MP PET Math Sample Paper

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MP PET Math Sample Paper

1. Evaluate (2i+5j+9k)+(3i-5k)

a.  5i+5j+4k               b. 2i+3j+9k              c.   5i-4k              d. 4i+5j

2. Find Dr’s of (2,6,8)   (5,8,3)

a. 8,5,3              b. 3 ,2,-5              c. -5,6,8              d. 7,-5,6

3. Find the Distance between two vector equation 2i+3j+4k and 5i+8j+9k

a. 39                                  b. (59)^1/2              c. (58)^1/2                             d. 9

4.The coordinate of Point of triangle are (9,5,4),(5,4,6),(8,2,6).Find the centroid of tiangle?

a. 5,8,4                               b. 8,7,6/5              c. 22/3,11/3,16/3                        d. 21/3,16/3,7/3

5.one end of the diameter of the circle x²+y²-4x-2y-4=0 is(5,-6).so find the another end point

a. ( 4,-9)                b.(-9,-4)              c.(4,9)                   d.(9,-4)

6.The next term of the sequence is 1,3,6,10……………….is

a.16                        b. 13              c.15                          d.14

7.Equation of line passing through the point (1,1,1) and parallel to the plane 2x+3y+3z+5=0 is

a.(x-1)/1=(y-1)/2=(z-1)/1                                b.(x-1)/-1=(y-1)/1=(z-1)/-1

c.(x-1)/3=(y-1)/2=(z – 1)/1                              d. (x – 1)/2 = (y – 1)/3 =(z – 1)/1

8. tan (cot -1x) is equal to

a. π/4 – x               b. cot (tan -1x)           c. tan x           d. none of the above

9. Integrating factor of differential equation cos x (dy/dx) + y sin x = 1 is

a.sin x                          b.sec x              c.tan x                         d. cos x

10. The sum of the series 1/2 + 1/3 + 1/6 + ……. to 9 terms is

a. -5/6                          b. -1/2               c. 1                              d. -3/2

11. The three lines 3x + 4y + 6 = 0, (2)^1/2x + (3)^1/2y + 2(2)^1/2 = 0, and 4x + 7y + 8 = 0 are

a. sides of a triangle                     b. concurrent              c. parallel                   d. none of the above

12. Equation of the sphere with centre (1, -1, 1) and radius equal to that of sphere 2×2 + 2y2 +

2z2 – 2x + 4y – 6z = 1 is

b. x² + y² + z² – 2x + 2y – 2z + 1 = 0                            b. x² + y² + z² + 2x – 2y + 2z + 1 = 0

c. x² + y² + z² – 2x + 2y – 2z – 1 = 0                             d. none of the above

13. If H is the harmonic mean between P and Q, then H/P + H/Q is

a. (P + Q)/PQ               b. PQ/(P + Q)               c. 2   d. none of the above

14. If the roots of x2 – bx + c = 0 are  consecutive integers, then b² – 4c is equal to

a. 4                       b. 3               c. 2                       d. 1

15.  Integrate sin^-1x

a.1/(1-x²)^1/2                                   b.cos^-1x               c.xsin_-1x+(1-x²)^1/2                     d.non of this

16. The system of equation – 2x + y + z = a, x -2y + z = b,

x + y -2z = c is consistent, if :

a. a + b – c = 0                                      b. a -b + c = 0

c. a + b + c ¹ 0                                      d. a + b + c = 0

17. If A + B =π/2, then (1 + tan A) (1 + tan B) is equal to :

a.2                   b.1              c.3                     d. (3)^1/2

18. If the second, third and sixth terms of an AP are in GP, then the common ratio of the GP is :

a.2                              b 5               c. 4                          d 3

19. The value of l, for which the three points(1, 1), (4, -1), (-2, l) are collinear, is :

a.1/2               b. 0              c. 3                 d. -2

20. the poin of intersection of line x-5/3=y-7/-1=z+2/1    and    x+3/-36=y-3/2=z-6/4…

a. (5, 7, -2)                      b. (-3, 3, 6)              c. (2, 10, 4)                       d.(21,5/3,10/3)

21. The distance of the point (1, 2, 3) from the line through(-1, 2, 5) and (2, 3, 4) is :

a.(6/11)^1/2                  b 2 (6)^1/2

c.2(6/11)^1/2                        d.(6)^1/2

 

22.

The equation of the plane through the line  2x -y = 0 = y -3z and perpendicular to 4x + 5y – 3z = 8

is:

a. 8x – y – 9z = 0                    b. 2x – 6y + 15z = 0

c. 10x – 6y + 3z = 0                 d. 28x -17y + 9z = 0

 

23. The value of l, for which the three points, whose  position vectors are i+ j,j + k,-i + j +l k will be

Colliner….

a. 2            b.-1

c. -2           d.1

 

24.if a,b,c are unit vector such that ax(bxc)=1/2 b.then angle between a and c..

a. π/6                b. π/4

c. π/2                  d. π/3

 

25. If a,b,c are any vectors, then [a,b,+ c a,+ b+ c] is

equal to :

a. [a,b,c]              b. 2[a,b,c]

c. 0                        d. b.c +c.a + a.b

 

1. Find the value of dY/dX (sinx)³ =?
   1. 2(sinx)².cosx                              2. (3cosx)².sinx                  3. 3(sinx)².cosx²

4.  3(sinx).(sinx).cosx

 

27.     Find the value of dY/dX(1/x)=?

1.  –x                                                     2. -1(x)^-1-1                            3.  (1/x²)

4.  2(x)²

 

28.     dy/dx sin^-1(2x/1+x²) =?

1.  2/(1+x²)                                          2.  1/(1+x)                          3.  2(1+x²)

4. 3/(2+x)

 

29.

1.    2.

3.    4.  3

 

30.         if the one of triangle is (a+b) ,second side is ab and third side is (a-b),but second side is as a                                                                                             diagonal of the triangle then the correct answer according to Pythagoreon Theorem –

1. a²+b²=c²          2.  (a-b)²+c²=(a²+b²)       3.  (a+b)²+(a-b)²=(ab)²                   4. None of these.

 

 

31.            is equal to =?

1.                  2.                              4.                                 4.

 

 

 

32.          is equal to –

1. 2.

3.               4.

 

33.           2(sin 2A).(sin 2B) is equal to –

1.   sin (A+B/2)                   2. cos(A+B)+cos(B-A)     3. sin (A+B)+sin (A-B)

4. cos (A+B/2).cos(B-A/2)

 

34.          If  x+y=4, y+z=6 and z+x=10 then the value of x,y,z is repectively =

1.    4,0,6               2.  2,0,5                 3. 5,2,0                  4. 0,6,4

 

35.          Find the sum of (1/1^1/2+2^1/2)+ (1/3^1/2+4^1/2)+ (1/5^1/2+6^1/2)+……………… (1/80^1/2+81^1/2) is-

1.  8                        2.  10                      3.  16                      4.  1/81

 

36.          Which of the following statements is not correct?

1.  log₁₀ 10 = 1                    2.   log (2 + 3) = log (2 x 3)              3.            log₁₀ 1 = 0

4.  log (1 + 2 + 3) = log 1 + log 2 + log 3

37 .         If log a + log b = log (a + b), then:

1.  a + b = 1                      2.  a – b = 1                           3.  a = b                 4.  a² – b² = 1

 

38.        In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What                              is the probability that it is neither red nor green?

1.   1/3                                   2.   3/4                                   3.  7/19 4.  8/21

 

39.          What is the probability of getting a sum 9 from two throws of a dice?

1.  1/6                                    2.  1/8                    3.  1/9                                    4.  1/12

 

40.          From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

1.  149 m                              2.  156 m              3. 173 m               4.  200 m

 

41.          Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

1.  173 m                              2.  200 m              3.  273 m              4.  300 m

 

42.          if  2f(x+1)+f(1/x+1)=2x , then f(2) is equal :

1.  5/3                                                2.  5/2                    3.  -1                      4.  2

 

 

43.          If x = a (t sin t), y = a (1 cos t), then dy/dx is  equal to :

 

1. cot 1                              2.  cot(1/2t)        3.  tan(1/2t)        4.  tan t

 

 

44.          ∫e^x(x²+1/(x+1)²)dx is equal to :

 

1.  –e^x/x+1                       2.  e^x+1                   3.  e^x(x-1)/(x+1)  4. None of these.

 

 

45.       if A+B=π/2 ,then (1+tan A)(1+tan B) is equal to :

1. 2                                      2.  3/2                    3.  1                        4. 1/2

 

46.          the value of A , for which  the three points (1, 1), (4, 1), (2, A) are collinear, is :

 

1. 1/2                                 2. 0                         3.  3                        4.  -2

 

 

47.          The limiting points of the coaxal system of circles x2 + y2 + Ax + 1 = 0 are :

 

1.  (±A/2,0)                      2.  (±2,0)              3.  (±1,0)                              4.  (±5,0)

 

48.          The sum of the series 1/2.3 +1/4.5 + 1/6.7 + + + + ¥ is :

1.  loge 2              2.  loge 2 -1                      3. 1 – loge 2         4.  1 + loge 2

 

49.          An equilateral triangle is inscribed in the parabola y2 = 4ax with is one vertex at the origin. The origin of its side is :

 

1. 8a(1.73)        2.  8a                                      3.  4a                      4.4a(1.73)

 

 

50.          The distance between the two foci of the ellipse 5x²+4y²=20  is :

1. 1                      2.  2                                        3.  4/5                    4.  5/2

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