Can you give me question paper for Maharashtra common entrance test for mathematics subject soon ?

Here I am giving you question paper for Maharashtra common entrance test for mathematics subject in a PDF file attached with it so you can get it easily.

1. All letters of the word ‘CEASE’ are arranged randomly in a row then the probability that two E
are found together is :
(1) 7 (2) 3 (3) 2 (4) 1
5 5 5 5
2. Three numbers are selected randomly between 1 to 20. Then the probality that they are
consecutive numbers will be :
(1) 7 (2) 3 (3) 5 (4) 1
190 190 190 3
3. If the four positive integers are selected randomly from the set of positive stegers then the
probability that the number 1, 3 , 7, 9 are in the unit place in the product of 4 digitsosetected is :
(1) 7 (2) 2 (3) 5 (4) 16
625 5 625 625
∧∧∧∧∧∧∧∧∧
4. If the position vectors of the vertices A, B, C are 6i, 6j, k respectively w.r.t. origin O then the
volume of the tetranedron OABC is :
(1) 6 (2) 3 (3) 1 (4) 1
6 3
∧∧∧∧∧∧∧∧∧∧∠§ï€ âˆ§ï€ âˆ§âˆ§ï€ âˆ§ï€ âˆ§âˆ§ï€ âˆ§ï€ âˆ§âˆ§ï€ â ˆ§ï€ âˆ§âˆ§ï€ âˆ§
5. If three vectors 2i – j - k, i + 2j – 3k, 3i + j + 5 k are coplanar then the value of is :
(1) – 4 (2) – 2 (3) – 1 (4) 0
∧∧∧∧∧∧∧∧∧∧∠§ï€ âˆ§ï€ âˆ§âˆ§ï€ âˆ§ï€ âˆ§âˆ§ï€ âˆ§
6. The vector perpendicular to the vectors 4i, - j + 3k and – 2i + j - 2k whose magnitude is 9 :
∧∧∧∧∧∧∧∧∠§
(1) 31 + 6j – 6k (2) 31 – 6j + 6k (3) – 3i + 6j + 6k (4) none of these
7. The area of the region bounded by the curves x2 + y2 = 8 and y 2 = 2x is :
(1) 2+ 1 (2) + 1 (3) 2+ 4 (4) + 4
3 3 3 3

8. The value of 0 log (1 + cos x) dx is :
(1) - log 2 (2) log 1 (3) log 2 (4) log 2
2 2 2
4
9. The value of 3 √√√(4 – x) (x – 3) dx is :
(1) (2) (3) (4) 
16 8 4 2
10. The value of dx is :
x(xn + 1)
(1) 1 log xn + c
n xn + 1
(2) log xn + 1 + c
xn
(3) 1 log xn + 1
n
xn
(4) log xn + c
xn + 1
11. The value of cos (log x) dx is :
(1) 1 [sin(log x) + cos (log x)] + c
2
(2) x [sin(log x)] + cos(log x)] + c
2
(3) x [sin(log x) – cos(log x)] + c
2
(4) 1 [sin(log x) – cos(log x)] + c
2
12. The value of ex (1 + sin x ) dx is :
( 1 + cos x)
(1) 1 ex sec x + c (2) ex sec x + c
2 2 2
(3) 1 ex tan x + c (4) ex tan x + c
2 2 2
13. The value of 1 is dx :
3 sin x – cos x + 3
(1) tan-1 tan x + 1 + c
2
(2) 1 tan-1 2 tan x + 1 + c
2 2
(3) tan-1 2 tan x + 1 + c
2
(4) 2tan-1 2 tam x + 1 + c
2
14. Divide 10 into two parts such that the sum of double of the first and the square of the second
is minimum :
(1) 6,4 (2) 7,3 (3) 8, 2 (4) 9,1
15.. The value of sin 2x dx is ;
sin4x + cos4 x
(1) tan-1 (cot2 x) + c (2) tan-1 (cos2x) + c
(3) tan-1 (sin2x) + c (4) tan-1 (tan2x) + c
16. The value of √1 + sec x dx is :
(1) 1 sin-1 (√2 sin x) +c
(2) – 2sin-1 (√2 sin x/2) + c
(3) 2sin-1 (√2 sin x ) + c
(4) 2sin-1 (√2x/2) + c
17. The value of (x2 + 1 ) dx is :
x4 + x2 + 1
(1) 1 tan-1 x – 1/x + c
√3 √3
(2) 1 log (x – 1/x) - √3 + c
2√3 ( x – 1/x) + √3
(3) tan-1 x + 1/x + c
√3
(4) tan-1 x – 1/x + c
√3
1
18. The value of x2 ( 1 – x2)3/2 dx is :
0
(1) 1 (2) (3) (4) 
32 8 16 32
∞
19. The value of xdx is :
0 ( 1 + x ) ( x2 + 1 )
(1) 2(2) (3) (4) 
16 32
20. y2 = 8x and y = x
(1) 64 (2) 32 (3) 16 (4) 8
3 3 3 3
21. If in a triangle ABC , O and O′are the incentre and orthocenter respectively then (OA + OB
+ OC) is equal to :
→→→→
(1) 20′0 (2) O′0 (3) OO′(4) 200′
→→→→→→→→
22. If a + b + O = a and _a_ = 5 _b_ = 3, _c_ = 7 then angle between a and b is :
(1) (2) (3) (4) 
2 3 4 6
23. i.(j k) + j.(k x i) + k.(j x i) is equal to :
(1) 3 (2) 2 (3) 1 (4) 0
24. One card is drawn at random from a pack of playing cards the probability that it is an ace or
black king or the queen of the heart will be :
(1) 3 (2) 7 (3) 6 (4) 1
52 52 52 52
25. 15 coins are tossed then the probability of getting 10 heads tails will be :
(1) 511 (2) 1001 (3) 3003 (4) 3005
32768 32768 32768 32768
26. The odds against solving a problem by A and B are 3 : 2 and 2 : 1 respectively then the
probability that the problem will be solved is :
(1) 3 (2) 2 (3) 2 (4) 11
5 15 5 15
27. The pole of the line x = my +n =0 w.r.t. the parabola y2=4ax will be :
(1) -n , - 2am (2) -n , 2 am
1 1 1 1
(3) n , -2am (4) n , 2am
1 1 1 1
28. If 2x + y + = 0 is normal to the parabola y2= 8x then is :
(1) -24 (2) ≠8 (3) -16 (4) 24
29. If the line x = my + n = 0 is tangent to the parabola y2= 4ax then :
(1) mn= a2 (2) m=an2 (3) n=am2 (4) none of therse
30. f: R→R, f(x) = x x will be :
(1) many one onto (2) one one onto
(3) many are into (4) one one into
31. lim (sec x – tan x) is equal to :
x→/2
(1) 2 (2) -1 (3) 1 (4) 0

Attached Files

MHT CET Mathematics Paper.pdf (263.9 KB, 66 views)