# MCET Sample Paper for Mathematics

**MCET Sample Paper for Mathematics**

Maharashtra Common Entrance Test is a single CET conducted by government of Maharashtra for Health science , Engineering and Pharmacy degree courses. MCET is now renamed as MTCET by the state government. The following is a MCET Sample Paper for Mathematics given to help you with this entrance exam and get high scores in Mathematics Paper. Lets have a detail of type of questions being asked.

**1. Three non-zero complex numbers z1, z2, z3 satisfying |z1|2 + |z2|2 + |z3|2 = |z1z2| + |z2z3| + |z3z1| lie on a circle with centre**

(A) (0, 0) (B) (1, 1) (C) (i, i) (D) none of these

** 2. Number of values of θ ϵ [-π/2,π/2]which satisfies the equation sin[π/2√2×cosθ] = cos[π/2√2×sinθ] is equal to**

(A) 0 (B) 1 (C) 2 (D) 4

** ****3. The value of (i^8 + i)^3 + (i^8 – i)^6 is**

(A) 1 + i (B) -2 + 10i (C) 1 + 3i (D) 1 – i

** 4. If abc = 8 and a, b, c > 0, then the minimum value of (2 + a) (2 + b) (2 + c) is**

(A) 32 (B) 64 (C) 8 (D) 10

**5. The sum of 19 terms of an A.P., whose n^th terms is 2n + 1 is**

(A) 390 (B) 399 (C) 499 (D) none of these

**6 If the first term of a G.P. is 1 and the sum of the third and fifth terms is 90. Then the common ratio if G.P. is**

(A) + -1 (B)+ – 2 (C) +-3 (D) + – 4

**7. The total number of real roots of the equation 2x^4 + 5x^2 + 3 = 0 is**

(A) 4 (B) 0 (C) 2 (D) 3

** 8. Let α,β,γ,δ are the roots of equation x^4 + x^2 + 1 = 0 then the equation chose roots are α^2,β^2,γ^2,δ ^2 is**

(A) (x^2 – x + 1)^2 = 0 (B) (x^2 + x + 1)^2 = 0 (C) x^4 – x^2 + 1 = 0 (D) x^2 + x + 1 = 0

**9. n-1C3 + n-1C4 > nC3, then value of ‘n’ can be**

(A) 4 (B) 6 (C) 7 (D) 8

**10. The number of committees of 3 members can be formed from 6 gentlemen and 4 ladies**

(A) 6C5 (B) 10P5 (C) 252 (D) 120

**11. The number of all possible selections of one or more questions from 8 given questions, each question having an alternative is**

(A) 2^8 – 1 (B) 3^8 – 1 (C) 4^8 – 1 (D) none of these

**12. The coefficient of x4 in the expansion of (1+x+x2+x3)^n is**

(A)nC4 (B) nC4+ nC2 (C) nC4+ nC1+ nC4 nC2 (D) nC4+ nC2+ nC1 nC2

**13. The system of linear equations x + y –z = 6, x + 2y – 3z = 14 and 2x + 5y – z = 9 ( R) has a unique solution if**

** **(A) = 8 (B) 8 (C) = 7 (D) = 7

**14. A square matrix A = [aij]n× n is called a lower triangular matrix iff aij = 0 for**

(A) i = j (B) i < j (C) i > j (D) none of these

**15. If A, B and C be the three square matrices such that A = B + C, then det A is equal to**

(A) det B + det C (B) det B (C) det C (D) none of these

**16. If sec θ+ tan θ = 1, then one root of the equation a (b – c)x^2 + b(c – a)x + c(a – b) = 0 is**

(A) tan θ (B) sec θ (C) cos θ (D) sin θ

**17. If A, B, C are acute positive angles then is**

(A) < 8 (B) 8 (C) 2 (D) none of these

**18. The value of cos π/n + cos2π/n + cos3π/n + ………+ cos (n-1)π/n**

(A) 0 (B)π/n (C) n (D) none of these

**19. The number of values of x satisfying the condition sinx + sin 5x = sin 3x in the interval [0, π] is**

(A) 6 (B) 2 (C) 10 (D) 0

**20. If 2cos x + 2 cos 3x = cos y, 2 sin x + 2sin 3x = sin y, then the value of cos 2x is**

(A) – 7/8(B)1/8 (C) –1/8 (D)7/8

**21. If the angles A and B of the triangle ABC satisfy the equation sin A + sin B = √3(cos B – cos A), then they differ by**

(A)π/6 (B) π/3 (C) π/4(D) π/2

**22. If the radii of the circumcircle and incircle of an equilateral triangle are respectively 12cm and 8cm, each side is equal to**

(A) 20 cm (B) 28 cm (C) 24 cm (D) 32 cm

**23. The expression (a+b+c)(b+c-a)/(c+a-b)(a+b-c) is equal to**

(A) cos^2(A/2) (B) sin^2(A/2) (C) cot^2(A/2) (D) tan^2(A/2)

**24. In a triangle ABC if ,c os A/a = tan C /c then sin(B + C) is equal to**

(A) cos B cos C (B) cosA cos C (C) cosA cos B (D) sinB sinC

**25. The angle of elevation of the top of a tower at any point on the ground is /6 and after moving 20m forwards the tower it becomes /3. The height of the tower is equal to**

(A) 10√3 m m (B) 10/√3 m (C) (D) 5√3 m

**26. A vertical pole subtends an angle tan^-11/2 at a point P on the ground. The angle subtended by the upper half of the pole at the point P is**

(A) tan^-1 1/4 (B) tan^-1 2/9 (C) tan^-1 1/8 (D) tan^-1 2/3

** 27. A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If is the angle which the pole subtends at the mid point of the opposite side, the length of each side of the park is**

(A)(√3 /2 h)cotα (B)(2/√3 h)cotα (C)√3 /2 h)tanα (D) (2/√3 h) tan α

**28. From a point an the ground 100m away from the base of a building, the angle of elevation of the top of the building is 600. Which of the following is the best approximation for the height of the building?**

(A) 172m (B) 173 m (C) 174 m (D) 175 m

**29. The points P(a, b + c), Q(b, c + a) and R(c, a + b) are such that PQ = QR if**

(A) a, b, c are in A.P. (B) a, b, c are in G.P. (C) a, b, c are in H.P. (D) None of these

**30. The points A(2, 3); B(3, 5), C(7, 7) and D (4, 5) are such that**

(A) ABCD is a parallelogram (B) A, B, C, D are collinear (C) D lies inside the triangle ABC (D) D lies on the boundary of the triangle ABC

**31. Q, R and S are the point on the line joining the point P(a, x) and T(b, y) such that PQ = QR = RS = ST, then [5a+3b/8, 5x+3y/8] is the mid-point of**

(A) PQ (B) QR (C) RS (D) ST

**32. The extremities of a diagonals of parallelograms are the points (3, -4) and (-6, 5). If third vertex is (-2, 1) then the coordinates of the fourth vertex are**

(A) (1, 0) (B) (-1, 0) (C) (1, 1) (D) none of these

**33. If one end of diameter of the circle 2x^2 + 2y^2 –4x– 8y +2 = 0 is (3,2), the other end is**

(A) (2, 3) (B) (4, -2) (C) (2, -1) (D) (-1, 2)

**34. Locus of the centre of the circle which always passes through the fixed points (-a, 0) and (a, 0) is**

(A) x = 1 (B) x + y = 6 (C) x + y = 2a (D) x = 0

**35. The equation x2 + y2 + 4x + 6y + 13 = 0 represents**

(A) a circle (B) a pair of two distinct straight lines (C) a pair of coincident straight lines (D) a point

**36. The line joining (5, 0) to (10 cos , 12 sin ) is divided internally in the ratio 2 : 3 at P. If varies, then the locus of P is**

(A) a pair of straight line (B) a circle (C) a straight line (D) none of these

**37. The curve described parametrically by x = t^2 + t + 1, y = t^2 – t + 1 represents**

(A) a pair of straight line (B) an ellipse (C) a parabola (D) a hyperbola

**38. If 2x + y +α = 0, is a normal to the parabola y^2 = -8x, then α =**

(A) 12 (B) -12 (C) 24 (D) -24

**39. The angle between the tangents drawn from the origin to the parabola y2 = 4a(x – a) is**

(A) 90^0 (B) 30^0 (C) tan^-1(1/2) (D) 45^0

**40. The line y = mx + 1 is a tangent to the parabola y^2 = 4x if**

(A) m = 1 (B) m = 2 (C) m = 4 (D) m = 3

**41. A point on the line y = x whose perpendicular distance from the line x/4+y/3 = 1 is 4, has the co-ordinates**

(a) (8/7, 8/7) (b)(32/7, 32/7) (c)(3/2,3/2) (d) none of these

**42. If the line α x + βy = 1 is a normal to the circle 2x^2+2y^2-5x+6y-1=0, then**

(a) 5α – 6β = 2 (b) 4 + 5β = 6α (c) 4 + 6β = 5α (d) none of these

**43. If (2, – 8) is an end of a focal chord of the parabola, then the coordinates of other end of the chord is**

(a) (32, 32) (b) (32, – 32) (c) (–2, 8) (d) none of these

**44. The triangle formed by the tangents to a parabola at the ends of the latus rectum and the double ordinate through the focus is**

(a) equilateral (b) isosceles (c) right-angled isosceles (d) dependent on the value of a for its classification

**45. If two foci of an ellipse be (– 2, 0) and (2, 0) and its eccentricity is 2/3, then the ellipse has the equation**

(a)5x^2+9y^2=45 (b) 9x^2 +5y^2=45 (c)5x^2+9y^2=90 (d)9x^2+5y^2=90

**46. The foci of the ellipse x^2/16 + y^2/b^2 =1 and the hyperbola coincide, then the value of is**

(a) 5 (b) 7 (c) 9 (d) 1

**47. The domain of the function f (x) = where [.] denotes the greatest integer function, is**

(a) [0, 1) (b) [– 1, 1] (c) (–1, 0) (d) none of these

**48. If the function f : R→ R be such that f (x) = x – [x], (where [.] denotes the greatest integer function), then f^-1(x) is**

(a)1/x-[x] (b)[x]-x (c) not defined (d) none of these

**49. If f (x) = | x – 1 | – [x], (where [.] denotes the greatest integer function, then**

(a) *f *(1 + 0) = – 1, *f *(1 – 0) = 0 (b) *f *(1 + 0) = 0 = *f *(1 – 0) (c)lim(x→1) f(x) exists (d) none of these

**50. Let h(x) = min{x,x^2} for every real number x. Then which of the following is false?**

(a) *h *is continuous for all *x *(b) *h *is differentiable for all *x *(c) *h*‘(*x*) = 1 for all *x *> 1 (d) *h *is not differentiable at two values of *x *

**51. The equation of a curve is given by The inclination of the tangent to the curve at the point is**

(a)π/4 (b)π/3 (c)π/2 (d) 0 )

GET THE ANSWERS OF ABOVE MCET SAMPLE PAPER FOR MATHEMATICS IN PDF ANSWERS FOR MCET SAMPLE PAPER FOR MATHEMATICS

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