MCQs

A point moves along a straight line in such a way that after t seconds its distance from the origin
is s t = $2 t^{2} + 3 t$ metres.Find the average velocity of the points between t = 3 and t = 6 seconds.
1. 25m/s
2. 30m/s
3. 21m/s
4. 32m/s
A point moves along a straight line in such a way that after t seconds its distance from the origin
is s t = $2 t^{2} + 3 t$ metres.Find the instantanous velocity of the points between t = 3 and t = 6 seconds.
1. 15m/s and 29m/s
2. 15m/s and 27m/s
3. 18m/s and 25m/s
4. 19m/s and 27m/s
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance
of s t = $16 t^{2}$ in t seconds. How long does the camera fall before it hits the ground?
1. 5 secs
2. 10secs
3. 15secs
4. 20secs
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance
of s t = $16 t^{2}$ in t seconds. What is the average velocity with which the camera falls during the last 2 seconds?
1. 128ft/sec
2. 130ft/sec
3. 129ft/sec
4. 140ft/sec
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance
of s t = $16 t^{2}$ in t seconds.What is the instantaneous velocity of the camera when it hits the ground?
1. 120ft/sec
2. 140ft/sec
3. 159ft/sec
4. 160ft/sec
A particle moves along a line according to the law s(t) = $2 t^{3} - 9 t^{2} + 12 t - 4$ , where t ≥ 0 .
At what times the particle changes direction?
1. 1,3sec
2. 1,2 sec
3. 3,2 sec
4. 4,1 sec
A particle moves along a line according to the law s(t) = $2 t^{3} - 9 t^{2} + 12 t - 4$ , where t ≥ 0 .
Find the total distance travelled by the particle in the first 4 seconds.
1. 30sec
2. 15m
3. 34m
4. 30m
A particle moves along a line according to the law s(t) = $2 t^{3} - 9 t^{2} + 12 t - 4$ , where t ≥ 0 .
Find the particle’s acceleration each time the velocity is zero.
1. -6,6
2. 6,6
3. -6,-6
4. 0,-6
If the volume of a cube of side length x is v = $x^{3}$ . Find the rate of change of the volume with respect to x when x = 5 units.
1. 75 units
2. 70 units
3. 65 units
4. 40 units
If the mass m (x) (in kilograms) of a thin rod of length x (in metres) is given by, m (x) = $\sqrt{3 x}$ then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres.
1. 1/2kg/m,1/6kg/m
2. 1/3kg/m,1/6kg/m
3. 1/2kg/m,1/5kg/m
4. 1/3kg/m,1/5kg/m
A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shore line. How fast is the beam moving along the shore line when it makes an angle of 45°with the shore?
1. 2pie km/s
2. 7pie km/s
3. 14pie km/s
4. 4pie km/s
A conical water tank with vertex down of 12 metres height has a radius of 5 metres at the top. If water flows into the tank at a rate 10 cubic m/min, how fast is the depth of the water increases when the water is 8 metres deep?
1. 1pie
2. 2/3pie
3. 9/10pie
4. 8/20pie
A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5 m/s. When the base of the ladder is 8 metres from the wall. How fast is the top of the ladder moving down the wall?
1. 8/3m/s
2. -8/3m/s
3. 2/3m/s
4. -2/3m/s
A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5 m/s. When the base of the ladder is 8 metres from the wall.At what rate, the area of the triangle formed by the ladder, wall, and the floor, is changing?
1. 22.83 sq.m/sec
2. 29.88 squ.m/sec
3. 28.83 sq.m/sec
4. 26.83 sq.m/sec
A police jeep, approaching an orthogonal intersection from the northern direction, is chasing a speeding car that has turned and moving straight east. When the jeep is 0.6 km north of the intersection and the car is 0.8 km to the east. The police determine with a radar that the distance between them and the car is increasing at 20 km/hr. If the jeep is moving at 60 km/hr at the instant of measurement, what is the speed of the car?
1. 5km/hr
2. 70km/hr
3. 140km/hr
4. 75km/hr
Find the point on the curve y = $x^{2} - 5 x + 4$ at which the tangent is parallel to the line 3x + y = 7 .
1. (2,7)
2. (1,0)
3. (2,3)
4. (0,1)
Find the points on the curve $y^{2} - 4 x y = x^{2} + 5$ for which the tangent is horizontal
1. (-2,-1) and (2,1)
2. (1,1) and (-1,2)
3. (2,-1) and (-2,1)
4. (-2,1) and (2,2)
Find the equations of the tangents to the curve $y = 1 + x^{3}$ for which the tangent is orthogonal with the line x +12y =12
1. 12x-y=15; 12x-y= 17
2. 12x-y=15; 12x-y= -17
3. 5x-y=15; 12x-y=-17
4. 12x-y=15; 2x-y=-17
Find the angle between the rectangular hyperbola xy = 2 and the parabola $x^{2} + 4 y = 0$ .
1. $\cos^{- 1} (3)$
2. $\tan^{- 1} (3)$
3. $\tan (3)$
4. $\cos (3)$
A race car driver is racing at 20th km. If his speed never exceeds 150 km/hr, what is the maximum distance he can cover in the next two hours.
1. 300km
2. 320km
3. 400km
4. 420km
Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x -axis for the following functions : f (x) = $x^{2} - x$ , x $\in$ [ 0,1 ]
1. 1/6
2. 1/2
3. 1/7
4. 2/3
Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x -axis for the following functions : $f (x) = \frac{x^{2} - 2 x}{x + 2}, x \in [- 1, 6]$
1. $2 + 2 \sqrt{2}$
2. $- 2 + 2 \sqrt{2}$
3. $2 + \sqrt{2}$
4. 2
Using the Rolle’s theorem, determine the values of x at which the tangent is parallel to the x -axis for the following functions : $f (x) = \sqrt{x} - \frac{x}{3}, x \in [0, 9]$
1. 9/4
2. 9
3. 3/10
4. 10
Evaluate the limit, if necessary use l’Hôpital Rule :
$l i m \frac{1 - \cos x}{x^{2}}_{x \to 0}$
1. 1
2. 1/5
3. 1/2
4. 1/3
Find the local extrema for the function using second derivative test f (x) = $- 3 x^{5} + 5 x^{3}$
1. local minimum= -2 and local maximum= 4
2. local minimum= -2 and local maximum= 2
3. local minimum= -4 and local maximum= 2
4. local minimum= -1 and local maximum= 2
Find the local extrema for the function using second derivative test: f (x) = x log x
1. local minimum=-1/e
2. local minimum=1/e
3. local minimum=-1/pie
4. local minimum=1/pie
Find two positive numbers whose sum is 12 and their product is maximum.
1. 24
2. 36
3. 96
4. 48
Find two positive numbers whose product is 20 and their sum is minimum.
1. $4 \sqrt{5}$
2. 4
3. $2 \sqrt{3}$
4. $4 \sqrt{3}$
A garden is to be laid out in a rectangular area and protected by wire fence. What is the largest possible area of the fenced garden with 40 metres of wire.
1. 48
2. 120
3. 100
4. 180
The curve y = $a x^{4} + b x^{2}$ with ab > 0
1. has no horizontal tangent
2. is concave up
3. is concave down
4. has no points of inflection
A stone is thrown up vertically. The height it reaches at time t seconds is given by x = 80t −16 $t^{2}$ .
The stone reaches the maximum height in time t seconds is given by
1. 2
2. 2.5
3. 3
4. 3.5
The point of inflection of the curve y = $(x - 1)^{3}$ is
1. (0,0)
2. (0,1)
3. (1,0)
4. (1,1)

MCQs

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