
(a) CH3SiCl3 and Si(CH3)4
(b) (CH3)2SiCl2 and (CH3)3SiCi
(c) (CH3)SiCl2 and CH3SiCl3
(d) SiCl4 and (CH3)3SiCl                                                                                                                                   
Ans (b)
8. The correct statement(s) regarding,
(i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4 is(are)
(a) the number of Cl = O bonds in (ii) and (iii) together is two
(b) the number of lone pair of electrons on Cl in (ii) and (iii) together is three
(c) the hybridization of Cl in (iv) is sp3
(d) amongst (i) to (iv), the strongest acid is (i)                                                                                    
Ans (b,c)
9. The pair(s) of ions where both the ions are precipitated upon passing H2S gas in presence of dilute HCl, is(are)
(a) Ba2+, Zn2+                                                     
(b) Bi3+, Fe3+
(c) Cu2+, Pb2+                                                     
(d) Hg2+, Bi3+                                                                      
Ans (c,d)
10. Enthalpy of dissociation (in kJ mol-1) of acetic acid obtained from the experiment 2 is
(a) 1.0                                                                  
(b) 10.0
(c) 24.5                                                                
(d) 31.4                                                                                
Ans (a)
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