Practice Questions

Q72.The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is (1) If the squares of two numbers are equal, then the (2) If the squares of two numbers are not equal, then numbers are not equal the numbers are equal (3) If the squares of two numbers are not equal, then (4) If the squares of two numbers are equal, then the the numbers are not equal numbers are equal

Q73.The proposition (~p) ∨(p ∧~q) is equivalent to (1) p →∼q (2) p∧∼q (3) q →p (4) none

Q74.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is (1) 35 (2) 40 (3) 25 (4) 30

Q80.If y = [x + √x2 −1] [x −√x2 −1] (1) 224 y2 (2) 125 y (3) 225 y (4) 225 y2

Q80.The function f defined by f(x) = x3 −3x2 + 5x + 7 is: (1) Decreasing in R (2) Increasing in R (3) Increasing in (0, ∞) and decreasing in (−∞, 0) (4) Decreasing in (0, ∞) and increasing in (−∞, 0)

Q82.If ∫ 3 = k+5 1 (x2−2x+4) 2 (1) 4 (2) 2 (3) 3 (4) 1 lim = 601 for some positive real number a, then a is equal to 1a+2a+…+na ) (n+1)a−1[(na+1)+(na+2)+…+(na+n)]

Q89.An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) 127 (2) 63 128 64 (3) 255 (4) 1 256 2

Q62.The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there 2√2 units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by : (1) 1 + i (2) 2 + 2i (3) −2 −2i (4) −1 −i

Q72.The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is (1) 2 (2) √3 √3 (3) 4 (4) 4 3 √3

Q75.The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is (1) if the area of a square increases four times, then (2) if the area of a square increases four times, then its side is not doubled. its side is doubled. (3) if the area of a square does not increase four (4) if the side of a square is not doubled, then its area times, then its side is not doubled. does not increase four times.

Q75.The Boolean Expression (p∧∼q) ∨q ∨(∼p ∧q) is equivalent to (1) p ∨q (2) p ∨∼q (3) ∼p ∧q (4) p ∧q

Q76.Consider the following two statements: P : If 7 is an odd number, then 7 is divisible by 2 . Q : If 7 is a prime number, then 7 is an odd number. If V1 is the truth value of the contrapositive of P and V2 is the truth value of contrapositive of Q, then the ordered pair (V1, V2) equals (1) (F, T) (2) (F, F) (3) (T, F) (4) (T, T)

Q65.If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is: (1) 12 (2) 10 (3) 6 (4) 9

Q69.The points (0, 38 ), (1, 3) and (82, 30) (1) form an obtuse angled triangle (2) form an acute angled triangle (3) lie on a straight line (4) form a right angled triangle

Q74.The negation of ∽s ∨(∽r ∧s) is equivalent to JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) s ∧ r (2) s ∧~r (3) s ∧(r ∧~s) (4) s ∨(r ∨~s)

Q74.If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is: (1) 1 (2) √2 −1 2 (3) √2−1 (4) 2√2−1 2 2

Q75.The contrapositive of the statement "If it is raining, then I will not come", is (1) if I will come, then it is not raining. (2) if I will come, then it is raining. (3) if I will not come, then it is raining. (4) if I will not come, then it is not raining.

Q75.The mean of a data set comprising of 16 observations is 16 . If one of the observation value 16 is deleted and three new observations valued 3 , 4 and 5 are added to the data, then the mean of the resultant data is (1) 14 .0 (2) 16 .8 (3) 16 .0 (4) 15 .8

Q76.A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively.If per day mean wage of the day shift workers is, ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹ ) is : (1) 75 (2) 74 (3) 69 (4) 66

Q79.Let tan−1 y = tan−1 x + tan−1( 1−x22x ), where |x| < √31 ,Then a value of y is (1) 3x+x3 (2) 3x−x3 1+3x2 1−3x2 (3) 3x+x3 (4) 3x−x3 1−3x2 1+3x2 is differentiable, then the value of k + m is

Q86.In a parallelogram ABCD, AB→ = a, AD→ = b & AC→ = c. DB→ ⋅AB→ has the value: (1) 1 2 (a2 + b2 + c2) (2) 14 (a2 + b2 −c2) (3) 3 1 (b2 + c2 −a2) (4) 12 (a2 −b2 + c2)

Q88.If the points (1, 1, λ) & (−3, 0, 1), are equidistant from the plane, 3x + 4y −12z + 13 = 0, then λ satisfies the equation: (1) 3x2 + 10x + 7 = 0 (2) 3x2 + 10x −13 = 0 (3) 3x2 −10x + 7 = 0 (4) 3x2 −10x + 21 = 0 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q62.For all complex numbers z of the form 1 + iα, α ∈R, if z2 = x + iy, then (1) y2 −4x + 4 = 0 (2) y2 + 4x −4 = 0 (3) y2 −4x + 2 = 0 (4) y2 + 4x + 2 = 0

Q68.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 (1) 4x + 7y + 3 = 0 (2) 2x −9y −11 = 0 (3) 4x −7y −11 = 0 (4) 2x + 9y + 7 = 0

Q69.The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x2 + y2 = 16 as the diameter is (1) x2 + y2 + 3x + y + 1 = 0 (2) x2 + y2 + 3x + y −22 = 0 (3) x2 + y2 + 3x + y −11 = 0 (4) x2 + y2 + 3x + y −2 = 0