BITSAT 2021

The slope of the tangent to the curve x = t2 + 3t \(-\) 8, y = 2t2 \(-\) 2t \(-\) 5 at the point t = 2 is

The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

\({{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} =\)

Equation of circle which passes through the points (1, \(-\)2) and (3, \(-\)4) and touch the X-axis is

If Re(z + 2) = | z \(-\) 2 |, then the locus of z is

\(\int\limits_0^1 {{{\log (1 + x)} \over {1 + {x^2}}}dx}\) is equal to :

Solution of \(\left( {{{x + y - 1} \over {x + y - 2}}} \right){{dy} \over {dx}} = \left( {{{x + y + 1} \over {x + y + 2}}} \right)\), given that y = 1 when x = 1 is

The solution of \({x^3}{{dy} \over {dx}} + 4{x^2}\tan y = {e^x}\sec y\) satisfying y (1) = 0, is

If \(y = \sin \left( {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right)\), then \({{dy} \over {dx}}\) is :

If f(x) = 4x \(-\) x2, x\(\in\)R, and f(a + 1) \(-\) f(a \(-\) 1) = 0, then a is equal to

The maximum value of the function y = x(x \(-\) 1)2, is

Find the area enclosed by the loop in the curve 4y2 = 4x2 \(-\) x3.

If x = 9 is the chord of contact of the hyperbola x2 \(-\) y2 = 9, then the equation of the corresponding pair of tangent is

\(\int {{1 \over {1 - 2\sin x}}dx}\) is equal to

The minimum value of \({({\sin ^{ - 1}}x)^3} + {({\cos ^{ - 1}}x)^3}\) is equal to

The value of \(\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}\) is

If \(f(x) = \left\{ {\matrix{ {a{x^2} + 1,} & {x \le 1} \cr {{x^2} + ax + b,} & {x > 1} \cr } } \right.\) is differentiable at x = 1, then

The linear programming problem minimize z = 3x + 2y subject to constrains x + y \(\ge\) 8, 3x + 5y \(\ge\) 15, x \(\ge\) 0 and y \(\ge\) 0, has

If log7 5 = a, log5 3 = b and log3 2 = c, then the logarithm of the number 70 to the base 225 is

Which of the following is always true?

If p\(\ne\) q \(\ne\) r and \(\left| {\matrix{ 0 & {x - p} & {x - q} \cr {x + p} & 0 & {x - r} \cr {x + q} & {x - r} & 0 \cr } } \right| = 0\), then the value of x which satisfy the equation is

Matrix \(A = \left| {\matrix{ x & 3 & 2 \cr 1 & y & 4 \cr 2 & 2 & z \cr } } \right|\), if xyz = 60 and 8x + 4y + 3z = 20, then A(adj A) is equal to

The origin is shifted to (1, 2). The equation y2 \(-\) 8x \(-\) 4y + 12 = 0 changes to y2 = 4ax, then a is equal to

The maximum number of points of intersection of 10 circles is :

Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings?

If A and B are two independent events such that \(P(A) = {1 \over 2}\) and \(P(B) = {1 \over 5}\), then which of the following is correct?

Box I contains 5 red and 2 blue balls, while box II contains 2 red and 6 blue balls. A fair coin is tossed. If it turns up head, a ball is drawn from box I, else a ball is drawn from box II. The probability ball drawn is from box I, if it i...

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30\(^\circ\) to 60\(^\circ\) is :

If a\(\in\)R, b\(\in\)R, then the equation x2 \(-\) abx \(-\) a2 = 0 has

The solution of the inequality \({4^{ - x + 0.5}} - {7.2^{ - x}} < 4\), x \(\in\)R is

If a + 2b + 3c = 12, (a, b, c \(\in\)R+), then the maximum value of ab2c3 is

Sum of n terms of the infinite series
1.32 + 2.52 + 3.72 + ..... \(\infty\) is

Which of the following is not an equivalence relation in z?

For a random variable X, E(X) = 3 and E(X2) = 11. The variable of X is :

The sum of 10 items is 12 and the sum of their squares is 18, then the standard deviation will be

The runs of two players for 10 innings each are as follows

The more consistent player is

The equations of the bisector of the angles between the straight lines 3x + 4y + 7 = 0 and 12x + 5y \(-\) 8 = 0 are :

Angle between the diagonals of a cube is

Consider the two lines
\({L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}\) and \({L_2}:{{x - 2} \over 1} = {{y + 2} \over 2} = {{z - 3} \over 3}\)
The unit vector perpendicular to both the lines L1 and L2 is

The distance between the line \(r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda (\widehat i - \widehat j + 4\widehat k)\) and the plane \(a\,.\,(\widehat i + 5\widehat j + \widehat k) = 5\) is

If \({\cos ^3}x\,.\,\sin 2x = \sum\limits_{m = 1}^n {{a_m}\sin mx}\) is identity in x, then

Total number of solutions of \(\left| {\cot x} \right| = \cot x + {1 \over {\sin x}},x \in [0,3\pi ]\) is equal to

The points with position vectors \(10\widehat i + 3\widehat j\), \(12\widehat i - 5\widehat j\) and \(a\widehat i + 11\widehat j\) are collinear, if a is

Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), then the value of (a + b + c) is

For non-zero vectors a, b, c; |(a \(\times\) b) . c| = |a| |b| |c| holds if and only if