List of top Questions asked in BITSAT- 2021

The dot product of a vector with the vectors i+ j-3 k, i+3 j-2 k, 2 i+ j+4 k are 0,5 and 8 respectively. The vector is
If the line through the points A(k,1,-1) and B(2k,0,2) is perpendicular to the line through the points B and C(2+2k,k,1), then the value of k is
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
If int xlog(1+(1)/(x))dx = f(x)log(x+1)+g(x)x²+Lx+C, then
2¹/4·2²/8·2³/16·2⁴/32⋯ is equal to
Let a, b, c be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then | a+ b+ c| in terms of θ is equal to
If sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+3Cᵣ=(3)/(a+3), then a-n is equal to
If R(t)= beginpmatrix cos t & sin t
-sin t & cos t endpmatrix, then R(s)R(t) equals
If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is
If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to
Statement–1: A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216. Statement–2: If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is (5)/(4) times as thick as the plate forming the cylindrical sides, find the ratio of the radius to the height of the cylinder using minimum material for the same capacity.
The equation of one of the common tangents to the parabola y²=8x and the circle x²+y²=12x+4 is
If f(x)=cos⁻1[(1-(log x)²)/(1+(log x)²)], then the value of f'(e) is equal to
The maximum value of z=3x+2y subject to x+2y\ge2, x+2y\le8, x,y\ge0 is
The area under the curve y=|cos x-sin x|, 0≤ x≤ (π)/(2), above the x-axis is
The number of roots of the equation cos 3θ=0 for 0≤θ\le2π is
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x≠ 0
0, & x=0 endcases then f(x) is
If int (cos x-1)/(sin x+eˣ)dx is equal to
If x is a real number, then (x)/(x²-5x+9) must lie between
The value of cot⁻17+cot⁻18+cot⁻118 is
If f(x)=xˣ, then f(x) is increasing in interval
The value of limₓtₒᵢₙfty(fraca₁¹/x+a₂¹/x+⋯+aₙ¹/xn)ⁿx, aᵢ>0 is
After striking the floor a certain ball rebounds (4)/(5)th of its height from which it has fallen. The total distance that the ball travels before coming to rest if it is gently released from a height of 120m is
An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30^∘. After 3 minutes this angle becomes 60^∘. After how much more time will the car reach the tree?