List of top Questions asked in BITSAT- 2015

The arithmetic mean of the data \(0,1,2,\ldots,n\) with frequencies \(1,{}^nC_1,{}^nC_2,\ldots,{}^nC_n\) is
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
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
Minimise \( Z=\sum_{i=1}^{n}\sum_{j=1}^{m} c_{ij}x_{ij} \) subject to \[ \sum_{i=1}^{m} x_{ij}=b_j,\; j=1,2,\ldots,n, \] \[ \sum_{j=1}^{n} x_{ij}=b_i,\; i=1,2,\ldots,m. \] This is an LPP with number of constraints equal to
The number of real roots of the equation \[ e^{x-1}+x-2=0 \] is
The mean square deviation of a set of observations \(x_1,x_2,\ldots,x_n\) about point \(c\) is defined as \[ \frac1n\sum_{i=1}^n(x_i-c)^2. \] The mean square deviations about \(-2\) and \(2\) are 18 and 10 respectively. The standard deviation of the set of observations is
If \[ \frac{e^x+e^{5x}}{e^{3x}}=a_0+a_1x+a_2x^2+a_3x^3+\cdots, \] then the value of \(2a_1+2^3a_3+2^5a_5+\cdots\) is
The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) is
If \(\cos^{-1}x-\cos^{-1}\frac{y}{2}=\alpha\), then \(4x^2-4xy\cos\alpha+y^2\) is equal to
The total number of 4-digit numbers in which the digits are in descending order is
Universal set, \[ U=\{x\mid x^5-6x^4+11x^3-6x^2=0\}; \quad A=\{x\mid x^2-5x+6=0\}; \quad B=\{x\mid x^2-3x+2=0\}. \] What is \((A\cap B)'\)?
Let \(\vec a,\vec b,\vec c\) be three vectors satisfying \(\vec a\times\vec b=\vec a\times\vec c\), \(|\vec a|=|\vec c|=1\), \(|\vec b|=4\) and \(|\vec b\times\vec c|=\sqrt{15}\). If \(\vec b-2\vec c=\lambda \vec a\), then \(\lambda\) equals
If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] 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
The period of \(\tan 3\theta\) is
If \(g\) is the inverse of function \(f\) and \(f'(x)=\sin x\), then \(g'(x)\) is equal to
The area of the region \(R=\{(x,y):|x|\le |y| \text{ and x^2+y^2\le1\}\) 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 \(x=0\), \(f(x)\)
If \(\omega\) is the complex cube root of unity, then the value of \[ \omega+\omega\!\left(\frac12+\frac38+\frac{9}{32}+\frac{27}{128}+\cdots\right) \] is
Shikha is mother-in-law of Ekta who is sister-in-law of Ankit. Pankaj is father of Sanjay, the only brother of Ankit. How is Shikha related to Ankit?
\(\displaystyle \lim_{x\to\infty}\frac{\int_{0}^{2x} x e^{x^{2}}\,dx}{e^{4x^{2}}}\) equals
In a queue of children, Arun is fifth from the left and Suresh is sixth from the right. When they interchange their places among themselves, Arun becomes thirteenth from the left. Then, what will be Suresh’s position from the right?
The value of \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots \text{ up to } n \text{ terms is} \]
The root of the equation \[ 2(1+i)x^2-4(2-i)x-5-3i=0 \] which has greater modulus is
Neeraj starts walking towards South. After walking 15 m, he turns towards North. After walking 20 m, he turns towards East and walks 10 m. He then turns towards South and walks 5 m. How far is he from his original position and in which direction?