List of top Questions asked in BITSAT

The slope of the tangent to the curve \(y=e^x\cos x\) is minimum at \(x=\alpha,\;0\le\alpha\le2\pi\). Then the value of \(\alpha\) is
The function \(f(x)=\dfrac{x}{2}+\dfrac{2}{x}\) has local minimum at
Let \(M\) be a \(3\times3\) non-singular matrix with \(\det(M)=\alpha\). If \(|M^{-1}\operatorname{adj}(M)|=K\), then the value of \(K\) 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
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
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
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 number of real roots of the equation \[ e^{x-1}+x-2=0 \] is
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 arithmetic mean of the data \(0,1,2,\ldots,n\) with frequencies \(1,{}^nC_1,{}^nC_2,\ldots,{}^nC_n\) 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
The line which is parallel to X-axis and crosses the curve \(y=\sqrt{x}\) at an angle \(45^\circ\) 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 \((A\cap B)'\)?
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
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
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 \(g\) is the inverse of function \(f\) and \(f'(x)=\sin x\), then \(g'(x)\) is equal to
The period of \(\tan 3\theta\) 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 \(x=0\), \(f(x)\)
The area of the region \(R=\{(x,y):|x|\le |y| \text{ and x^2+y^2\le1\}\) is
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 value of \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots \text{ up to } n \text{ terms is} \]
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?