List of practice Questions

The value of \(\lambda\), for which the lines \(3x-4y=13\), \(8x-11y=33\) and \(2x-3y+\lambda=0\) are concurrent is
The interval in which the function \(2x^3+15\) increases less rapidly than the function \(9x^2-12x\), is
The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and cost $48 per hour at 16 miles per hour. The most economical speed if the fixed charges (i.e., salaries etc.) amount to $30 per hour is:
Evaluate: \[ \int \frac{1}{1+3\sin^2 x+8\cos^2 x}\,dx \]
\[ \int_{0}^{10}\frac{x^{10}}{(10-x)^{10}+x^{10}}\,dx \] is equal to
If M.D. is 12, the value of S.D. will be:
A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. Find the probability that they are of the same colour.
Find the value of \(\tan^{-1}\!\left(\dfrac{1-\frac{\pi}{5}}{2}\right)\).
If \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in A.P., then \[ \left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\left(\frac{1}{b}+\frac{1}{c}-\frac{1}{a}\right) \] is equal to:
The product of \(n\) positive numbers is unity, then their sum is:
If \(P_1\) and \(P_2\) be the lengths of perpendiculars from the origin upon the straight lines \(x\sec\theta+y\cosec\theta=a\) and \(x\cos\theta-y\sin\theta=a\cos2\theta\) respectively, then the value of \(4P_1^2+P_2^2\) is:
The angle of intersection of the two circles \(x^2+y^2-2x-2y=0\) and \(x^2+y^2=4\) is:
An arch of a bridge is semi-elliptical with major axis horizontal. If the length of the base is \(9\) m and the highest part of the bridge is \(3\) m from the centre of the horizontal axis, the best approximation of the height of the arch \(2\) m from the centre of the base is:
The complex number \(z=z+iy\) which satisfies the equation \[ \left|\frac{z-3i}{z+3i}\right|=1 \] lies on:
The number of all three element subsets of the set \(\{a_1,a_2,a_3,\ldots,a_n\}\) which contain \(a_3\) is:
In how many ways can a committee of 5 be formed out of 6 men and 4 women containing at least one woman?
If \(T_0,T_1,T_2,\ldots,T_n\) represent the terms in the expansion of \((x+a)^n\), then \((T_0-T_2+T_4-\cdots)^2+(T_1-T_3+T_5-\cdots)^2=\)
\(\cos^2\!\left(\frac{\pi}{6}+\theta\right)-\sin^2\!\left(\frac{\pi}{6}-\theta\right)=\)
The solution of \(\cos(2x)-1(3+2\cos x)=0\) in the interval \(0\le x\le2\pi\) is:
\(2^{3n}-7n-1\) is divisible by:
The greatest positive integer which divides \(n(n+1)(n+2)(n+3)\) for all \(n\in\mathbb{N}\), is:
If \(z=x+iy,\; z^{1/3}=a-ib\), then \(\dfrac{x}{a}-\dfrac{y}{b}=k(a^2-b^2)\), where \(k\) is equal to:
\(i^{57}+\dfrac{1}{i^{25}}\), when simplified has the value:
Which of the following can possibly be used as analgesic without causing addiction and modification?
Which among the following is not an antibiotic?