#jeemain
- Which of the following is a polyester? Answer is (a) Dacron 1
- Which of the following have the maximum melting point? Answer is (a) Acetic acid Carboxylic acids with even number carbon atoms have higher melting point than those with odd number carbons atom.... 2
- In the production of which of the following compound, H2 is used? Answer : (b) NH3 Solution: N2 + 3H2 ⇌ 2NH3 In production of NH3 , H2 is used 1
- X is hcp, Y is 2/3 of tetrahedral voids…. Find percentage of X in the lattice Answer : 42.85 Explaination : X is hcp So atom per unit cell = 6 Y at 2/3 of T-void = 2/8 × 12 = 8 % of X = 6/14× 100 = 42.85% 1
- There are 6 batsmen, 7 bowlers and 2 wickets keepers. Find the number of ways of forming Team Size =11 players Case 1: 4 batsmen and 5 bowlers and 2 wicket-keepers ⇒ ⁶C_(4 )× ⁷C₅ × ²C₂ = (6×5/2) × (7×6/2) × 1 = 315 Case 2: 4 bats... 1
- If vector a,b,c are three mutually perpendicular vectors equally inclined to vector a + b + c at angle θ, then find the value of 36 cos^2 2θ. Answer: 4 Let vec s = vec a + vec b + vec c. Since the vectors are mutually perpendicular, vec a·vec b = vec b·vec c = vec c·vec a = 0, so v... 1
- The mean of 6 numbers is 6.5 and its variance is 10.25. If 4 numbers are 2,4,5 and 7, then find the other two. Answer: the other two numbers are 10 and 11 Let the other two numbers be a and b. Mean: sum of all six = 6×6.5 = 39. The given four add to 2... 1
- One of the diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If A and B are the points Let O be the centre of circle M be mid point of AB. Then, OM ⊥ AB ⇒ M (1,4) Since, slope of AB = 0 Equation of straight line MO is x = 1 and... 1
- If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations Correct option is 4) βγ α x² + 2β x + γ = 0 Let β = α t, γ = α t² therefore α x² + 2α tx + α t² = 0 ⇒ x² + 2tx + t² = 0 ⇒ (x + t)² = 0 ⇒ x =... 1
- The Boolean expression ∼(p⇒(∼q)) is equivalent to : Correct option is A) p^q Explaination:: ∼(p⇒(∼q)) as p⇒q \ is \ same \ as \ ∼p v q we get ∼((∼p) v(∼q)) = p^q 1
- A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is: Correct option is 2) ( 1/3,rm 2) Explanation:: 1
- The equation of the common tangent to the curves y^2 = 16x and xy = - 4 is Answer: (a) x - y + 4 = 0 Any tangent to the parabola y² = 16x (here 4a = 16, so a = 4) with slope m is y = mx + 4/m For it to touch the hyp... 1
- The equation of the common tangent to the curves y^2 = 8x and xy = - 1 is Correct option is (d) y=x+2 Explaination:: tangents to the curve y²=8x is y=mx+2/m, so it must satisfy xy=-1 x(mx+2/m)=-1 mx²+2/mx+1=0, sinc... 1
- The general solution of the differential equation (y^2 – x^3 )dx – xydy = 0 (x ≠ 0) is : The correct option is 2) y²+2x³+cx²=0 Detailed explaination 1
- Let a ∈ (0,π/2) be fixed. If the integral ∫ tan x + tan α/tan x - tan α dx = A(x) cos 2α + B(x) sin 2α + C, where C is a Correct option is (4) x – α and log_e|sin(x – α)| Detailed Explaination: ∫ (tan x + tan α)/(tan x - tan α) dx = ∫ ((sin x)/(cos x)+ (sin α)/... 1
- A particle is moving along a circular path with a constant speed 30 m/s. Correct Answer is option B) 30sqrt2 https://youtu.be/1hcDKwGYKlE 1
- A coil of inductance 300 mH and resistance 2 is connected to a source of voltage 2 V. Correct answer is option d) 0.1 s Explaination: During growth of charge in an inductance, I = I₀ (1 – e ^(–Rt/L)) or I₀/2 = I₀(1 – e^( –Rt/L... 1
- When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced Correct option is 2) 1.67H Explaination EMF = L × di/dt 50 = L × ((5-2))/0.1 = L × 30 L = 5/3 = 1.67 1
- A rectangular loop is present in the magnetic field region of an infinite long wire. Now the loop is being rotated as shown in the figure. option B is correct 1
- A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate Correct solution is option A) 2aα B Explaination: "a" at any time "t", the side of the square a= (a₀-α_t) , where α₀ side at t=0. at this in... 1
- Suppose that f is differentiable for all x and that f’(x) ≤ 2 for all x. If f(1) = 2 and f(4) = 8, then f(2) has the value equal to LMV Theorem for f in [1, 2] forall c in(1, 2) (f(2)-f(1))/(2-1) =f'(c) ≤ 2 f(2)-f(1) ≤ 2 ⇒ f(2) ≤ 4 ...(1) Again, using LMV Theorem in [2, 4... 1
- A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is Correct option is A) 25ω²/2g Explaination:: Applying pressure equation from A to B p_o+ρ.Rω²/2.R-ρ gh= p_o ρ.R²ω²/2=ρ gh h=R²ω²/2g=5²ω²/2g=2... 1
- The image of an object, formed by a plano-convex lens at a distance of 8m behind the lens, is real and is one third the size of the object. Correct option is d) 3m Explaination:: μ =λ₀over λ_m=3over2 1over f=(μ-1)over R=1over 2R 1over f=1over V-1over u 1over8-(1over24)=1over2R 3+... 1
- An electromagnetic wave can be produced, when charge is Amoving with a constant velocity Correct option is D) both B and C An accelerated charge is the source of electromagnetic waves (EMWs). When the charge is in a circular moti... 1