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Odisha JEE Maths Practice Question Paper

30 practice questions for Orissa Joint Entrance Exam (Odisha JEE) Maths entrance exam with answers given at the end of each question.

Ques. The arithmetic mean between two numbers is A and S is the sum of n arithmetic means between these numbers, then
(a) S = nA
(b) A = nS
(c) A= S
(d) none of these
Ans. (a)

Ques. l, m, n are real, l m, then roots of the equation (l – m)x2 – 5(l + m)x – 2(l – m) = 0 are
(a) real and equal
(b) complex
(c) real and unequal
(d) none of these
Ans. (c)

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Ques. The intercept of a line between the coordinate axes is divided by point (– 5, 4) in the ratio 1 : 2. The equation of the line will be
(a) 5x – 8y + 60 = 0
(b) 8x – 5y + 60 = 0
(c) 2x – 5y + 30 = 0
(d) None of these
Ans. (b)

Ques. If the vertex and the focus of a parabola are (–1, 1) and (2, 3) respectively, then the directrix is
(a) 3x + 2y + 14 = 0
(b) 3x + 2y – 25 = 0
(c) 2x – 3y + 10 = 0
(d) none of these
Ans. (a)

Ques. The value of expression k – 1Ck – 1 + kCk– 1 + ……..+ n + k – 2Ck – 1 is
(a) n + k – 1Ck + 1
(b) n + k – 1Ck
(c) n + k Ck
(d) none of these
Ans. (b)

Ques. The number of common tangents to the circles x2 + y2 = |x| is
(a) 2
(b) 1
(c) 3
(d) 4
Ans. (c)

Ques. A straight line moves so that the sum of the reciprocals of its intercepts on the co-ordinate axes is unity. Then
(a) the straight line always passes through fixed point (1, 1)
(b) it does not pass through any fixed point
(c) it passes through the origin
(d) none of these
Ans. (a)

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Ques. A bag contains (2n + 1) coins. It is known that n of these have a head on both the sides, whereas the remaining (n + 1) coins are fair. A coin is picked up at random from the  bag and tossed. If the probability that the toss results in a head is 31/42, then value of n is
(a) 10
(b) 8
(c) 76
(d) 25
Ans. (a)

Ques. Let ABC be an  isosceles triangle  with  AB = BC.  If  base  BC  is  parallel  to
x-axis and  m1 and  m2  be the  slopes  of  medians drawn through  the  angular  points  B and C, then ;
(a) m1m2 = –1
(b) m1 + m2  = 0
(c) m1 m2 = 2
(d)  m1 + 2m2 = 0
Ans. (b)

Ques. The equation of plane passing through (1, 2,3) and at the maximum distance from origin is
(a) x + 2y + 3z = 14
(b) x + y + z = 6
(c) x + 2y + 3z = –14
(d) 3x + 2y + z = 14
Ans. (a)

Ques. Workers work in three shifts I, II, III in a factory. Their wages are in the ratio 4 : 5 : 6 depending upon the shift. Number of workers in the shifts are in the ratio 3 : 2 : 1. If total number of workers working is 1500 and wages per worker in shift I is Rs. 400. Then mean wage of a worker is
(a) Rs. 467
(b) Rs. 500
(c) Rs. 600
(d) Rs. 400
Ans. (a)

Ques. Total number of books is 2n + 1. One is allowed to select a minimum of the one book and a maximum of n books. If total number of selections if 63, then value of n is :
(a) 3
(b) 6
(c) 2
(d) none of these
Ans. (a)

Ques. The number of different garlands, that can be formed using 3 flowers of one kind and 3 flowers of other kind, is
(a) 60
(b) 20
(c) 4
(d) 3
Ans. (d)

Ques. The number of  roots of the equation z6 = -64, whose real parts are non-negative, is
(a) 2
(b) 3
(c) 4
(d) 5
Ans. (c)

Ques. For all complex numbers z1, z2 satisfying |z1| = 12 and |z2 – 3 – 4i| = 5, the minimum value of |z – z2| is
(a) 4
(b) 3
(c) 1
(d) 2
Ans. (d)

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Ques. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
(a) a function
(b) Transitive
(c) not symmetric
(d) reflexive
Ans. (c)

Ques. The major axis of the ellipse, whose axes are the coordinates with latus rectum 20, whose minor axis is the distance between the foci, is
(a) 18
(b) 20
(c) 36
(d) 40
Ans. (d)

Ques. If x1, x2, x3 and y1, y2, y3 are both G.P. with the same common ratio, then the points (x1, y1), (x2, y2) and (x3, y3)
(a) lie on a straight line
(b) lie on an ellipse
(c) are vertices of a triangle
(d) lie on a circle
Ans. (a)

Ques. The tangent to the curve y = x3 at the point P(t, t3) cuts the curve again at the point Q. The point Q is
(a) (0, 0)
(b) (2t, 4t3)
(c) (2t, 8t3)
(d) (-2t, -8t3)
Ans. (d)

Ques. Let A and B be non–singular matrices of one and the same order such that AB = BA. Then
(a) A = B
(b) A2 = B2
(c) AB–1 = B–1A
(d) A–1 = B–1
Ans. (c)

Ques. If the normal to the rectangular hyperbola xy = c2 at the point (ct, c/t) meets the curve again at (ct’, c/t’), then
(a) t3 t’ = 1
(b) t3t’ = –1
(c) t t’ = 1
(d) t t’ = –1
Ans. (b)

Ques. A body is projected vertically upwards from a tower of height 192 ft. If it strikes the ground in 6 seconds, then the velocity with which the body is projected is
(a) 64 ft./sec
(b) 32 ft./sec
(c) 16 ft./sec
(d) none of these
Ans. (a)

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Ques. If  f(x) =  {x2}  – ({x})2  where  {x}  denotes  the  fractional part  of   x then
(a) f(x)  is  continuous  at x = 2 but not  at  x = –2
(b) f(x)  is  continuous  at x = –2 but not  at  x = 2
(c) f(x)  is  continuous   at  x = –2  but  x = –2
(d) f(x) is  discontinuous  at  x = 2 and  x = –2
Ans. (a)

Ques. A function f such that f ¢(a) = f ¢¢(a) = f ¢¢¢(a) = … = f (2n)(a) = 0 and f has a local maximum value b at x = a, if f(x) is
(a) (x – a)2n + 2
(b) b – 1 – (x + 1 – a)2n + 1
(c) b – (x – a)2n + 2
(d) (x – a)2n + 2 – b
Ans. (c)

Ques. Number of ways of distributing 10 identical objects among 8 persons (one or many persons may not be getting any object), is
(a) 810
(b) 108
(c) 17C7
(d) 10C8
Ans. (c)

Ques. If  a  and  b  are   distinct positive  real  numbers such that  a, a1, a2, a3, a4, a5, b  are  in A.P.; a,  b1,b2 , b3,  b4, b5, b  are  in G.P.   and  a,  c1,  c2, c3 , c4,  c4, c4, c5, b  are   in H.P. ,  then  roots  of  a3x2 + b3x +  c3 = 0  are;
(a) real and distinct
(b) real and equal
(c) imaginary
(d) none of these
Ans. (c)

Ques. A differential equation is called linear, if its
(a) degree is 1
(b) order is 1
(c) degree and order both are 1
(d) none of these
Ans. (d)

Ques. A man firing at a distant target has 10%. Chance of hitting the target in one shot. The number of times he must fire at the target to have about 50% chance of hitting target is
(a) 11
(b) 9
(c) 7
(d) 5
Ans. (c)

Ques. In an examination, a candidate is required to pass four different subjects. The numbers of ways he can fail is
(a) 4
(b) 10
(c) 15
(d) 24
Ans. (c)

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Ques. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are
(a) 7, 6
(b) 6, 3
(c) 5, 1
(d) 8, 7
Ans. (b)

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