This Maharashtra CET Mathematics Practice sample paper is based on Mah CET Maths syllabus.

Ques: If cosh y = sec x, then the value of tanh² (y/2) is
(a) tan² (x/2)
(b) cot² x/2
(c) sin² (x/2)
(d) cos² x/2

Ans. (a)

Ques. The triangle formed by the tangent to the curve f(x) = x² + 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: The number of values of c such that the straight line y = 4x + c touches the curve x²/4 + y² = 1 is
(a) 0
(b) 1
(c) 2
(d) Infinite

Ans. (c)

Ques: The vector b = 3j + 4k is to be written as the sum of a vector b₁ parallel to a = I + j and a vector b₂

perpendicular to a. Then b₁ =
(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: The number of reflexive relations of a set with four elements is equal to
(a) 2¹⁶
(b) 2¹²
(c) 2⁸
(d) 2⁴

Ans. (d)

Ques. The solution of the differential equation sec² x tan ydx + sec² y tan xdy = 0 is
(a) tan x = c tan y
(b) tan x = c tan (x + y)
(c) tan x = c cot y
(d) tan x sec y = c

Ans. (c)

Ques. If (1 + x – 2x²)⁶ = 1 + a₁x + a₂x² + a₃x³ . . . . . then the value of a₂ + a₄ + a₆ + . . . .+ a₁₂ will be
(a) 32
(b) 31
(c) 64
(d) 1024

Ans. (b)

Ques. If f’(x) = g(x) and g’(x) = –f(x) for all x and f(2) = 4 = f’(2), then f² (24) + g² (24) is
(a) 32
(b) 24
(c) 64
(d) 48

Ans. (a)

Ques. If ⁿP₃ + ⁿC_n–2 = 14n, then n =
(a) 5
(b) 6
(c) 8
(d) 10

Ans. (a)

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Ques: The triangle formed by the tangent to the curve f(x) = x² + 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: 49ⁿ + 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 x² + y² – 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 point (4, -3) with respect to the ellipse 4x² + 5y² = 1 is
(a) lies on the curve
(b) is inside the curve
(c) is outside the curve
(d) is focus of the curve

Ans. (c)

Ques: The area of the triangle formed by the line 4x² – 9xy – 9y² = 0 and x = 2 is
(a) 2
(b) 3
(c) 10/3
(d) 20/3

Ans. (c)

Ques: The differential equation for the family of curves x² + y² – 2ay = 0, where a is an arbitrary constant, is
(a) (x² + y²)y’ = 2xy
(b) 2(x² + y²)y’ = 2xy
(c) (x² – y²)y’ = 2xy
(d) 2(x² – y²)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 (x₀, f(x₀))
(b) Tangent to the curve y = f(x) at the point (x₀, f(x₀))
(c) The straight line through the point (x₀, f(x₀)) having the gradient 1/f’(x₀)
(d) The ordinate through the point (x₀, f(x₀))

Ans. (b)

Ques. The coefficient of x⁴ in the expansion of (1 + x + x² + x³)¹¹ is
(a) 900
(b) 909
(c) 990
(d) 999

Ans. (c)

Ques. Let PQR be a right angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is
(a) 3x² – 3y² + 8xy + 20x + 10y + 25 = 0
(b) 3x² – 3y² + 8xy – 20x – 10y + 25 = 0
(c) 3x² – 3y² + 8xy + 10x + 15y + 20 = 0
(d) 3x² – 3y² – 8xy – 10x – 15y – 20 = 0

Ans. (b)

Ques. Let function f (x) = x² + x + sin x – cos x + log (1 + |x|) be defined over the interval [0, 1]. The odd extensions of f(x) to interval [–1, 1] is
(a) x² + x + sin x + cos x – log (1 + |x|)
(b) –x² + x + sin x + cos x – log (1 + |x|)
(c) –x² + x + sin x – cos x + log (1 + |x|)
(d) None of these

Ans. (b)

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Ques. The product of lengths of perpendiculars from any point of the hyperbola x² – y² = 8 to its asymptotes is
(a) 2
(b) 3
(c) 4
(d) 8

Ans. (c)

Ques. The roots of the equation 3^2x – 10.3^x + 9 = 0 are
(a) 1, 2
(b) 0, 2
(c) 0, 1
(d) 1, 3

Ans. (b)

Ques. The curve y – e^xy + x = 0 has a vertical tangent at the point
(a) (1, 1)
(b) at no point
(c) (0, 1)
(d) (1, 0)

Ans. (d)

Ques. If are in A.P. 10^{ax + 10} , 10^{bx + 10} , 10^{cx + 10} are in
(a) A.P.
(b) G.P. when x > 0
(c) G.P. for all x
(d) G.P. when x < 0

Ans. (c)

Ques. If log 2, log (2ⁿ – 1) and log (2ⁿ + 3) are in A.P., then n =
(a) 5/2
(b) log₂ 5
(c) log₃ 5
(d) 3/2

Ans. (b)

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Ques. The normal chord of a parabola y² = 4ax at (x₁,x₁) subtends a right angle at the
(a) Focus
(b) Vertex
(c) (–a, 0)
(d) None of these

Ans. (a)

Ques. The binary equivalent of octal number (5473.64)₈ is
(a) (110100111011.110101)₂
(b) (101100111011.110100)₂
(c) (100100111011.110100)₂
(d) (101100111101.110100)₂

Ans. (b)

Ques. The area of the triangle formed by the line x + y = 3 and the angle bisectors of the pair of straight lines x² – y² + 2y = 1 is
(a) 2
(b) 4
(c) 6
(d) 8

Ans. (a)

Ques. If iz³ + z² – z + i = 0 then the value of |z| is
(a) 1
(b) 2
(c) < 1
(d) > 1

Ans. (a)

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Ques. Ranks of 10 students of a class in two subjects are (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is
(a) 0
(b) – 1
(c) 1
(d) 0.5

Ans. (b)

Ques. A particle is dropped under gravity from rest from a height h(g = 9.8 m/sec²) and then it travels a distance 9h/25 in the last second. The height h is
(a) 100 metre
(b) 122.5 metre
(c) 145 metre
(d) 167.5 metre

Ans. (b)

Ques. The number of distinct terms in the expansion of (x + 2y – 3z + 5w – 7u)ⁿ is
(a) n + 1
(b) ⁿ⁺⁴C₄(c) ⁿ⁺⁴C_n+2(d) none of these

Ans. (b)

Ques. cot x – tan x =
(a) cot 2x
(b) 2 cot² x
(c) 2 cot 2x
(d) cot² 2x

Ans. (c)

Ques. The tangents are drawn from the point (4, 5) to the circle x² + y² – 4x – 2y – 11 = 0. The area of quadrilateral formed by these tangents and radii, is
(a) 15 sq. units
(b) 75 sq. units
(c) 8 sq. units
(d) 4 sq. units

Ans. (c)

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Ques. Sum of coefficients in the expansion of (x + 2y + z)¹⁰ is
(a) 2¹⁰
(b) 3¹⁰
(c) 1
(d) none of these

Ans. (d)

Ques. If the roots of the equations x² – bx + c = 0 and x² – cx + b = 0 differ by the same quantity, then b + c is equal to
(a) 4
(b) 1
(c) 0
(d) –4

Ans. (d)

Ques. The coefficient of x⁵ in the expansion of (1 + x²)⁵ (1 + x)⁴ is
(a) 30
(b) 60
(c) 40
(d) None of these

Ans. (b)

Ques. If the angles A, B, C are the solutions of the equation tan³x –3k tan² x –3 tan x + k = 0 then the triangle ABC is
(a) isosceles
(b) equilateral
(c) acute angled
(d) such a triangle does not exist

Ans. (d)

Ques. If the distances of two points P and Q from the focus of a parabola y²= 4x are 4 and 9 respectively, then the distance of the point of intersection of tangents at P and Q of the parabola from the focus is
(a) 8
(b) 6
(c) 5
(d) 13

Ans. (b)

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/sec² is
(a) 1464.8 N
(b) 1784.8 N
(c) 1959.8 N
(d) 1104.8 N

Ans. (d)

Ques. The value of sin² 5^o + sin² 10^o + sin² 15^o + … + sin² 85^o + sin² 90^o is equal to
(a) 7
(b) 8
(c) 9
(d) 9 ½

Ans. (d)

Ques. The co-ordinates of the point from where the tangents are drawn to the circles x² + y² = 1, x² + y² + 8x + 15 = 0 and x² + y² + 10y + 24 = 0 are of same length, are
(a) (2, 5/2)
(b) (–2, –5/2)
(c) (–2, 5/2)
(d) (2, –5/2)

Ans. (b)

Ques. If a₁, a₂, a₃, ….. a_n are n distinct odd natural numbers not divisible by any prime greater than or equal to 7, then the value of 1/a₁ + 1/a₂ + … + 1/a_n is always less than
(a) 1
(b) 15/8
(c) ½
(d) ¾

Ans. (b)

Ques. Two trains A and B, 100 kms apart, are travelling to each other with starting speed of 50 km/hr for both. The train A is accelerating at 18 km/hr² and B is decelerating at 18 m/h². The distance where the engines cross each other from the initial position of A is
(a) 50 kms
(b) 68 kms
(c) 32 kms
(d) 59 kms

Ans. (d)

Ques. If 2z₁ – 3z₂ + z₃ = 0 then z₁, z₂, z₃ are represented by
(a) three vertices of a triangle
(b) three collinear points
(c) three vertices of a rhombus
(d) none of these

Ans. (b)

Ques. The sums of n terms of three A.P.’s whose first term is 1 and common differences are 1, 2, 3 are s₁, S₂, S₃ respectively. The true relation is
(a) S₁ + S₃ = S₂
(b) S₁ + S₃ = 2S₂(c) S₁ + S₂ = 2S₃
(d) S₁ + S₂ = S₃

Ans. (b)

Ques. The circle x² + y²–2x –6y + 2 = 0 intersects the parabola y² = 8x orthoganally at the point P. The equation of the tangents to the parabola at P can be
(a) x –y –4 = 0
(b) 2x + y –2 = 0
(c) x + y –4 = 0
(d) 2x –y +1 = 0

Ans. (d)

Ques. The equation of the common tangent to the curves y² = 8x and xy = –1 is
(a) 3y = 9x + 2
(b) y = 2x + 1
(c) 2y = x + 8
(d) y = x + 2

Ans. (d)

Ques. If a > b > c and the system of equations ax + by + cz = 0, bx + cy + az = 0 and cx + ay + bz = 0 has a non trivial solution, then both the roots of the quadratic equation at² + bt + c = 0 are
(a) at least one positive root
(b) opposite in sign
(c) positive
(d) imaginary

Ans. (a)

Ques. A man in a balloon, rising vertically with an acceleration of 4.9 m/sec² releases a ball 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the ball is
(a) 14.7 m
(b) 19.6 m
(c) 9.8 m
(d) 24.5 m

Ans. (a)

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Ques. The figure formed by the lines x² + 4xy + y² = 0 and x – y = 4, is
(a) A right angled triangle
(b) An isosceles triangle
(c) An equilateral triangle
(d) None of these

Ans. (c)

Ques. Equation of the straight line, passing through the point (3, 4) and farthest from the circle
x² + y² + 8x + 6y + 16 = 0, is
(a) x – y + 1 = 0
(b) 3x + 4y = 25
(c) x + y – 7 = 0
(d) none of these

Ans. (c)

Ques. Let ABC be a triangle and O be its orthocentre. If R and R₁ are the circum radii of triangles ABC and AOB, then
(a) R₁ > R
(b) R₁ = R
(c) R₁ < R
(d) nothing can be said

Ans. (b)

Ques. The root of the equation x³ + x – 3 = 0 lies in interval (1, 2) after second iteration by false position method, it will be in
(a) (1.178, 2.00)
(b) (1.25, 1.75)
(c) (1.125, 1.375)
(d) (1.875, 2.00)

Ans. (a)

Ques. The number of solution of the following equations x₂ – x₃ = 1, –x₁ + 2x₃ = –2, x₁ – 2x₂ = 3 is
(a) Zero
(b) One
(c) Two
(d) Infinite

Ans. (a)

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Ques. If ⁵⁶P_r+6 : ⁵⁴P_r+3 = 30800 : 1, then r =
(a) 31
(b) 41
(c) 51
(d) None of these

Ans. (b)

Ques. The resultant of two forces P and Q is R. If Q is doubled, R is doubled and if Q is reversed, R is again doubled. If the ratio P² : Q² : R² = 2 : 3 : x, then x is equal to
(a) 5
(b) 4
(c) 3
(d) 2

Ans. (d)

Ques. If x = log₃ 5, y = log₁₇ 25, which one of the following is correct
(a) x < y
(b) x = y
(c) x > y
(d) None of these

Ans. (c)

Ques. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0 is
(a) x² + y² – 2xy – 4x + 4y – 4 = 0
(b) x² + y² – 2xy + 4x – 4y – 4 = 0
(c) x² + y² + 2xy – 4x + 4y – 4 = 0
(d) x² + y² + 2xy – 4x + 4y + 4 = 0

Ans. (c)

Ques. A root of the equation x³ – 3x – 5 = 0 lies between 2 and 2.5. Its approximate value, by applying bisection method 3 times is
(a) 2.0625
(b) 2.3125
(c) 2.3725
(d) 2.4225

Ans. (b)

Ques. Given that the equation z² + (p + iq)z + r + I s = 0, where p, q, r, s are real and non-zero has a real root, then
(a) pqr = r² + p² s
(b) prs = q² + r² p
(c) qrs = p² + s² p
(d) pqs = s² + q² r

Ans. (d)

Ques. If the product of roots of the equation x² – 3kx + 2e^{2 log k} – 1 = 0 is 7, then its roots will real when
(a) k = 1
(b) k = 2
(c) k = 3
(d) None of these

Ans. (b)

Ques. If cos (u + iv) = x + iy, then x² + y² + 1 is equal to
(a) cos² u + sinh² v
(b) sin² u + cosh² v
(c) cos² u + cosh² v
(d) sin² u + sinh² v