If \[x=\frac{\sqrt{8}+\sqrt{2}}{2}\] and \[y=\frac{\sqrt{8}-\sqrt{2}}{2},\] then the value of \[{{\log }_{121}}\,({{x}^{2}}+4xy+{{y}^{2}})\] is equal to ______.
In the figure given below, AB is a diameter of the circle with centre O. If AC is a chord and OM is perpendicular on it where AB = 13 cm and BC = 5 cm, then the length of OM is ____.
If \[A=\frac{1}{1+\cos \theta }+\frac{1}{1-\cos \theta }\] and \[B=\frac{1}{1+\sin \theta }+\frac{1}{1-\sin \theta }\] then \[\frac{A}{B}\] is equal to _______.
The value of \[{{\log }_{\sin \theta }}\left[ \text{cose}{{\text{c}}^{2}}\theta \,\,\left\{ {{(\cos \theta -\sin \theta )}^{2}}+2\sin \theta \cos \theta \right\} \right]\] is equal to ______.
The list price of a LED TV is Rs. 27000. The shopkeeper sold it by allowing a 5% discount and charged 6% sales tax on it. By mistake, while calculating the bill, he considered 4% discount and 5% sales tax. As a result his customer has paid _______.
A container has 80 litres of milk. From this container, 8 litres of milk was taken out and replaced by water. The process was further repeated twice. The volume of milk in the container after that is ________.
The surface area of a sphere of radius 30 cm is six times the area of the curved surface of a cone of radius 24 cm. Find the volume of the cone. \[\left[ Take\,\pi =\frac{22}{7} \right]\]
A number 'a' is selected from the numbers 1, 2, 3 and then the second number 'b' is randomly selected from the numbers 1, 4 and 9. The probability that the product 'ab' of the two numbers will be less than 8 is _____.
Average of 6 distinct natural numbers is 53. If the average of the three largest numbers is found to be 61, then find the sum of the highest and the lowest possible median of these six numbers.
A bag contains x white balls, 24 red balls and y black balls. A ball is drawn at random from the bag. If the probability that the drawn ball is white, is \[\frac{1}{4}\] and the probability that the drawn ball is black, is \[\frac{5}{12},\] then the values of x and y are respectively _______.
Direction: In each of the questions given below there are four statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known facts.
Direction: In each of the questions given below there are four statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known facts.
Direction: Study the following information carefully and answer the questions given below:
M, D, P, K, R, T and W are sitting around a circle facing at the centre. D is second to the right of P who is third to the right of K. T is third to the right of W who is not an immediate neighbour of D. M is third to the left of R.
Direction: Study the following information carefully and answer the questions given below:
M, D, P, K, R, T and W are sitting around a circle facing at the centre. D is second to the right of P who is third to the right of K. T is third to the right of W who is not an immediate neighbour of D. M is third to the left of R.
In which of the following pairs is the second person sitting to the immediate right of the first person?
Direction: Study the following information carefully and answer the questions given below:
M, D, P, K, R, T and W are sitting around a circle facing at the centre. D is second to the right of P who is third to the right of K. T is third to the right of W who is not an immediate neighbour of D. M is third to the left of R.
Direction: Study the following information carefully and answer the questions given below:
M, D, P, K, R, T and W are sitting around a circle facing at the centre. D is second to the right of P who is third to the right of K. T is third to the right of W who is not an immediate neighbour of D. M is third to the left of R.
In a certain code language, 'come now' is written as 'ha na', 'now and then' is written as 'pa da na' and 'go then' is written as 'sa pa'. How is 'and' written in that code language?
In a four digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and the last digit is equal to 2 more than the second digit. Finally, the sum of the first and third digit is equal to the second digit. If all the digits of the number are distinct, then what will be the second digit of the number?
A set of consecutive positive integers beginning with 1 is written on a blackboard. A student comes along and erases one number. The average of the remaining numbers is \[35\,\,\frac{7}{17}\]. What was the number erased?
Anubhav has Rs. 170 in one denomination. He has been asked to allocate them into a number of bags such that any amount required between Rs. 1 and Rs. 170 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?
Let n be the number of different five digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the number. What is the value of n?
If \[\frac{\sqrt{\sqrt{\sqrt{\sqrt{\left( {{5}^{x-1}}-{{7}^{x-3}} \right)}}}}}{{{\left( {{8}^{x-2}}+{{3}^{x-1}}-17 \right)}^{\frac{-5}{2}}}{{.24}^{\frac{25}{8}}}}={{(13824)}^{\frac{2}{3}}}\] then what will be the value of x?
The value of \[\frac{4}{1+2{{\log }_{{{a}^{2}}{{b}^{2}}}}c}+\frac{4}{1+2{{\log }_{{{a}^{2}}{{c}^{2}}}}b}+\frac{4}{1+2{{\log }_{{{b}^{2}}{{c}^{2}}}}a}\]is equal to _______.