Starting from a point P, Sachin walked 20 metres towards South. He turned left and walked 30 metres. He then turned left and walked 20 metres. He again turned left and walked 40 metres and reached a point Q. How far and in which direction is the point Q from the point P?
In an examination, Raj got more marks than Mukesh but not as many as Priya. Priya got more marks than Gaurav and Kavita. Gaurav got less marks than Mukesh but his marks are not the lowest in the group. Who is second in the descending order of marks?
If the first ten letters of the English alphabet are written in reverse order and rest of the letters are left as it is, then which of the following letters will be the sixth to the left of the twelfth letter from the right end?
If \[-\] means \[\div \], \[+\] means \[\times \], \[\div \] means \[-\], \[\times \] means \[+\], then the mathematical expression which is equal to 56 is
In the following series, how many such even numbers are there which are divisible by 4 or 6, then followed by even number and preceded by odd number? 4 7 3 1 6 2 9 2 6 6 5 9 1 8 4 3 8 7 1 8 1 4 2 6
If it is possible to make a meaningful word with the fourth, sixth, eighth and thirteenth letters of the word 'ENCULTURATION', which of the following will be the third letter of the word? If no such word can be made give X as the answer and if more than one such word can be made, give M as the answer.
Six persons A, B, C, D, E and F were playing a game of cards. A's father, mother and uncle were in the group. There were two women. B, the mother of A, got more points than her husband D got more points than E but less than F. Niece of E got lowest points. Father of A got more points than F but could not win the game. Who is the husband of B?
Let A, B, C be three mutually independent events. Consider the two statements \[{{S}_{1}}\]and \[{{S}_{2}}\] \[{{S}_{1}}:A\]and \[B\cup C\]are independent. \[{{S}_{2}}:A\]and \[B\cap C\]are independent, then
If \[\vec{a},\vec{b},\vec{c}\] are non-coplanar vectors and \[\vec{p},\vec{q},\vec{r}\] are defined as \[\vec{p},=\frac{\vec{b}\times \vec{c}}{[\vec{b}\vec{c}\,\vec{a}]},\vec{q}=\frac{\vec{c}\times \vec{a}}{[\vec{c}\vec{a}\,\vec{b}]},\vec{r}=\frac{\vec{a}\times \vec{b}}{[\vec{a}\,\vec{b}\,\vec{c}]}\]
The equation of the plane containing the lines \[\vec{r}={{\vec{a}}_{1}}+\lambda \,{{\vec{a}}_{2}}\] and \[\vec{r}={{\vec{a}}_{2}}+\lambda \,{{\vec{a}}_{1}}\] is
If \[f(x)\,\,=co{{s}^{2}}\,x+co{{s}^{2}}\left( x+\frac{\pi }{3} \right)+sin\text{ }x\text{ }sin\,\left( x+\frac{\pi }{3} \right)\]and\[g\text{ }\left( \frac{5}{4} \right)=3\], then (gof)(x) is equal to __.
Suppose\[p\,(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}\]. If\[|p\,(x)|\,\le \,|{{e}^{x}}^{-1}-1|\]for all \[x\ge 0,\] then ____.
If \[\underset{x\to 0}{\mathop{lim}}\,\left( \frac{\cos \,4x\,+a\,\cos \,2x\,+b}{{{x}^{4}}} \right)\] is finite, then the value of a, b respectively are
The area bounded by the curves \[y={{x}^{4}}-2{{x}^{3}}+\]\[{{x}^{2}}+3\]the x-axis and two ordinates corresponding to the points of minimum of this function is
In a business, Aman and Raj invested amounts in the ratio 2:1, whereas the ratio between amounts invested by Aman and Ansh was 3 : 2. If Rs. 1,57,300 was their profit, how much amount did Ansh receive?
An ant climbing up a vertical pole ascends 12 metres and slips down 5 metres in every alternate hour. If the pole is 63 metres high, how long will it take it to reach the top?
Amitabh has a list of 24 friends. He wishes to invite some of them in such a manner that he can enjoy maximum number of parties, but in each party the number of friends (i.e., invitees) be same and each party must have different set of persons. Then how many parties can Amitabh enjoy?
A class prefect goes to meet the principal every week. His class has 30 people besides him. If he has to take groups of three every time he goes to the principal, in how many weeks will he be able to go to the principal without repeating the group of same three which accompanies him?
Purnima borrowed a sum of money and returned it in three equal quarterly installments of Rs. 17576 each. Find the sum borrowed, if the rate of interest charged was 16% per annum compounded quarterly. Find also the total interest charged.
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Use the picture of the ice cream cone to answer the question below. Which letter best represents the location of the length of the slant height of the ice cream cone on the number line shown below?
The probability that a student will pass in Mathematics is 3/5 and the probability that he will pass in English is 1/3. If the probability that he will pass in both Mathematics and English is 1/8, what is the probability that he will pass in at least one subject?
A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?