Maths Practice Questions for AMUEEE

Ques. The rationalising factor of a^1/3 + a^–1/3 is
(a) a^1/3 + a^–1/3
(b) a^2/3 + a^–2/3
(c) a^2/3 – a^–2/3
(d) a^2/3 + a^–2/3 – 1
Ans:- (d)

Ques. A uniform rod BC of length 6 cm  and weight 2 kg can turn freely about the fixed point B. The rod is attached to the point A by a string AC of length 8 cm. The points A and B are in a horizontal line at a distance 10 cm. The tension in the string is
(a) 3/5 kg -wt
(b) 1/5 kg-wt
(c) 2/5 kg-wt
(d)  None of these
Ans:- (a)

Ques. In a certain test a_i students gave wrong answers to at least i questions where i = 1, 2, 3, … k. No student gave more than k wrong answers. The total numbers of wrong answers given is
(a)a₁ + 2a₂ + 3a₃ + … + ka_k
(b) a₁ + a₂ + a₃ + … + a_k
(c) Zero
(d) None of these
Ans:- (b)

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Ques. Two candidates attempt to solve the equation x2 + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6 and the other starts with a wrong value of q and find the roots to be 2 and – 9. The roots of the original equation are
(a)  2, 3
(b)  3, 4
(c) –2, – 3
(d) – 3, – 4
Ans:- (d)

Ques. The upper ¾ th portion of a vertical pole subtends an angle tan^–1 (3/5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is
(a) 20 m
(b) 40 m
(c) 60 m
(d) 80 m
Ans:- (b)

Ques. x² = xy is a relation which is
(a) Symmetric
(b) Reflexive
(c) Transitive
(d) None of these
Ans:- (b)

Ques. If the portion of the line lx + my = 1 falling inside the circle x² + y² = a² subtends an angle of 45^o at the origin, then
(a) 4[a² (l² + m²) – 1] = a² (l² + m²)
(b) 4[a² (l² + m²) – 1] = a² (l² + m²) – 2
(c) 4[a² (l² + m²) – 1] = [a² (l² + m²) – 2]²
(d) None of these
Ans:- (c)

Ques. The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point
(a) (1/2, 3/4)
(b) (1, 3)
(c) (3, 1)
(d) (3/4, 1/2)
Ans:- (d)

Ques. A ball is thrown vertically upwards from the ground with velocity 15 m/s and rebounds from the ground with one-third of its striking velocity. The ratio of its greatest heights before and after striking the ground is equal to
(a) 4 : 1
(b) 9 : 1
(c) 5 : 1
(d) 3 : 1
Ans:- (b)

Ques. Which of the following, in case of a discrete data, is not equal to the median
(a) 50th percentile
(b) 5th decile
(c) 2nd quartile
(d) Lower quartile
Ans:- (d)

Ques. If 3x = 2y –1 and 2x + 3y + 1 = 0 are two lines of regression, then the coefficient of correlation will be
(a) 0
(b) – 1
(c) 1
(d) None of these
Ans:- (a)

Ques. In any group the number of improper subgroups is
(a) 2
(b) 3
(c) Depends on the given group
(d) 1
Ans:- (a)

Ques. Binary equivalent of decimal number 0.3125 is
(a) 0101
(b) .1010
(c) .0101
(d) .1101
Ans:- (c)

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Ques. In a triangle R  and r are the circumradius and inradius respectively. The harmonic mean of the exradii of the triangle is
(a) R + 3r
(b) R + 2r
(c) R + r
(d) 3r
Ans. (d)