Part Test IITJEE

Maths Class Test / Time – 1 Hour / Total Marks -72 Each question is of single correct choice type. Marking scheme is +4/-1 1) If 0  x 

(a)

 2

, then minimum value of

3

(b) 1/2

cos3 x sin 3 x  is sin x cos x (c) 1/3

2) The number of real solutions of the equation

(a) two

(b) one

(d) 1

6 x x is/are  2 2 x 4 x2 (c) zero

(d) none of these

3) The solution set of log 2 4  5 x  2 is 8  (a)  ,   5 

4 8 (b)  ,  5 5

8  (c) (, 0)   ,   5 

4) The minimum value of P  bcx  cay  abz , when xyz  abc , is (b) 6abc (c) abc (a) 3abc 5) If tan x  a  (a) 2a

1 , then sec   tan   4a 1 (b) 2a, 2a

(c) 2a, 

1 2a

(d) none of these

(d) 4abc

(d) 2a,

1 2a

6) lim x ( x  c  x )  x 

(a) c / 2

(b) c / 3

(c) c / 4

(d) none of these

ax  bx  x 0 x

7) lim

a b

(b) log  

(a) log( ab)

 b  (where a  1 ) = x  a  (b) a log b

b a

(c) log  

(d) none of these

(c) b

(d) a

8) lim a x sin  x 

(a) b log a

9) lim  x 2

2x    cos x

(a) 1

(b) 2

(c) -2

(d) 0

10) The line y  x  2  0 divides the join of points (3, 1) and (8,9) in the ratio (a) 1:2 (b) 2:3 (c) 3:4 (d) 1:1 11) If the points (a, b), (c, d ) and (a  c, b  d ) are collinear, then (b) ac  bd (c) ad  bc (a) ab  cd

(d) none of these

12) A polygon has 44 diagonals, then the number of its sides are (a) 11 (b) 7 (c) 8

(d) none of these

13) If some or all of n things be taken at a time, the number of combinations is (a) 2n (b) 2n  1 (c) 2n  1

(d) none of these

14) If the roots of a (b  c) x 2  (c  a ) x  (a  b)  0 be equal, then a, b, c are in (a) A.P (b) G.P (c) H.P (d) none of these 15) If the roots of the equation ax 2  bx  c  0 are of the form is equal to (a) b 2  4ac

(b) b 2  2ac

k 1 k2 and , then (a  b  c) 2 k k 1

(c) 2b 2  ac

(d)  a 2

16) There are n A.M’s between 3 and 29 such that 6th mean: ( n  1) th mean::3:5, then the value of n is (a) 10 (b) 11 (c) 12 (d) none of these

17) Twenty eight matches were played in a football tournament. Each team met its opponent only once. The number of teams that took part in the tournament, is (a) 7 (b) 8 (c) 14 (d) none of these 18) An infinite G.P has first term x and sum 5, then x belongs to (a) x  10 (b) 10  x  0 (c) 0  x  10

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(d) x  10