#jeemain-2019-maths
- 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 plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y + 2z – 2 = 0, passes through the point :0 Correct option is (4) (2, –4, 1) Explaination:: From question, the equations of planes given are: 2x – y + 2z – 4 = 0 X + 2y + 2z – 2 = 0 Th... 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 bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45° 20sqrt3-1 is the correct answer 2
- If x = √3/2 + i/2(i = √-1), then (1 + iz + z5 + iz8)9 is equal to - The correct answer is A) -1 Detailed solution:: 1
- If (z - α)/(z + α) (α ∈ R) is a purely imaginary number and |z| = 2, then a value of α is : The correct answer is B) 2 Explanation :: dfrac z -α z +α +dfrac overline z -α overline z +α =0 z z̅ + z α - α z̅ - α ^ 2 + z z̅ - z α + z̅... 1
- Let A={θϵ(-π/2π):3+2isinθ/1-2isinθ is purely imaginary} then the sum of elements in A is The correct answer is D)2π/3 Detailed answer 1
- The value of cos π/2^2.cosπ/2^3..... .cosπ/2^10.sinπ/2^10 The correct answer is option B)1/512 Detailed solution 1
- tanA/(1-cotA) + cotA/(1-tanA) can be written as The correct answer is b) secA cosecA+1 1
- cos210° - cos10°cos50° + cos250° is equal to (1) 3/2 (2) 3/4 (3) 3/2(cos20° + 1) (4) 3/4(cos20° + 1) The correct answer is 2) 3/4 Detailed solution :: 1
- Two vertical poles of heights, 20 m and 80 m stand a part on a horizontal plane The correct answer is B)16 Detailed solution: 1
- If cos (α + β) = 4/5 and sin (α – β) = 5/13 , where they lie between 0 and π/4, find the value of tan2α Correct option is D) 63/16 Detailed solution: 1
- If alpha=cos^-1(3/5) , beta=tan^-1(1/3), where 0<alpha,beta<π/4 , then alpha-beta is equal to Correct answer is A) sin⁻¹ 9over5√(10) Detailed answer 1
- The maximum value of 3cos theta+5sin{theta-π/6) for any real value of theta is The correct option is A) √(19) Detailed solution: 1