Trigonometry
if 2cos 3θ = √ 3, then θ ?
θ = 10 degrees
A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is
10 km/hr
From a rectangular solid of dimensions 42cm * 30cm * 20cm, a conical cavity of base diameter 14cm and depth 24cm is drilled out. find the surface area of the remaining solid.
(√ 680 = 26 approx.)
5796 cm^2
In the figure displayed on the whiteboard, O is the centre of the circle. If angle ONY = 50° and angle OMY= 15° , find angle MON.
angle MON = 70°
What is the net prime number following the number 7?
11
4cot θ = 3, then (sinθ -cosθ )/ sinθ + cosθ = ?
1/7
Solve for x and y:
-> ax/b - by/a = a + b
-> ax - by = 2ab
=> y=-a
=> x=b
A cylindrical pipe has inner diameter of 7cm and water flows through it at 192.5 litres per minute. Find the rate of flow in kilometers per hour.
3 km/hr
Given a right angled- triangle ABC. The lengths of the sides containing the right angle are 6cm and 8cm. A circle is inscribed in triangle ABC. Find the radius of the circle.
2cm
What three numbers have the same result when added or multiplied together?
(1), (2) and (3)
If the angle of elevation of a tower from a distance of 100 metres from its foot is 60o, then the height of the tower is
height= 173.2 m
if one zero of the cubic polynomial x^3 + ax^2 + bx + c is -1, then the product of the other two zeroes is?
answer: b-a+1
A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions
25 revolutions
ABCD is a trapezium, such that AB, DC are parallel and BC is perpendicular to them. If DAB = 45°, BC = 2 cm and CD = 3 cm then AB is?
5 cm
Apart from one, I am the first positive number that is both a square and a cube.
64
(sin540 + cos900)
In a certain factory, each day the expected number of accidents is related to the number of overtime hours by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported, and on another day there were 400 overtime hours logged and 5 accidents. What are the expected numbers of accidents when no overtime hours are logged?
3
The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?
246.4 cm^3
Two circles of radius 1 cm touch at point P. A third circle is drawn through the points A, B and C such that PA is the diameter of the first circle, and BC - perpendicular to AP - is the diameter of the second circle. The radius of the third circle is
5/3
How many sides does an “enneadecagon” have?
19
if A and B are 2 acute angles such that tan A = 1/2 and tan B = 1/3, then find A+B using the tangent addition formula.
A+B = 45°
Katrina walks down an up-escalator and counts 150 steps. Priyanka walks up the same escalator and counts 75 steps. Katrina takes three times as many steps in a given time as Priyanka. How many steps are visible on the escalator?
120
Four horses are tethered at 4 corners of a square field of side 70 metres so that they can just about reach one another. The area left ungrazed by the horses is:
1050 m^2
Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. the ant would not go within one metre of any insect repellent. Find the minimum distance in metres the ant must traverse to reach the sugar particle
π + 1
What is the only number that has letters in the alphabetical order?
Forty