Maths

HOTS

Probability:

Question 1à  In a group there are three women & four men. Three persons are selected at random from this group. Find the probability that two women & one man or one woman & two men are selected.

Question 2à  A problem in mathematics is given to three students whose chances of solving it are ½,1/3 & ¼ respectively. What is probability that the problem will be solved?

Question 3 à A speaks truth in 60% of the cases & B in 70% of the cases. In what percentage of cases they are likely to

(i)                 Contradict each other

(ii)               Agree with each other, in stating the same fact?

Question 4à  A man is known to speak truth three out of four times. He throws a dice & reports that it is six. Find the probability that it is actually a six.

Question 5à In a hurdle race, a player has to cross 8 hurdles. The probability that he will clear each hurdle is 4/5. What is the probability that he will knock down fewer than 2 hurdles?

3D GEOM:

Question 6 à  Show that the lines vect. (r) = - î -3Ĵ-5 unitvect.(k) + λ (3î +5Ĵ+7 unit vect.(k)) And

                    Vect.(r) = (2 î +4Ĵ +6 unitvect.(k)) + u (î + 3Ĵ + 5 unit vect.(k)) intersect each other.

Question 7 à  Find the equation of the plane passing through the point (-1, -1, 2) and perpendicular to the planes x+ 2y- 3z=1 and 5x- 4y+ 3z=5

Question 8 à Find the foot of the perpendiculars from the point (0, 2,7) on the line                      

Question 9 à If the points (1,2,p) and(-3, 0,-1) be equidistant from the plane

 vect. (r) .(3 î +4Ĵ - 12unitvect.(k)) + 17 = 0, then find the value of ‘P’.

 Question 10 à  Find the angle between the line     

and the plane 2x +y- 3z =4

VECTORS

Question 11 à If vect.(a) is any vector prove that

      vect.(a)= (vect.(a).vect.(i)) î +  (vect.(a).vect.(j)) Ĵ + (vect.(a).vect.(k)) unit Vect. (k).

Question 12 à If vectors vect.(a) , Vect.(b), Vect.(c) are such that each is perpendicular to sum of the other two and I vect(a) I = 6, I vect(b) I = 8, and I vect(c) I =10, find I vect(a) + vect(b)ı+ vect(c) I .

Question 13 -à  If vect. (α)=3î-Ĵ and vect.(β)= 2î+Ĵ-5 unit vect.(k), express vect.(β) as a sum of vectors vect.(β1) and vect. (β2), where vect. (β1) ıı vect.(α) and vect.(β2)ııα.

Question 14à vect.(a), vect.(b), Vect.(c) are unit vectors.

Suppose vect. (a) . vect.(b)= Vect (c). vect (a)=0 and angle between vect.(b) and Vect ()c) is π/3, prove that vect.(a)=±(2/√3 ) (vect(b) x Vect (c).

Question 15 à If vect (a) x Vect. (b) = Vect (c) x vect (a) ‡ vect (0), show that vect (b) + Vect (c) = t vect (a) for some scalar t.