### 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 x^{3} + 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 x_{2} – x_{3} = 1, –x_{1} + 2x_{3} = –2, x_{1} – 2x_{2} = 3 is

(a) Zero

(b) One

(c) Two

(d) Infinite

**Ans. **(a)

**Ques.** If ^{56}P_{r+6} : ^{54}P_{r+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 5*W* and 3*W* 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 P^{2} : Q^{2} : R^{2} = 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) x^{2} + y^{2} – 2xy – 4x + 4y – 4 = 0

(b) x^{2} + y^{2} – 2xy + 4x – 4y – 4 = 0

(c) x^{2} + y^{2} + 2xy – 4x + 4y – 4 = 0

(d) x^{2} + y^{2} + 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 = log_{3} 5, y = log_{17} 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 x^{3} – 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 z^{2} + (p + iq)z + r + I s = 0, where p, q, r, s are real and non-zero has a real root, then

(a) pqr = r^{2} + p^{2} s

(b) prs = q^{2} + r^{2} p

(c) qrs = p^{2} + s^{2} p

(d) pqs = s^{2} + q^{2} r

**Ans.** (d)

**Ques.** The value of the root nearest to the 2 after first iteration of the equation x^{4} – 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 x^{2} + y^{2} + 1 is equal to

(a) cos^{2} u + sinh^{2} v

(b) sin^{2} u + cosh^{2} v

(c) cos^{2} u + cosh^{2} v

(d) sin^{2} u + sinh^{2} 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 x^{2} – 3kx + 2e^{2 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 x^{2} + 4xy + y^{2} = 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/sec*^{2} 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 y^{2} = 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 s_{1}, S_{2}, S_{3} respectively. The true relation is

(a) S_{1} + S_{3} = S_{2}

(b) S_{1} + S_{3} = 2S_{2
}(c) S_{1} + S_{2} = 2S_{3}

(d) S_{1} + S_{2} = S_{3}

**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 x^{2} + y^{2} = 1, x^{2} + y^{2} + 8x + 15 = 0 and x^{2} + y^{2} + 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 sin^{2} 5^{o} + sin^{2} 10^{o} + sin^{2} 15^{o} + … + sin^{2} 85^{o} + sin^{2} 90^{o} 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/hr*^{2} and *B* is decelerating at 18 *m*/*h*^{2}. 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 x^{2} – bx + c = 0 and x^{2} – 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*/*sec*^{2} is

(a) 1464.8 *N*

(b) 1784.8 *N*

(c) 1959.8 *N*

(d) 1104.8 *N
*

**Ans.**(d)

**Ques.** The coefficient of x^{5} in the expansion of (1 + x^{2})^{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 x^{2} + y^{2} – 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/sec^{2}) 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)

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