There are four towns P, Q, R and T. Q is to the South-west of P, R is to the east of Q and South-east of P, and T is to the north of R in line with QP. In which direction of P is T located?
How many such numbers are there in the arrangement each of which is immediately preceded by a symbol but not immediately followed by a letter? \[\uparrow 9\,B\,Q=\$\,2\,5\,R\,J\,\partial\,L\,3\,Y\,M\,E\,6\,8*\div\,D\,F\,4\,\beta\,H\,7\]
Find out which of the letter series follows the given rule: "Number of letters skipped in between adjacent letters in the series decreases by one each time."
A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger size. Also no face of any of Black the bigger cubes is painted blue.
How many cubes have at least one face painted blue?
In a group of persons travelling in a bus, 7 persons can speak French, 14 can speak Spanish and 6 can speak English. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?
The following question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Choose a figure from the given options which would most closely resemble the unfolded form of Fig. (Z).
The relationship among the three words in the question can be best represented by one of the four diagrams given below. Choose the correct answer. Nitrogen, Ice, Air
If the system of equations x + ay + az = 0, bx + y + bz = 0 and ex + cy + z = 0 where a, b, c are non-zero non unity, has a non-trivial solution, then the value of \[\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}\]
Let A, B, C be three events. If the probability of occurring exactly one event out of A and B is\[1-a\], out of B and C is\[\alpha =\pm \text{ }1,\beta =1\], out of C and A is \[1-a\] and that of occurring three events simultaneously is \[{{a}^{2}}\], then the probability that at least one out of A, B, C will occur is
If \[\vec{a}=\hat{i}+\hat{j}+\hat{k},\,\,\vec{b}=4\hat{i}+3\hat{j}+4\hat{k}\] and \[\vec{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}\] are linearly dependent vectors and \[|\vec{c}|=\sqrt{3}\], then
A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted, If one item is chosen at random, the probability that it is rusted or is a nail is
The length of the perpendicular from the origin to the plane passing through the point \[\vec{a}\] and containing the line\[\vec{r}=\vec{b}+\lambda \,\vec{c}\].
For any four points P, Q, R and \[S;\text{ }\!\!|\!\!\text{ }\overrightarrow{PQ}\times \overrightarrow{RS}-\] \[\overrightarrow{QR}\times \overrightarrow{PS}+\overrightarrow{RP}\times \overrightarrow{QS}|\]is equal to 4 times the area of the triangle ___.
One hundred identical coins, each with probability p of showing up heads, are tossed. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is
Let \[\frac{d}{dx}\,F(x)\,=\left( \frac{{{e}^{\sin \,x}}}{x} \right),x>0.\] If \[\int\limits_{1}^{4}{\frac{3}{x}{{e}^{\sin \,{{x}^{3}}}}}dx\] \[=f(k)-F(1)\]then one of the possible values of k is __
Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is
The income of Raj on the \[{{n}^{th}}\] day is Rs.\[({{n}^{2}}+2)\]and the expenditure of Raj on the \[{{n}^{th}}\] day is\[(2n+1)\]. In how many days his total savings will Rs.1240?
Dev and Tukku can do a piece of work in 45 and 40 days respectively. They began the work together, but Dev leaves after some days and Tukku finished the remaining work in 23 days. After how many days did Dev leave?
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each there in 23 seconds. The ratio of their speeds is
A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field?
There are ten subjects in the school day at St. Vincent's High School, but the sixth standard students have only 5 periods in a day. In how many ways can we form a time-table for the day for the sixth standard students?
In a market survey, 20% opted for product A whereas 60% opted for product 8. The remaining individuals were not certain. If the difference between those who opted for product S and those who were uncertain was 720, how many individuals were covered in the survey?
A can lay railway track between two given stations in 16 days and S can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then C alone can do the job in
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal?s selection is 1/3 and that of Monica's selection is 1/5. Find the probability that only one of them will be selected.
Entry fee in an exhibition was Rs.1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is ___.
The domain of the function \[f(x)=si{{n}^{-1}}\left( \frac{1+{{x}^{3}}}{2{{x}^{3/2}}} \right)\]\[+\sqrt{\sin \,(sin\,x)}+\,{{\log }_{(3\{x\}+1)}}({{x}^{2}}+1)\] where {.} represents fractional part function, is ___.