List of top Questions asked in BITSAT- 2015

Cobalt $(60)$ isotope is used in the treatment of :

In a $\Delta ABC$, the lengths of the two larger sides are $10$ and $9$ units, respectively. If the angles are in AP, then the length of the third side can be

Let \(S\) be the focus of the parabola \(y^2=8x\) and \(PQ\) be the common chord of the circle \(x^2+y^2-2x-4y=0\) and the given parabola. The area of \(\triangle PQS\) is

The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is

Let \(f(x)\) be a polynomial of degree three satisfying \(f(0)=-1\) and \(f'(0)=0\). Also, 0 is a stationary point of \(f(x)\). If \(f(x)\) does not have an extremum at \(x=0\), then the value of \[ \int \frac{f(x)}{x^3-1}\, dx \] is

\(\displaystyle \lim_{x\to\infty}\frac{\int_{0}^{2x} x e^{x^{2}}\,dx}{e^{4x^{2}}}\) equals

If \(\displaystyle \lim_{x\to\infty}x\sin\!\left(\frac1x\right)=A\) and \(\displaystyle \lim_{x\to0}x\sin\!\left(\frac1x\right)=B\), then which one of the following is correct?

If complex numbers \(z_1,z_2\) and \(0\) are vertices of an equilateral triangle, then \(z_1^2+z_2^2-z_1z_2\) is equal to

Area of the circle in which a chord of length \(\sqrt{2}\) makes an angle \(\pi/2\) at the centre is

If the lines \(p_1x+q_1y=1\), \(p_2x+q_2y=1\) and \(p_3x+q_3y=1\) are concurrent, then the points \((p_1,q_1), (p_2,q_2)\) and \((p_3,q_3)\) are

If \(g\) is the inverse of function \(f\) and \(f'(x)=\sin x\), then \(g'(x)\) is equal to

The number of real roots of the equation \[ e^{x-1}+x-2=0 \] is

If a function \(f(x)\) is given by \[ f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2x+1)}+\frac{x}{(2x+1)(3x+1)}+\cdots+\infty, \] then at \(x=0\), \(f(x)\)

Let \(f:\mathbb R\to\mathbb R\) be a function such that \(f(x+y)=f(x)+f(y)\) for all \(x,y\in\mathbb R\). If \(f(x)\) is differentiable at \(x=0\), then which one of the following is incorrect?

If \(y=\left(x+\sqrt{1+x^2}\right)^n\), then \((1+x^2)\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}\) is

The total number of 4-digit numbers in which the digits are in descending order is

If binomial coefficients of three consecutive terms of \((1+x)^n\) are in H.P., then the maximum value of \(n\) is

A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is

A bag contains \((2n+1)\) coins. It is known that \(n\) of these coins have a head on both sides, whereas the remaining \((n+1)\) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is \(\frac{31}{42}\), then \(n\) is equal to

If \(0 < x < \dfrac{\pi}{2}\), then

In a \(\triangle ABC\), the lengths of the two larger sides are 10 and 9 units respectively. If the angles are in A.P., then the length of the third side can be

If \(\dfrac{\cos A}{\cos B}=n,\ \dfrac{\sin A}{\sin B}=m\), then the value of \(m^2-n^2\) is

If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then \(4x^2-4xy\cos\alpha+y^2\) is equal to

The period of \(\tan 3\theta\) is

Complete the series by replacing ‘?’ mark: \[ \text{G4T, J9R, M20P, P43N, S90L} \]