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Does Salt Make Fire Burn Hotter

Generally, inorganic salts are also noncombustible. In general, salts containing organic groups are combustible, but they can burn with... View Article

Does Chemisorption Occur Rapidly

Chemisorption is a type of adsorption between the surface and the adsorbate that requires a chemical reaction. New chemical bonds are formed at... View Article

If F X Then At X 0 F Has

1) a local maximum 2) a local minimum 3) no local extremum 4) no local maximum Solution: (1) a local maximum... View Article

On The Interval 0 1 The Function X 25 1 X 75 Takes Its Maximum Value At The Point

1) 0 2) 1/4 3) 1/2 4) 1/3 Solution: (2) 1 / 4 f (x) = x25 (1 - x)75 f’ (x) = 25 x24 + (1 - x)75 + 75 x25 (1 - x)74 = x24 [1... View Article

The Function F X A Sinx 1 3 Sin 3x Has Maximum Value At X Pi 3 The Value Of A Is

1) 3 2) 1/3 3) 2 4) 1/2 Solution: (3) 2 f (x) = a sinx + (1 / 3) sin 3x f’ (x) = a cosx + (1 / 3) cos 3x (3) f’ (x) = a cosx + 3... View Article

Observe The Statements Given Below Assertion A F X Xe X Has The Maximum At X 1

1) Both A and R are correct and R is the correct reason for A 2) Both A and r correct but R is not the correct reason for A 3) A is... View Article

The Condition F X X 3 Px 2 Qx R X Belongs To R To Have No Extreme Value Is

1) p2 < 3q 2) 2p2 < q 3) p2 < 1/4q 4) p2 > 3q Solution: (1) p2 < 3q f (x) = x3 + px2 + qx + r f’ (x) ≠ 0 f’ (x) =... View Article

The Length Of Tangent Subtangent Normal And Subnormal For The Curve

1) B, D, A, C 2) B, A, C, D 3) A, B, C, D 4) B, A, D, C Solution: (4) B, A, D, C y = x2 + x - 1 (dy / dx) = 2x + 1 (dy / dx)(1, 1) = 3 A... View Article

The Line X A Y B 2 Touches The Curve X N A N Plus Y N B N 2 At

1) (b, a) 2) (-b, -a) 3) (a, b) 4) None of these Solution: (3) (a, b) (xn / an) + (yn / bn) = 2 [nxn-1 / an] + [nyn-1 / bn] y’ =... View Article

The Maximum Value Of F X X 4 X X 2 On 1 1 Is

1) - (1/3) 2) - (1/4) 3) 1/4 4) 1/6 Solution: (4) 1 / 6 f (x) = x / [4 + x + x2] f’ (x) = 0 f’’ (x1) > 0, [x = x1 minimum]... View Article

The Maximum Slope Of The Curve Y X 3 3x 2 2x 27 Is

1) 5 2) -5 3) 1/5 4) None of these Solution: (1) 5 y = - x3 + 3x2 + 2x - 27 y’ = - 3x2 + 6x + 2 y’’ = - 6x + 6 = 0 y’’’ = -6... View Article

If The Curves X 2 9a 9 Y And X 2 A Y 1 Intersect Orthogonally Then The Value Of A Is

1) 3 2) 4 3) 5 4) 7 5) 9 Solution: (2) 4 x2 = 9a(9 - y) --- (1) x2 = a(y + 1) ---- (2) From equation (1) and (2), 9a(9 - y)... View Article

The Length Of The Subtangent To The Curve X 2 Y 2 A 4 At A A Is

1) a/2 2) 2a 3) a 4) a/3 Solution: (2) 2a x2y2 = a4 y2 = a4 / x2 2y (dy / dx) = - 2a4 / x3 (dy / dx)(-a, a) = - 2a4 / [2... View Article

A Missile Is Fired From The Ground Level Rises X Metres Vertically Upwards In T Sec

1) 200 m 2) 125 m 3) 190 m 4) 300 m Solution: (1) 200 m x = 100t - (25 / 2) t2 Maximum height will be reached when dx / dt = 0.... View Article

The Point On The Curve Y 2 X The Tangent At Which Makes An Angle 45 With X Axis Is

1) (1 / 4, 1 / 2) 2) (1 / 2, 1 / 4) 3) (1 / 2, - 1 / 2) 4) (1 / 2, 1 / 2) Solution: (1) (1 / 4, 1 / 2) Slope of the tangent = m =... View Article

If The Function F X 2x 3 9ax 2 12a 2x 1 Attains Its Maximum And Minimum At P And Q

1) 0 2) 1 3) 2 4) None of these Solution: (3) 2 f (x) = 2x3 - 9ax2 + 12a2x + 1 f’ (x) = 6x2 - 18ax + 12a2 = 0 f’’ (x) = 12x -... View Article

The Maximum Area Of The Rectangle That Can Be Inscribed In A Circle Of Radius R Is

1) πr2 2) r2 3) πr2 / 4 4) 2r2 Solution: (4) 2r2 (2r)2 = l2 + b2 4r2 = l2 + b2 b2 = 4r2 - l2 b = √4r2 - l2 Area = l *... View Article

The Angle Between The Tangents At Those Points On The Curve X T 2 1 And Y T 2 T 6

1) ± tan-1 (4 / 29) 2) ± tan-1 (5 / 49) 3) ± tan-1 (10 / 49) 4) ± tan-1 (8 / 29) Solution: (3) ± tan-1 (10 / 49) x = t2 + 1 dx /... View Article

If The Function F X X 2 E 2x X 0 Then The Maximum Value Of F X Is

1) 1/e 2) 1/2e 3) 1/e2 4) 4/e4 Solution: (3) 1 / e2 f (x) = x2 e-2x f’ (x) = e-2x (2x) - (2x2) e-2x f’ (x) = 2e-2xx (1 - x)... View Article

The Minimum Value Of 2x 3y When Xy 6 Is

1) 9 2) 12 3) 8 4) 6 Solution: (2) 12 f (x) = 2x + 3y f (x) = 2x + (18 / x) f’ (x) = 2 - (18 / x2) Put f’ (x) = 0 for maximum... View Article

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