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Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese. Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French. Based on the above information, which girl is learning the most difficult pair of languages?
Consider a system described by ẋ = Ax + Bu y = Cx + Du The system is completely output controllable if and only if Where: x = State vector (n-vector) u = Control vector (r-vector) y = Output vector (m-vector) A = n × n matrix B = n × r matrix C = m × n matrix D = m × r matrix
From a large cone of volume 600 cm3, a small cone is cut whose height is 70% of the height of the large cone. If the radius of the small cone is 50% of the radius of the large cone, then find the volume of the remaining part left after cutting the small cone.
The sum and difference of the slant height and height of cone A are in the ratio 3 ∶ 1, while the sum and difference of the slant height and height of cone Y are in the ratio 5 ∶ 1. If the volume of cone A is 30% of the volume of cone B, then the height of cone A is what percentage of the height of cone B.
Curved surface area of Cone P is seven times the curved surface area of Cone Q. Slant height of Cone Q is seven times the slant height of Cone P. What will be the ratio of the area of the base of Cone P to the area of the base of Cone Q?
In a survey of 100 students, it was found that 25 students have enrolled for Navy AA test series, 26 students have enrolled for NDA test series, 26 students have enrolled for Airforce group X test series, 9 students have enrolled for both Navy AA and Airforce group X test series, 11 students have enrolled for both Navy AA and NDA test series, 8 students have enrolled for both NDA and Airforce group X test series whereas 3 students have enrolled in all three test series. Find the number of students who has not enrolled in any of the test series.
In a survey of 100 students, it was found that 25 students have enrolled for Navy AA test series, 26 students have enrolled for NDA test series, 26 students have enrolled for Airforce group X test series, 9 students have enrolled for both Navy AA and Airforce group X test series, 11 students have enrolled for both Navy AA and NDA test series, 8 students have enrolled for both NDA and Airforce group X test series whereas 3 students have enrolled in all three test series. Find the number of students who have enrolled exactly in any two test series.
In a survey of 100 students, it was found that 25 students have enrolled for Navy AA test series, 26 students have enrolled for NDA test series, 26 students have enrolled for Airforce group X test series, 9 students have enrolled for both Navy AA and Airforce group X test series, 11 students have enrolled for both Navy AA and NDA test series, 8 students have enrolled for both NDA and Airforce group X test series whereas 3 students have enrolled in all three test series. Find the number of students who have enrolled in exactly one test series.
A plane cuts a cone such that the volume of the whole cone is 125 times of the smaller cone formed. Find the height of the smaller cone if the height of the full cone is 15 cm.
A right circular cone of circular base radius R and H resting on a plane. The cone is cut by a plane parallel to the base. The new circular cone-formed has a 12.5% volume of the older cone. What is the height of the new cone?