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)x^{2} – 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 – 1}C_{k – 1} + ^{k}C_{k} _{– 1} + ……..+ ^{n + k – 2}C_{k – 1} is

(a) ^{n + k – 1}C_{k + 1}

(b) ^{n + k – 1}C_{k
}(c) ^{n + k }C_{k
}(d) none of these

Ans. (b)

**Ques. **The number of common tangents to the circles *x*^{2} + *y*^{2} = |*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 m_{1} and m_{2} be the slopes of medians drawn through the angular points B and C, then ;

(a) m_{1}m_{2} = –1

(b) m_{1} + m_{2} = 0

(c) m_{1} m_{2} = 2

(d) m_{1} + 2m_{2} = 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 *z*^{6} = -64, whose real parts are non-negative, is

(a) 2

(b) 3

(c) 4

(d) 5

Ans. (c)

**Ques. **For all complex numbers z_{1}, z_{2 }satisfying |z_{1}| = 12 and |z_{2} – 3 – 4i| = 5, the minimum value of |z – z_{2}| 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 x_{1}, x_{2}, x_{3} and y_{1}, y_{2}, y_{3} are both G.P. with the same common ratio, then the points (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})

(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 = x^{3} at the point P(t, t^{3}) cuts the curve again at the point Q. The point Q is

(a) (0, 0)

(b) (2t, 4t^{3})

(c) (2t, 8t^{3})

(d) (-2t, -8t^{3})

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) A^{2} = B^{2
}(c) AB^{–1} = B^{–1}A

(d) A^{–1} = B^{–1
}Ans. (c)

**Ques. **If the normal to the rectangular hyperbola xy = c^{2} at the point (ct, c/t) meets the curve again at (ct’, c/t’), then

(a) t^{3 }t’ = 1

(b) t^{3}t’ = –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) = {x^{2}} – ({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) 8^{10}

(b) 10^{8
}(c) ^{17}C_{7}

(d) ^{10}C_{8
}Ans. (c)

**Ques. **If a and b are distinct positive real numbers such that a, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, b are in A.P.; a, b_{1},b_{2} , b_{3}, b_{4}, b_{5}, b are in G.P. and a, c_{1}, c_{2}, c_{3} , c_{4}, c_{4}, c_{4}, c_{5}, b are in H.P. , then roots of a_{3}x^{2} + b_{3}x + c_{3} = 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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