The Equation Of The Tangent Of The Curve X A N Y B N 2 At A B Is 1) [x / a] + [y / b] = 2 2) [x / a] + [y / b] = 1 / 2 3) [x / a] - [y / b] = 2 4) ax + by = 2 Solution: (1) [x / a] + [y / b] = 2... View Article
The Triangle Formed By The Tangent To The Curve F X X 2 Bx B At The Point 1 1 And The Coordinate Axes Lie In The First Quadrant If Its Area Is 2 Then The Value Of B Is 1) -1 2) 3 3) -3 4) 1 Solution: (3) -3 y = f (x) = x2 + bx - b m = dy / dx = 2x + b = (2 + b) The equation of the tangent at (1,... View Article
The Number Of Points Where F X Attains Its Minimum Value Is The number of points, where f (x) attains its minimum value, is 1) 1 2) 2 3) 3 4) infinitely many Solution: (1) 1 -1 < sin (1... View Article
The Equation Of Normal Of The Curve Y 1 X Y Sin 1 Sin 2 X At X 0 Is 1) x + y = 1 2) x - y = 1 3) x + y = - 1 4) x - y = - 1 Solution: 1) x + y = 1 y = 1y + 0 y = 1, slope of normal = -1 / (dy /... View Article
The Minimum Value Of X Log X Is 1) e 2) 1/e 3) e2 4) e3 Solution: (1) e f (x) = x / log x f’ (x) = [log x - 1] / [log x]2 For maxima and minima put f’ (x) =... View Article
The Greatest And Least Value Of Sin 1 X 2 Cos 1 X 2 Are Respectively 1) π2 / 4 and 0 2) π2 / 4 and - π / 2 3) 5π2 / 4 and π2 / 8 4) π4 / 4 and -π2 / 4 Solution: (3) 5π2 / 4 and π2 / 8 (sin-1 x)2 +... View Article
If F 1 And X Equals 2 Are Extreme Points Of F X Alpha Log Modulus X Beta X 2 X Then 1) α = -6, β = 1 / 2 2) α = -6, β = - 1 / 2 3) α = 2, β = -1 / 2 4) α = 2, β = 1 / 2 Solution: (3) α = 2, β = -1 / 2 f (x) = α log... View Article
The Rate Of Change Of The Surface Area Of The Sphere Of Radius R When The Radius Is Increasing At The Rate Of 2 Cm S Is Proportional To 1) 1/r2 2) 1/r 3) r2 4) r Solution: (4) r S = 4Ï€r2 ds / dt = 8Ï€r * (dr /dt) (ds / dt) = 8Ï€r * 2 ds / dt = 16Ï€r It is... View Article
If A Stone Thrown Upwards Has An Equation Of Height H 490t 4 9t 2 Then The Maximum Height Reached By It Is 1) 24500 2) 12500 3) 12250 4) 25400 Solution: (3) 12250 m h = 490t - 4.9t2 dh / dt = 0 (for maximum height) 490 [dt / dt] -... View Article
If The Radius Of A Circular Plate Is Increasing At The Rate Of 0 01cm S When The Radius Is 12 Cm Then The Rate At Which The Area Increases Is 1) 0.24 π sq cm/s 2) 60 π sq cm/s 3) 24 π sq cm/s 4) 1.2 π sq cm/s Solution: (3) 24 π sq cm/s dr / dt = 0.01cm / s r = 12cm r =... View Article
A Right Circular Cylinder Which Is Open At The Top And Has A Given Surface Area Will Have The Greatest Volume If Its Height H And Radius R Are Related By 1) 2h = r 2) h = 4r 3) h = 2r 4) h = r Solution: (4) h = r Volume of the cylinder = V = πr2h Surface area = S = 2πrh + πr2 ---... View Article
A Ladder 10 M Long Rests Against A Vertical Wall With The Lower End On The Horizontal Ground The Lower End Of The Ladder Is Pulled Along The Ground Away From The Wall At The Rate Of 3cm S 1) 4√3 m 2) 5√3 m 3) 5√2 m 4) 8 m 5) 6 m Solution: (5) 6m x2 + y2 = 102 x2 + y2 = 100 dx / dt = 3 cm/sec dy / dt = 4... View Article
A Spherical Iron Ball 10 Cm In Radius Is Coated With A Layer Of Ice Of Uniform Thickness That Melts At A Rate Of 50 Square Cm Min When The Thickness Of Ice Is 5 Cm Then The Rate At Which The Thickness Of Ice Decreases Is 1) 5/6π cm/min 2) 1/54π cm/min 3) 1/18π cm/min 4) 1/36π cm/min Solution: (3) 1/18π cm/min R = (10 + x) V = (4 / 3) πr3 V = (4... View Article
A Spherical Balloon Is Being Inflated At The Rate Of 35 Cc Min The Rate Of Increase Of The Surface Area Of The Balloon When Its Diameter Is 14 Cm Is 1) 7 sq cm/min 2) 10 sq cm/min 3) 17.5 sq cm/min 4) 28 sq cm/min Solution: (3) 10 sq cm / min V = (4 / 3) πr3 (dV / dt) = (4 /... View Article
A Particle Moves In A Straight Line So That S Root Of T Then Its Acceleration Is Proportional To 1) (velocity)3 2) velocity 3) (velocity)2 4) (velocity)3/2 Solution: 1) (velocity)3 s = √t = t1/2 V = ds / dt = (1 / 2) t-½... View Article
The Radius Of A Circle Is Increasing At The Rate Of 0 1 Cm S When The Radius Of The Circle Is 5 Cm The Rate Of Change Of Its Area Is 1) -π cm2/s 2) 10π cm2/s 3) 0.1π cm2/s 4) 5π cm2/s 5) π cm2/s Solution: (5) πcm2/s dr /dt = 0.1 A = πr2 dA / dt = 2πr (dr /... View Article
If A Particle Moves Such That The Displacement Is Proportional To The Square Of The Velocity Acquired Then Its Acceleration Is 1) proportional to s2 2) proportional to 1/s2 3) proportional to 1/s 4) a constant Solution: (4) a constant According to the... View Article
The Circumference Of A Circle Is Measured As 56 Cm With An Error 0 02 Cm The Percentage Error In Its Area Is 1) 1/7 2) 1/28 3) 1/14 4) 1/56 Solution: (3) 1 / 14 Let r = radius, C - circumference, A - area C = 2πr A = πr2 ΔC = (dC / dr)... View Article
If The Radius Of A Circle Is Increasing At A Uniform Rate Of 2 Cm S The Area Of Increasing Of The Area Of A Circle At The Instant When The Radius Is 20 Cm Is 1) 70 π cm2 / s 2) 70 cm2 / s 3) 80 π cm2 / s 4) 80 cm2 / s Solution: (3) 80πcm2 s-1 When r = 20cm, dr / dt = 2cms-1 A = πr2... View Article
What Is Meant By The Vapour Pressure Of Water The vapour pressure is the pressure of the vapour above the sample liquid in a closed container. The vapour pressure is determined by the type of... View Article
