List of top Mathematics Questions asked in BITSAT

If the third term in the expansion of
\( \left( x + x \log_{10}^{x} 5 \right) \)
is \( 10^6 \), then \( x \) may be
If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is
A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of ten steps he is one step away from the starting point is
All the words that can be formed using alphabets A, H, L, U and R are written in a dictionary (no alphabet is repeated). Rank of the word RAHUL is
The parabola having its focus at (3,2) and directrix along the y-axis has its vertex at
If the sum of odd numbered terms and even numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
If sumᵣ=0ⁿ+2ⁿCᵣ=2⁸-1, then n=
The number of values of r satisfying ³9C₃r-1=³9Cᵣ²-1=³9C₃r is
The length of the chord x+y=3 intercepted by the circle x²+y²-2x-2y-2=0 is
The locus of the point of intersection of two tangents to the parabola y²=4ax, which are at right angle to one another is
The lengths of the tangent drawn from any point on the circle 15x²+15y²-48x+64y=0 to the circles 5x²+5y²-24x+32y+75=0 and 5x²+5y²-48x+64y+300=0 are in the ratio
At an extreme point of a function f(x), the tangent to the curve is
The number of integral values of λ for which x²+y²+λ x+(1-λ)y+5=0 is the equation of a circle whose radius exceeds 5, is
A ray of light coming from the point (1,2) is reflected at a point A on the x-axis and then passes through the point (5,3). The coordinates of the point A are
The equation x²-2√(3)xy+3y²-3x+3√(3)y-4=0 represents
The curve y=xeˣ has minimum value equal to
The line joining (5,0) to (10cosθ,10sinθ) is divided internally in the ratio 2:3 at P. If θ varies, the locus of P is
Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]: I. f(x) is continuous in [-1,1]. II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0 endcases then f(x) is
The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x/4-sin²x/4)+(a-1)x is decreasing is
What is the x-coordinate of the point on the curve f(x)=√(x)(7x-6), where the tangent is parallel to the x-axis?
The number of points at which the function f(x)=(1)/(log|x|) is discontinuous is
If \( [x] \) denotes the greatest integer less than or equal to \( x \), and \( -1 < x < 0 < y < 1 < z < 2 \), then the value of the determinant

\( \begin{vmatrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{vmatrix} \)
is
Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ x+alpha₂ y=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then
If the matrix beginpmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endpmatrix is singular, then λ=