This Maharashtra CET Mathematics Practice sample paper is based on Mah CET Maths syllabus and consist 34 questions.

**Ques:** If cosh y = sec x, then the value of tanh^{2} (y/2) is

(a) tan^{2} (x/2)

(b) cot^{2} x/2

(c) sin^{2} (x/2)

(d) cos^{2} x/2

Ans:- (a)

**Ques:** P, Q, R and S have to give lectures to an audience. The organiser can arrange the order of their presentation in

(a) 4 ways

(b) 12 ways

(c) 256 ways

(d) 24 ways

Ans:- (d)

**Ques:** The number of values of *c* such that the straight line y = 4x + c touches the curve x^{2}/4 + y^{2} = 1 is

(a) 0

(b) 1

(c) 2

(d) Infinite

Ans:- (c)

**Ques:** Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2), will be

(a) x – 7y + 12 = 0

(b) 7x + y – 12 = 0

(c) x – 7y + 16 = 0

(d) 7x + y + 16 = 0

Ans:- (a)

**Ques:** The vector b = 3j + 4k is to be written as the sum of a vector b_{1} parallel to a = I + j and a vector b_{2} perpendicular to a. Then b_{1} =

(a) 3/2 (i + j)

(b) 2/3 (I + j)

(c) ½ (I + j)

(d) 1/3 (i + j)

Ans:- (a)

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**Ques:** A man of mass 80 *kg*. is travelling in a lift. The reaction between the floor of the lift and the man when the lift is ascending upwards at 4 *m*/*sec*2 is

(a) 1464.8 *N*

(b) 1784.8 *N*

(c) 1959.8 *N*

(d) 1104.8 *N*

Ans:- (d)

**Ques:** A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is

(a) 1/5

(b) 2/5

(c) 4/5

(d) None of theses

Ans:- (d)

**Ques:** G = {e, a, b, c} is an abelian group with *e* as identity element. The order of the other elements are

(a) 2, 2, 2

(b) 3, 3, 3

(c) 2, 2, 4

(d) 2, 3, 4

Ans:- (a)

**Ques:** The electronic components used in third generation of computers are

(a) Vacuum tubes

(b) Transistors

(c) Integrated circuit

(d) All of these

Ans:- (c)

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**Ques:** The triangle formed by the tangent to the curve f(x) = x^{2} + bx – b at the point (1, 1) and the co-ordinate axes, lies in the first quadrant. If its area is 2 then the value of *b* is

(a) –1

(b) 3

(c) –3

(d) 1

Ans:- (c)

**Ques:** 49^{n} + 16n – 1 is divisible by

(a) 3

(b) 19

(c) 64

(d) 29

Ans:- (c)

**Ques:** Two tangents *PQ* and *PR* drawn to the circle x^{2} + y^{2} – 2x – 4y – 20 = 0 from point P (16, 7). If the centre of the circle is *C*, then the area of quadrilateral PQCR will be

(a) 75 *sq*. *units
*(b) 150

*sq*.

*units*

(c) 15

*sq*.

*units*

(d) None of these

Ans:- (a)

**Ques:** The area of the triangle formed by the line 4x^{2} – 9xy – 9y^{2} = 0 and x = 2 is

(a) 2

(b) 3

(c) 10/3

(d) 20/3

Ans:- (c)

**Related:** Trigonometry Ratios Practice Questions

**Ques:** The differential equation for the family of curves x^{2} + y^{2} – 2ay = 0, where *a* is an arbitrary constant, is

(a) (x^{2} + y^{2})y’ = 2xy

(b) 2(x^{2} + y^{2})y’ = 2xy

(c) (x^{2} – y^{2})y’ = 2xy

(d) 2(x^{2} – y^{2})y’ = xy

Ans:- (c)

**Ques:** If one root of the equation f(x) = 0 is near to x_{o} then the first approximation of this root as calculated by Newton-Raphson method is the abscissa of the point where the following straight line intersects the *x*-axis

(a) Normal to the curve y = f(x) at the point (x_{0}, f(x_{0}))

(b) Tangent to the curve y = f(x) at the point (x_{0}, f(x_{0}))

(c) The straight line through the point (x_{0}, f(x_{0})) having the gradient 1/f’(x_{0})

(d) The ordinate through the point (x_{0}, f(x_{0}))

Ans:- (b)

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