Practice Questions

Q89.If the lines x−1 1 = y−22 = z+31 and x−a2 = y+23 = z−31 intersects at the point P , then the distance of the point P from the plane z = a is : (1) 16 (2) 28 (3) 10 (4) 22 n ≥2

Q89.Two dice A and B are rolled. Let the numbers obtained on A and B be α and β respectively. If the variance of α −β is pq , where p and q are co-prime, then the sum of the positive divisors of p is equal to (1) 72 (2) 36 (3) 48 (4) 31

Q89.If the lines x−1 2 = 2−y−3 = z−3α and x−45 = y−12 = βz intersect, then the magnitude of the minimum value of 8αβ is _____. JEE Main 2023 (06 Apr Shift 2) JEE Main Previous Year Paper

Q89.For 𝑚, 𝑛> 0, let 𝛼𝑚, 𝑛= ∫0 𝑡𝑚1 + 3𝑡𝑛𝑑𝑡. If ,11𝛼10, 6 + 18𝛼11, 5 = 𝑝146, then 𝑝 is equal to JEE Main 2023 (11 Apr Shift 1) JEE Main Previous Year Paper

Q89.If the equation of the plane passing through the point ( 1, 1, 2 ) and perpendicular to the line 𝑥- 3𝑦+ 2𝑧- 1 = 0 = 4𝑥- 𝑦+ 𝑧 is 𝐴𝑥+ 𝐵𝑦+ 𝐶𝑧= 1, then 140 ( 𝐶- 𝐵+ 𝐴) is equal to

Q89.Let 𝑓𝑛= ∫0 2 ∑𝑘=𝑛 1 sin𝑘- 1𝑥∑𝑘=𝑛 1 (2𝑘- 1)sin𝑘- 1𝑥cos𝑥𝑑𝑥, 𝑛∈ℕ. Then 𝑓21 - 𝑓20 is equal to

Q90.Let the image of the point 𝑃( 1, 2, 3 ) in the plane 2𝑥– 𝑦+ 𝑧= 9 be 𝑄. If the coordinates of the point 𝑅 are ( 6, 10, 7 ) , then the square of the area of the triangle 𝑃𝑄𝑅 is _______ . JEE Main 2023 (06 Apr Shift 1) JEE Main Previous Year Paper

Q90.A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is (1) 38 (2) 15 16 16 (3) 21 (4) 81 16 64 JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let 𝜃 be the angle between the planes 𝑃1 = →𝑟· ^𝑖+ ^𝑗+ 2 ^𝑘= 9 and 𝑃2 = →𝑟· 2 ^𝑖- ^𝑗+ ^𝑘= 15. Let L be the line that meets 𝑃2 at the point 4, - 2, 5 and makes an angle 𝜃 with the normal of 𝑃2. If 𝛼 is the angle between 𝐿 and 𝑃2 then tan2𝜃cot2𝛼 is equal to _____ . JEE Main 2023 (31 Jan Shift 1) JEE Main Previous Year Paper

Q90.A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q . If p : q = m : n, where m and n are co-prime, then m + n is equal to JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q90.Let the probability of getting head for a biased coin be 1 . It is tossed repeatedly until a head appears. Let N 4 be the number of tosses required. If the probability that the equation 64x2 + 5Nx + 1 = 0 has no real root is p , where p and q are co-prime, then q −p is equal to.......... q JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q90.Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S = {x ∈Z : x(66 −x) ≥59 M} and the event A = {x ∈S : x is a multiple of 3 }. Then P(A) is equal to (1) 15 (2) 1 44 3 (3) 1 (4) 7 5 22 JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper

Q90.Two dice are thrown independently. Let A be the event that the number appeared on the 1st die is less than the number appeared on the 2nd die, B be the event that the number appeared on the 1st die is even and that on the second die is odd, and C be the event that the number appeared on the 1st die is odd and that on the 2nd is even. Then JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper (1) The number of favourable cases of the event (2) A and B are mutually exclusive (A ∪B) ∩C is 6 (3) The number of favourable cases of the events A , (4) B and C are independent B and C are 15, 6 and 6 respectively JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper

Q90.In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective then the probability that it is manufactured by the machine C is (1) 5 (2) 9 14 28 (3) 3 (4) 2 7 7 JEE Main 2023 (08 Apr Shift 1) JEE Main Previous Year Paper

Q90.Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space [0, 60] is less than or equal to a. If P(A) = 1136 , then a is equal to _____ . JEE Main 2023 (31 Jan Shift 2) JEE Main Previous Year Paper

Q90.A fair n (n > 1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is n , then n is equal to 9 JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper

Q90.There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ2 represent mean and variance of X, respectively, then 10(μ2 + σ2) is equal to (1) 20 (2) 250 (3) 25 (4) 30 JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper

Q90.The shortest distance between the lines = = and = = is equal to ______ 3 2 2 3 2 0 JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper

Q90.The urns A, B and C contains 4 red, 6 black; 5 red, 5 black and λ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0. 4, then the square of length of the side of largest equilateral triangle, inscribed in the parabola y2 = λx with one vertex at vertex of parabola is JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper

Q90.If the probability that the random variable X takes values x is given by P(X = x) = k(x + 1)3−x , x = 0, 1, 2, 3, … … , where k is a constant, then P(X ≥2) is equal to (1) 7 (2) 7 27 18 (3) 11 (4) 20 18 27 JEE Main 2023 (08 Apr Shift 2) JEE Main Previous Year Paper

Q1. Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is ρ and radius of the drop is r, then T = 3 is dimensionally correct, where K is dimensionless. K√ρr3S 2 Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below. (1) Both (A) and (R) are true and (R) is the correct explanation of (A) (2) Both (A) and (R) are true but (R) is not the correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true

Q1. Consider the efficiency of Carnot's engine is given by η = sinαβθ loge kTβx , where α and β are constants. If T is temperature, k is Boltzman constant, θ is angular displacement and x has the dimensions of length. Then, choose the incorrect option. (1) Dimensions of β is same as that of force. (2) Dimensions of α−1x is same as that of energy. (3) Dimensions of η−1 sin θ is same as that of αβ (4) Dimensions of α is same as that of β

Q1. Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of → → → → A − B, then the angle between A and B will be (1) cos−1( 35 ) (2) cos−1( 13 ) (3) sin−1( 13 ) (4) sin−1( 35 ) a + −b] = RT; P is pressure, V is volume, R is universal gas constant and 2 V

Q1. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s , the distance travelled by the toy in the next t s will be: (1) 10 m (2) 20 m (3) 30 m (4) 40 m

Q1. Assertion A: Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason: Coefficient of viscosity = VelocityForcegradient (1) Both A and R true, and R is correct explanation of (2) Both A and R are true but R is NOT the correct A. explanation of A. (3) A is true but R is false. (4) A is false but R is true.