List of practice Questions

If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$, is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha$, $\beta$ are integers, then $\alpha+\beta$ is equal to :
If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?
Find the sum of series: \(2*2^2 - 2*3^2 + 2*4^2 +\) \(….(20 \,terms)\)
Let the number of elements in sets \(A\) and \(B\) be five and two respectively. Then the number of subsets of \(A \times B\) each having at least 3 and at most 6 elements is:
See the adjacent figure and find the value of ∠A in the semicircle
See the adjacent figure and find the value of ∠A in the semicircle
Ram and Mohan can do a piece of work in 20 days. Mohan alone can do the work in 30 days. In how many days will Ram alone complete the work.
The base of hexadecimal system is
The resultant vector of the cross product of the two vectors\( î+2j-k; 2i+j+k\) is
In regression analysis independent variable is also called as
Given below are two statements:
Statement I: Line of regression of y on x is the line which gives the best estimate for the value of y for any specified value of x. 
Statement II: Line of regression of x on y is the line which gives the best estimate for the value of x for any specified value of y. 
In the light of the above statements, choose the correct answer from the options given below:
A solid metallic sphere of radius 6cm is melted and recasted into small solid balls of radius 0.6cm. Find the number of balls so formed.
If \(\sin\theta=\frac{5}{13}\), then find the value of \(\frac{1+\tan\theta}{\sec\theta}\)
In how much time will a sum of ₹ 3,300 become ₹ 3,399 at 6% per annum, interest compounded half yearly?
By selling 100 pens, a shopkeeper gains the selling price of 40 pens. Find his gain percent ( correct to 2 decimal places) :
Three men and 2 boys can do a piece of work in 10 days, which 2 men and 3 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?
Which of the following is the set of those elements which are common in both A and B?
The average of nine consecutive natural numbers is 25. Find the smallest number.
Simplify: \(\frac {\frac 34+\frac 15-\frac {1}{10}-1}{\frac 18+\frac 12-\frac 34}\)
The product of two numbers is 4840. If the first number is two fifth of the second number, then what is the first number?
In what time will a 640 m long train cross an electric pole if its speed is 96 km/h?
The sum of two numbers is 40 and their HCF is 8. How many pairs of numbers satisfy both the conditions?
Two numbers are 26% and 40% respectively of a third number what percentage is the first number of the second number?
A trader sold an article at a gain of 20% Had he purchased it for 40% more and sold for 24 less, he would have incurred a loss of 20%. What is the cost price of the article?
A certain sum of money on simple interest amounts to 1,278 in 3 years and to 1,593 in \(5\frac 12\) years. Find the rate of interest per annum.
Find the sum of the fourth proportional of 60, 24, 15 and the mean proportional of 5 and 20.