Question Bank covering whole syllabus for JEE Advanced Maths:
Ques. A line with direction cosines proportional to 2,1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the points of intersection are given by
(a) (2a, a, 3a), (2a, a, a)
(b) (3a, 2a, 3a), (a, a, a)
(c) (3a, 2a, 3a), (a, a, 2a)
(d) (3a, 3a, 3a), (a, a, a)
Ans. (b)
Ques. The root of the equation x3 + x – 3 = 0 lies in interval (1, 2) after second iteration by false position method, it will be in
(a) (1.178, 2.00)
(b) (1.25, 1.75)
(c) (1.125, 1.375)
(d) (1.875, 2.00)
Ans. (a)
Ques. Let the value of p = (x + 4y)a + (2x + y + 1)b and q = (y – 2x + 2)a + (2x – 3y – 1)b, where a and b are non-collinear vectors. If 3p = 2q, then the value of x and y will be
(a) – 1, 2
(b) 2, – 1
(c) 1, 2
(d) 2, 1
Ans. (b)
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Ques. A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it at least once is
(a) 7
(b) 8
(c) 9
(d) 6
Ans. (a)
Ques. The number of solution of the following equations x2 – x3 = 1, –x1 + 2x3 = –2, x1 – 2x2 = 3 is
(a) Zero
(b) One
(c) Two
(d) Infinite
Ans. (a)
Ques. If 56Pr+6 : 54Pr+3 = 30800 : 1, then r =
(a) 31
(b) 41
(c) 51
(d) None of these
Ans. (b)
Ques. A light rod AB of length 30 cm rests on two pegs 15 cm apart. At what distance from the end A the pegs should be placed so that the reaction of pegs may be equal when weight 5W and 3W are suspended from A and B respectively
(a) 1.75 cm, 15.75 cm
(b) 2.75 cm, 17.75 cm
(c) 3.75 cm, 18.75 cm
(d) None of these
Ans. (c)
Ques. The resultant of two forces P and Q is R. If Q is doubled, R is doubled and if Q is reversed, R is again doubled. If the ratio P2 : Q2 : R2 = 2 : 3 : x, then x is equal to
(a) 5
(b) 4
(c) 3
(d) 2
Ans. (d)
Ques. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0 is
(a) x2 + y2 – 2xy – 4x + 4y – 4 = 0
(b) x2 + y2 – 2xy + 4x – 4y – 4 = 0
(c) x2 + y2 + 2xy – 4x + 4y – 4 = 0
(d) x2 + y2 + 2xy – 4x + 4y + 4 = 0
Ans. (c)
Ques. The resultant of three forces represented in magnitude and direction by the sides of a triangle ABC taken in order with BC = 5 cm, CA = 5 cm, and AB = 8 cm, is a couple of moment
(a) 12 unit
(b) 24 unit
(c) 36 unit
(d) 16 unit
Ans. (b)
Ques. If x = log3 5, y = log17 25, which one of the following is correct
(a) x < y
(b) x = y
(c) x > y
(d) None of these
Ans. (c)
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Ques. A man is swimming with the uniform velocity of 6km / h straight across a river which is flowing at the rate of 2 km / h. If the breadth of the river is 300 m, the distance between the point and the man is initially directed to and the point it will reach on the opposite bank of the river is equal to
(a) 100 m
(b) 200 m
(c) 300 m
(d) 400 m
Ans. (a)
Ques. A root of the equation x3 – 3x – 5 = 0 lies between 2 and 2.5. Its approximate value, by applying bisection method 3 times is
(a) 2.0625
(b) 2.3125
(c) 2.3725
(d) 2.4225
Ans. (b)
Ques. Given that the equation z2 + (p + iq)z + r + I s = 0, where p, q, r, s are real and non-zero has a real root, then
(a) pqr = r2 + p2 s
(b) prs = q2 + r2 p
(c) qrs = p2 + s2 p
(d) pqs = s2 + q2 r
Ans. (d)
Ques. The value of the root nearest to the 2 after first iteration of the equation x4 – x – 10 = 0 by Newton-Raphson method, is
(a) 2.321
(b) 2.125
(c) 1.983
(d) 1.871
Ans. (d)
Ques. If cos (u + iv) = x + iy, then x2 + y2 + 1 is equal to
(a) cos2 u + sinh2 v
(b) sin2 u + cosh2 v
(c) cos2 u + cosh2 v
(d) sin2 u + sinh2 v
Ans. (c)
Ques. If A and B are square matrices of order 3 such that | A | = –1, | B | = 3, then | 3 AB | =
(a) – 9
(b) – 81
(c) – 27
(d) 81
Ans. (b)
Ques. A rod can turn freely about one of its ends which is fixed. At the other end a horizontal force equal to half the weight of the body is acting. In the position of equilibrium, the rod is inclined to the vertical at an angle
(a) 30°
(b) 45°
(c) 60°
(d) None of these
Ans. (b)
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Ques. If the product of roots of the equation x2 – 3kx + 2e2 log k – 1 = 0 is 7, then its roots will real when
(a) k = 1
(b) k = 2
(c) k = 3
(d) None of these
Ans. (b)
The coefficient of correlation between x and y is 0.6, then covariance is 16. Standard deviation of x is 4, then the standard deviation of y is
(a) 5
(b) 10
(c) 20/3
(d) None of these
Ans. (c)
Ques. Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is
(a) 69760
(b) 30240
(c) 99748
(b) None of these
Ans. (a)
Ques. The figure formed by the lines x2 + 4xy + y2 = 0 and x – y = 4, is
(a) A right angled triangle
(b) An isosceles triangle
(c) An equilateral triangle
(d) None of these
Ans. (c)
Ques. Two persons A and B take turns in throwing a pair of dice. The first person to through 9 from both dice will be avoided the prize. If A throws first then the probability that B wins the game is
(a) 9/17
(b) 8/17
(c) 8/9
(d) 1/9
Ans. (b)
Ques. The resultant of P and Q is R. If P is reversed, Q remaining the same, the resultant becomes R’. If R is perpendicular to R’, then
(a) 2P = Q
(b) P = Q
(c) P = 2Q
(d) None of these
Ans. (b)
Ques. A man in a balloon, rising vertically with an acceleration of 4.9 m/sec2 releases a ball 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the ball is
(a) 14.7 m
(b) 19.6 m
(c) 9.8 m
(d) 24.5 m
Ans. (a)
Ques. The sum of two weights of an Atwood’s machine is 16 lbs. The heavier weight descends 64 ft in 4 seconds. The value of weights in lbs are
(a) 10, 6
(b) 9, 7
(c) 8, 8
(d) 12, 4
Ans. (a)
Ques. The equation of perpendicular bisectors of the sides AB and AC of a triangle ABC are x – y + 5 = 0 and x + 2y = 0 respectively. If the point A is (1, –2), then the equation of line BC is
(a) 23x + 14y – 40 = 0
(b) 14x – 23y + 40 = 0
(c) 23x – 14y + 40 = 0
(d) 14x + 23y – 40 = 0
Ans. (d)
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Ques. The equation of the common tangent to the curves y2 = 8x and xy = –1 is
(a) 3y = 9x + 2
(b) y = 2x + 1
(c) 2y = x + 8
(d) y = x + 2
Ans. (d)
Ques. The sum of the series 4/1! + 11/2! + 22/3! + 37/4! + 56/5! + … is
(a) 6 e
(b) 6 e – 1
(c) 5 e
(d) 5 e + 1
Ans. (b)
Ques. Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean is
(a) 44.0
(b) 44.46
(c) 45.00
(d) 45.54
Ans. (b)
Ques. The sums of n terms of three A.P.’s whose first term is 1 and common differences are 1, 2, 3 are s1, S2, S3 respectively. The true relation is
(a) S1 + S3 = S2
(b) S1 + S3 = 2S2
(c) S1 + S2 = 2S3
(d) S1 + S2 = S3
Ans. (b)
Ques. The root of the equation 2x = cos x + 3 correct to three decimal places, is
(a) 1.504
(b) 1.479
(c) 1.524
(d) 1.897
Ans. (c)
Ques. A hockey stick pushes a ball at rest for 0.01 second with an average force of 50 N. If the ball weighs 0.2 kg, then the velocity of the ball just after being pushed is
(a) 3.5 m/sec
(b) 2.5 m/sec
(c) 1.5 m/sec
(d) 4.5 m/sec
Ans. (b)
Ques. The co-ordinates of the point from where the tangents are drawn to the circles x2 + y2 = 1, x2 + y2 + 8x + 15 = 0 and x2 + y2 + 10y + 24 = 0 are of same length, are
(a) (2, 5/2)
(b) (–2, –5/2)
(c) (–2, 5/2)
(d) (2, –5/2)
Ans. (b)
Ques. Let PS be the median of the triangle with vertices P (2, 2), Q(6, –1) and R (7, 3). The equation of the line passing through (1, – 1) and parallel to PS is
(a) 2x – 9y – 7 = 0
(b) 2x – 9y – 11 = 0
(c) 2x + 9y – 11 = 0
(d) 2x + 9y + 7 = 0
Ans. (d)
Ques. The value of sin2 5o + sin2 10o + sin2 15o + … + sin2 85o + sin2 90o is equal to
(a) 7
(b) 8
(c) 9
(d) 9 ½
Ans. (d)
Ques. Two trains A and B, 100 kms apart, are travelling to each other with starting speed of 50 km/hr for both. The train A is accelerating at 18 km/hr2 and B is decelerating at 18 m/h2. The distance where the engines cross each other from the initial position of A is
(a) 50 kms
(b) 68 kms
(c) 32 kms
(d) 59 kms
Ans. (d)
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Ques. The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S.D. respectively are
(a) 14.98, 39.95
(b) 39.95, 14.98
(c) 39.95, 224.5
(d) None of these
Ans. (b)
Ques. If the roots of the equations x2 – bx + c = 0 and x2 – cx + b = 0 differ by the same quantity, then b + c is equal to
(a) 4
(b) 1
(c) 0
(d) –4
Ans. (d)
Ques. A man of mass 80 kg. is travelling in a lift. The reaction between the floor of the lift and the man when the lift is ascending upwards at 4 m/sec2 is
(a) 1464.8 N
(b) 1784.8 N
(c) 1959.8 N
(d) 1104.8 N
Ans. (d)
Ques. The coefficient of x5 in the expansion of (1 + x2)5 (1 + x)4 is
(a) 30
(b) 60
(c) 40
(d) None of these
Ans. (b)
Ques. Two variables x and y are related by the linear equation ax + by + c = 0. The coefficient of correlation between the two is + 1, if
(a) a is positive
(b) b is positive
(c) a and b both are positive
(d) a and b are of opposite sign
Ans. (d)
Ques. The tangents are drawn from the point (4, 5) to the circle x2 + y2 – 4x – 2y – 11 = 0. The area of quadrilateral formed by these tangents and radii, is
(a) 15 sq. units
(b) 75 sq. units
(c) 8 sq. units
(d) 4 sq. units
Ans. (c)
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Ques. A particle is dropped under gravity from rest from a height h(g = 9.8 m/sec2) and then it travels a distance 9h/25 in the last second. The height h is
(a) 100 metre
(b) 122.5 metre
(c) 145 metre
(d) 167.5 metre
Ans. (b)
