During electrolysis under suitable conditions, 0.015 mol of chromium is deposited on the cathode when 0.090 mol of electrons is passed through a chromium containing electrolyte. Which of the following substances could have been the electrolyte?

1) CrCl₂
2) Na₂Cr₂O₇
3) CrF₅
4) CrCl₃

Young’s double slit experiment is carried out by using green,red and blue light, one colour at a time. The fringe widths recorded are β_G, β_R and β_B respectively then,

1) β _G > β_B > β_R
2) β_B > β_G > β_R
3) β_R > β_B > β_G
4) β_R > β_G > β_B

If y = k sin px, then the value of the determinant   is equal to  

1) 1
2) 0
3) -1
4) none

p: She is beautiful.
q:She is happy.
Then (∼p)⇒(∼q), means

1) If she is beautiful, then she is not happy.

2) If she is not beautiful, then she is happy.

3) If she is not beautiful, then she is not happy.

4) If she is not happy, then she is not beautiful.

A solid cube of wood of side 2a and mass M is resting on a horizontal surface as shown in the figure. The cube is free to rotate about the fixed axis AB. A bullet of mass m(<<M)and speed v is shot horizontally at the face opposite to ABCD at a height h above the surface to impart the cube an angular speed ω_c so that the cube just topples over. Then ω_c is (note: the moment of inertia of the cube about an axis perpendicular to the face and passing through the centre of mass is 2Ma^₃ /3 ).

A bag contains 17 tickets numbered 1 to 17. A tickets is drawn and replaced, then one more ticket is drawn and replaced. Probability that first drawn number is even and second is odd, is

1) $$\frac { 81 }{ 289 } $$
2) $$\frac { 72 }{ 289 } $$
3) $$\frac { 64 }{ 289 } $$
4) None of these

A train is moving on a straight track with speed $$20\, ms^{-1}.$$ It is blowing its whistle at the frequency of $$1000\, Hz$$. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to

1) $$12 \%$$
2) $$6 \%$$
3) $$18 \%$$
4) $$24 \%$$

I. H—C—H angle in CH₄
II. Cl—B—CI angle in BCl₃
III. F—I—F angle in IF₇ in a plane 
IV. I—I—I angle in I^-₃
Increasing order of above bond angles is

1) I < II < III < IV
2) II < I < III < IV
3) III < I < II < IV
4) IV < II < I < III

 Marsh test is used for

1)  arsenic

2)  potassium

3)  barium

4)  aluminium

There is an error of ± 0.04 cm in the measurement of the diameter of a sphere. When the radius is 10 cm, the percentage error in the volume of the sphere is  
1)  ± 1.2
2) ± 1.0
3) ± 0.8
4) ± 0.6