Maths SRM Entrance exam model Question papers

40 Maths SRM Entrance exam model questions with answers on mathematics for Sri Ramaswamy Memorial Institute of Science and Technology Engineering entrance exam.

Ques. A ray of light is sent along the line x + y = 1, after being reflected from the line y – x = 1, it is again reflected from the line y = 0, then the equation of the line representing the ray after second reflection may be given as
(a) x + y = 1
(b) x -y = 1
(c) y – x = 1
(d) none of these
Ans. (b)

Ques. If (2, 1), (–1, –2), (3, –3) are the midpoints of the sides BC, CA, AB respectively of triangle ABC, the equation of AB is
(a) 2(x + y) = 1
(b) x + y = 1
(c) x – y = 9
(d) x – y = 6
Ans. (d)

Ques. Radius of the largest circle which passes through the focus of the parabola y² = 4x and contained in it, is
(a) 8
(b) 4
(c) 2
(d) 5
Ans. (b)

Ques. The number of real common tangents that can be drawn to the ellipses 3x² + 5y² = 32 and
25x² + 9y² = 450 passing through (3, 5) is
(a) 0
(b) 2
(c) 3
(d) 4
Ans. (a)

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Ques. The locus of midpoints of chords of an ellipse, which are drawn through an end of minor axis, is
(a) straight line
(b) parabola
(c) ellipse
(d) circle
Ans. (c)

Ques. The necessary and sufficient condition for the equation (1– a²) x² + 2ax – 1 = 0 to have roots lying in the interval (0, 1) is
(a) a > 0
(b) a < 0
(c) a > 2
(d) None of these
Ans. (c)

Ques. The number of all three digits even numbers such that if 3 is one of the digits, then next digit is 5, is
(a) 359
(b) 360
(c) 365
(d) 380
Ans. (c)

Ques. If ax² + bx + 10 = 0 does not have two distinct real roots then the least value of 5a + b is
(a) –3
(b) –2
(c) 3
(d) None of these
Ans. (b)

Ques. If A is a square matrix then which one of the following is not a symmetric matrix
(a) A + A’
(b) AA’
(c) A’A
(d) A – A’
Ans. (d)

Ques. A box contains 24 balls of which 12 are black and 12 are white. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is
(a) 5/64
(b) 27/32
(c) 5/32
(d) ½
Ans. (c)

Ques. If f(x) = max {|16 – x²|, |x|}, the minimum value of f(x) in the interval [–3, 3] is
(a) 2
(b) 6
(c) 4
(d) none of these
Ans. (a)

Ques. The area bounded by the curves y = ln x, y = ln |x|, y = |ln x| and y = | ln |x| | is
(a) 5 sq. Units
(b) 2 sq. Units
(c) 4 sq. Units
(d) none of these
Ans. (c)

Ques. Total number of ways in which a person can put 8 different rings in the fingers of his right hand is equal to
(a) ¹⁶P₈
(b) ¹¹P₈
(c) ¹⁶C₈
(d) ¹⁶C₈
Ans. (b)

Ques. If a, b and c be three unequal positive quantities in H.P. then
(a) a^3/2 + b^3/2 > 2b^1/2
(b) a⁵ + b⁵ > 2b⁵
(c) a² + b² > 2b³
(d) none of these
Ans. (b)

Ques. A rectangle is 8 cm longer than its width. A square of side x cm has been cut out of it. If x cm is half the width of the rectangle, then the remaining area is
(a) (2x² + 8x)cm²
(b) (2x² + 16x) cm²
(c) (3x² + 8x) cm²
(d) (3x² + 16x) cm²
Ans. (d)

Ques. Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining  these points are
(a) 100
(b) 150
(c) 120
(d) None of these
Ans. (a)

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Ques. If the n^th term of an A.P. be (2n – 1), then the sum  of its first n terms will be
(a) n² – 1
(b) (2n – 1)²
(c) n²
(d) n² + 1
Ans: (c)

Ques. The Domain of function tan^–1 x + cos^–1 x² is
(a) R – [–1, 1]
(b) R – (–1, 1)
(c) (–1, 1)
(d) [–1, 1]
Ans. (d)

Ques. If AB = A and BA = B, where A and B are square matrices, then
(a) B² = B and A² = A
(b) B² = A and A² = B
(c) AB = BA
(d) none of these
Ans. (a)

Ques. Consider the family of lines, y – y₁ = m(x – x₁), in which m is a constant and
x₁² + y₁² = 1, then all the lines of the family are
(a) concurrent at origin
(b) normal lines to the circle x² + y^­2 = 2
(c) tangent lines to the circle x² + y² = 1
(d) none of these
Ans. (d)

Ques. The equation of a largest circle passing from points (1, 1) and (2, 2) and always in first quadrant is
(a) x² + y² – 4x – 2y + 4 = 0
(b) x² + y² + 2x + 4y + 4 = 0
(c) x² + y² – 3x – 3y + 4 = 0
(d) x² + y² – 5x – y + 4 = 0
Ans. (a)

Ques. If f is a periodic function and g is a non-periodic function then
(a) fog is always periodic
(b) gof is never periodic
(c) gof is always periodic
(d) none of these
Ans. (c)

Ques. The inclination of the normal with positive direction of x-axis, drawn at another end of a normal to the parabola y² = 4x is always
(a) 60°
(b) less than 60°
(c) more than 60°
(d) less than 45°
Ans. (c)

Ques. The angle between the asymptotes of the hyperbola 27x² – 9y² = 24 is
(a) 30°
(b) 150°
(c) 60°
(d) 90°
Ans. (c)

Ques. If a > 1, roots of the equation (1 – a)x² + 3ax – 1 = 0 are
(a) one positive and one negative
(b) both negative
(c) both positive
(d) both imaginary
Ans. (c)

Ques. The area bounded by the curve y = 2x – x² and the straight line y = –x is given by
(a) 9/2
(b) 43/6
(c) 35/6
(d) none of these
Ans. (a)

Ques. If 33! is divisible by 2ⁿ_, then the maximum value of n =
(a) 30
(b) 31
(c) 32
(d) 33
Ans. (b)

Ques. The sum of all odd proper divisors of 360 is
(a) 77
(b) 78
(c) 81
(d) none of these
Ans. (a)

Ques. In the polynomial (x – 1) (x – 2) (x – 3) … (x – 100). The co-efficient of x⁹⁹
(a) 5050
(b) –5050
(c) 100
(d) 99
Ans. (b)

Ques. The minimum number of times a fair coin must be tossed so that the probability of getting atleast one head is at least 0.8 is
(a) 7
(b) 6
(c) 5
(d) 3
Ans. (d)

Ques. Number of real roots of the equation a^x + b^x + c^x – d^x = 0 (where 0 < a < b < c < d) is
(a) 0
(b) 2
(c) 3
(d) none of these
Ans. (d)

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Ques. Equation of vertical tangent to the curve y = e^xy – x is possible at the point
(a) (1, 1)
(b) (0, 1)
(c) (1, 0)
(d) no point
Ans. (c)

Ques. The area of the region by the curve y = x |x|, x-axis and the ordinates x = 1, x = –1 is given by
(a) 0
(b) 1/3
(c) 2/3
(d) none of these
Ans. (c)

Ques. In a triangle PQR sin P, sin Q, sin R in A.P. then the Altitude are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Ans. (c)

Ques. The coefficient of x⁶ in the expansion of (1 + x² – x³)⁸ is
(a) 80
(b) 84
(c) 88
(d) 92
Ans. (b)

Ques. If m and M are the least and the greatest value of (cos^–1 x)² + (sin^–1 x)², then M/m is equal to
(a) 10
(b) 5
(c) 4
(d) 2
Ans. (d)

Ques. Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. The total number of persons in the room is
(a) 11
(b) 12
(c) 13
(d) 14
Ans. (b)

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. Let A be a set containing 10 distinct elements. Then the total number of distinct functions from A to A, is
(a) 10!
(b) 10¹⁰
(c) 2¹⁰
(d) 2¹⁰ – 1
Ans. (b)

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Ques. In a touring cricket team there are 16 players in all including 5 bowlers and 2 wicket-keepers. How many teams of 11 players from these, can be chosen, so as to include three bowlers and one wicket-keeper
(a) 650
(b) 720
(c) 750
(d) 800
Ans. (b)