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A solid cylinder of mass m is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure.

A solid cylinder of mass m is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The... View Article

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field ([latex]vec{E}[/latex] )and magnetic field ([latex]vec{B}[/latex]) components

a. Ex, Bz or Ez, Bx b. Ey, Bx or Ex, By c. Ex, By or Ey, Bx d. Ey, By or Ez, Bz Answer: (a) Therefore, for electromagnetic waves... View Article

An object of mass m₁ collides with another object of mass m₂, which is at rest.

An object of mass m1 collides with another object of mass m2, which is at rest. After the collision, the objects move at equal speeds in opposite... View Article

The decay of a proton to neutron is

a. Not possible as proton mass is less than the neutron mass b. Always possible as it is associated only with β+ decay c. Possible only... View Article

The area bounded by the curve y = x² -1, tangent to it at (2, 3) and y-axis is

a) 2/3b) 4/3c) 8/3d) 1Solution:Equation of tangent at (2, 3) is(y+3)/2 = 2x-1y+3 = 4x-24x-y = 5Required area = Ar(PAB) - = 8-(16/3)= 8/3Answer (c)... View Article

Find common tangent of the two curves y² = 4x and x²+y²-6x = 0.

a) y = (x/3)+3b) y = (x/√3) -√3c) y = (x/3)-3d) y = (x/√3) +√3Solution:Equation of tangent to the parabola y2 = 4x is y =... View Article

A plane parallel to y-axis passing through line of intersection of planes x+y+z =1 and 2x+3y-z-4 = 0 which of the point lie on the plane

a) (3,2,1)b) (−3,0,1)c) (−3,1,1)d) (3,1,−1)Solution:Required plane is π1+ λπ2 = 0(x+y+z-1)+λ(2x+3y-z-4) =... View Article

Consider the curves y = x² +2 and y = 10-x². Let θ be the angle between both the curves at point of intersection, then find ǀtan θǀ

a) 8/15b) 5/17c) 3/17d) 8/17Solution:x2 +2 = 10-x2x = ±2 and y = 4Point of intersection of curves = (±2, 4)y = x2+2; y =... View Article

Find the equation of line through (−4,1,3) and parallel to the plane x + y + z = 3 while the line intersects another line whose equation is x + y – z = 0 = x + 2y -3z + 5

a) Answer (c)... View Article

3 circles of radii a, b, c (a < b < c) touch each other externally and have x – axis as a common tangent then

a) a, b, c are in A.P. b) 1/√b = (1/√a) + (1/√c) c) √a, √b, √c are in A.P. d) (1/√c) + (1/√b) = (1/√a) Solution: PQ +QR = PR √(4ac) +... View Article

The value of 3(cos θ – sin θ)⁴ + 6(sin θ + cos θ)²+4 sin⁶θ is, where θ∈ (π/4, π/2)

a) 13-4 cos4θb) 13-4 cos6θc) 13-4 cos6θ+2 sin4θ cos2θd) 13-4 cos4θ+2 sin4θ cos2θSolution:3(cos2 θ+ sin2 θ -sin 2θ)2 +6(sin2 θ+ cos2 θ+ sin 2θ)... View Article

Consider the system of equations x+y+z = 1, 2x+3y+2z =1, 2x+3y+(a² -1)z = a+1 then

a) system has a unique solution for ǀaǀ = √3b) system is inconsistence for ǀaǀ = √3c) system is inconsistence for a = 4d) system is... View Article

If px+qy+r = 0 represent a family of straight lines such that 3p+2q+4r = 0 then

a) All lines are parallelb) All lines are inconsistentc) All lines are concurrent at (3/4, 1/2)d) All lines are concurrent at... View Article

If cos^-1(2/3x) + cos^-1(3/4x) = π/2, x>3/4 then x =

a) √145/11b) √145/12c) √146/10d) √146/11Solution:cos-1 (2/3x) = π/2 - cos-1(3/4x)cos-1 (2/3x) = cos-1... View Article

If slant height of a right circular cone is 3 cm then the maximum volume of cone is

a) 2√3 πcm3b) 4√3 πcm3c) (2+√3) πcm3d) (2-√3) πcm3Solution:l = 3r2 + h2 = 9r2 = 9 -h2V = (1/3)πr2h= (1/3)πh(9 -h2) V =... View Article

If eccentricity of the hyperbola [latex]\frac{x^{2}}{\cos ^{2}\theta }-\frac{y^{2}}{\sin ^{2}\theta } =1[/latex] is more than 2 when ∈(0, π/2) then values of length of latus rectum lies in the interval

a) (3, ∞)b) (1, 3/ 2)c) (2, 3)d) (-3, -2)Solution:For hyperbola, e2 = 1+(b2/a2)= 1+tan2 θ= sec2θe>2 ⇒ sec θ > 2∈(π/3, π/2)Length of... View Article

From a well shuffled deck of cards, 2 cards are drawn with replacement. If x represent numbers of times ace coming, then value of P(x = 1) + P(x = 2) is

a) 25/169b) 24/169c) 49/169d) 23/169Solution:P(x = 1) = 2C1×(4/52)×(48/52) = 24/169P(x = 2) = 2C2×(4/52)2= 1/169P(x = 1) + P(x... View Article

If y (x) is solution of x(dy/dx) +2y = x², y(1) = 1, then value of y(1/2)

a) -49/16b) 49/16c) 45/8d) -45/8Solution:x(dy/dx) + 2y = x2(dy/dx) + 2y/x = xThis is linear differential equation.I.F =e ∫(2/x)dx = e2 log x... View Article

If (A⊕B)∧(∼ A⊝ B) = [latex]Awedge B[/latex] what should be proper symbol in place of [latex]oplus[/latex] and ⊝ to hold the equation

a) Solution:By inspection ⊕ represents ∧ and ⊝ represents ∨ABA∧B~A~A∨B(A∧B)∧ (~A∨B)TTTFTTTFFFFFFTFTTFFFFTTF(A∧B)∧(~A∨B)≡ A∧BAnswer: (a)... View Article

Let A = [latex]\begin{bmatrix} \cos \theta &-\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/latex] find the value of A^-50 at θ = π/12.

a) Answer: (b)... View Article