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AIEEE 2003 (Maths) Mock Test

Medium 75 Questions 180 min 75 marks

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180 min · 75 marks · Full test mode with leaderboard

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A function from the set of natural numbers to integers defined by is:
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Let and be two roots of the equation , being complex. Further, assume that the origin, and form an equilateral triangle, then:
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If and are two non-zero complex numbers such that , and , then is equal to:
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If , then:
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If and vectors , and are non-coplanar, then the product equals:
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If the system of linear equations has a non-zero solution, then :
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If the sum of the roots of the quadratic equation is equal to the sum of the squares of their reciprocals, then , and are in:
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The number of real solutions of the equation is:
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The value of ' ' for which one root of the quadratic equation is twice as large as the other, is:
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If and , then:
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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is:
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The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by:
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If are the cube roots of unity, then is equal to:
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If denotes the number of combinations of things taken at a time, then the expression equals:
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The number of integral terms in the expansion of is:
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If is positive, the first negative term in the expansion of is:
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The sum of the series upto is equal to:
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Let be a polynomial function of second degree. If and are in A.P., then , and are in:
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If and are both in G.P. with the same common ratio, then the points , and :
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The sum of the radii of inscribed and circumscribed circles for an -sided regular polygon of side , is:
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If in a triangle , , then the sides and :
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In a triangle , medians and are drawn. If , and , then the area of the is:
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The trigonometric equation , has a solution for:
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The upper th portion of a vertical pole subtends an angle at 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:
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The real number when added to its inverse gives the minimum value of the sum at equal to:
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If satisfies , for all and , then is:
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If , then the value of is:
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Domain of definition of the function , is:
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is:
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If , the value of is:
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Let and their th derivatives exist and are not equal for some . Further if , then the value of is:
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The function is:
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If then is:
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If the function , where , attains its maximum and minimum at and respectively such that , then equals:
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If , for and , then:
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If , then is equal to:
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The value of is:
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The value of the integral is:
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is:
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Let , . If , then one of the possible values of , is:
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The area of the region bounded by the curves and is:
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Let be a function satisfying with and be a function that satisfies . Then the value of the integral , is:
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The degree and order of the differential equation of the family of all parabolas whose axis is the -axis, are respectively:
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The solution of the differential equation , is:
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If the equation of the locus of a point equidistant from the points and is , then the value of ' ' is:
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Locus of centroid of the triangle whose vertices are , and , where is a parameter, is:
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If the pair of straight lines and be such that each pair bisects the angle between the other pair, then:
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A square of side lies above the -axis and has one vertex at the origin. The side passing through the origin makes an angle () with the positive direction of -axis. The equation of its diagonal not passing through the origin is:
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If the two circles and intersect in two distinct points, then:
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The lines and are diameters of a circle having area as 154 sq units. Then the equation of the circle is:
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The normal at the point on a parabola meets the parabola again in the point , then:
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The foci of the ellipse and the hyperbola coincide. Then the value of is:
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A tetrahedron has vertices at , , and . Then the angle between the faces and will be:
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The radius of the circle in which the sphere is cut by the plane is:
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The lines and are coplanar if:
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The two lines , and , will be perpendicular, if and only if:
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The shortest distance from the plane to the sphere is:
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Two systems of rectangular axes have the same origin. If a plane cuts them at distances and from the origin, then:
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are 3 vectors, such that , , then is equal to:
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If and are three non-coplanar vectors, then equals:
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Consider points and with position vectors , , and respectively. Then is a:
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The vectors and are the sides of a triangle . The length of the median through is:
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A particle acted on by constant forces and is displaced from the point to the point . The total work done by the forces is:
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Let , and . If is a unit vector such that and , then is equal to:
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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set:
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In an experiment with 15 observations on , the following results were available: , . One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is:
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Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is:
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Events are mutually exclusive events such that , and . The set of possible values of are in the interval:
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The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then is:
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The resultant of forces and is . If is doubled then is doubled. If the direction of is reversed, then is again doubled. Then is:
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Let and respectively be the maximum ranges up and down an inclined plane and be the maximum range on the horizontal plane. Then are in:
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A couple is of moment and the force forming the couple is . If is turned through a right angle, the moment of the couple thus formed is . If instead, the forces are turned through an angle , then the moment of couple becomes:
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Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity and the other from rest with uniform acceleration . Let be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time:
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Two stones are projected from the top of a cliff meters high, with the same speed so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle to the horizontal then equals:
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A body travels a distance in seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration and in the second part with constant retardation . The value of is given by:

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