The pit bottom in a correlation survey is shown in the figure. Points C and D represent two suspended wires. The bearing of line CD is 286°00′00′′ and its length is 4.64 m. The angle CED is measured as 00°00′40′′. The length of line DE is 5.46 m. Considering the Weisbach triangle method, the bearing of the line CE is

Mr. X speaks ______ Japanese ______ Chinese.

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively. If R gets ₹ 1000 more than S, what is the share of Q (in ₹)?

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm. What is the shortest distance between PQ and SR (in cm)?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?

A random variable $X$ has the following probability mass function.

The expected value of the variable $X$ is ______ (round off to 1 decimal place).

P, Q, R, S, T, U, V, and W are seated around a circular table.

I. S is seated opposite to W.

II. U is seated at the second place to the right of R.

III. T is seated at the third place to the left of R.

IV. V is a neighbour of S.

Which of the following must be true?

The eigenvalues of the matrix

$A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix}$ are

The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 - 2018 is ______.

Rajiv Gandhi Khel Ratna Award was conferred____Mary Kom, a six-time world champion in boxing, recently in a ceremony_____the Rashtrapati Bhavan (the President’s official residence) in New Delhi.