Question 1 :
The tangent to the curve y = 2x² - x + 1 is parallel to the line y = 3x + 9 at the point whose co-ordinates are :

Question 2 :
If f(x) = p | sin x| + qe^|x| + r|x|³ and if f(x) is differentiable at x = 0, then

Question 3 :
P is a variable point on the curve y = f (x) and A is a fixed point in the plane not lying on the curve. If PA² is minimum, then the angle between PA and the tangent at P is-

Question 4 :
If f (x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e74bed5f511820358e68e7e' height='23' width='64' >, then f ' (x) is equals to -

Question 5 :
The function f(x) = 1+x(sin x) [cos x], 0 < x &le;&pi;/2 & [.] = G.I.F

Question 6 :
The value of c of the mean value theorem, If f(x) = x(x - 1) (x - 2) ; a = 0, b = 1/2 is :

Question 7 :
Let f : R &rarr; R be a function satisfying f(x + y) = f(x) + &lambda;xy + 3x²y² for all x, y &isin; R. If f(3) = 4 and f(5) = 52 then f ' (x) is equal to -

Question 8 :
If the equation a_nxⁿ + a_n-1x^n-1 + ..... + a₁x = 0 ; a₁&ne; 0, n &ge; 2, has a positive root x = &alpha;, then the equation na_nx^n-1+(n-1)a_n-1 x^n-2 + ...+a₁ = 0 has a positive root, which is -

Question 9 :
The normal to the curve x = a(1 + cos &theta;), y = a sin &theta; at '&theta;' point always passes through the fixed point -

Question 10 :
The value of a for which the function f(x) = sin x - cosx -ax + b decreases for all real values of x is given by

Question 11 :
The equation x³- 3x + [a] = 0, where [.] denotes the greatest integer function, will have real and distinct roots if

Question 12 :
The function f(x) = 1 + x sin x[cos x], 0 < x &le;/2, [&sdot;] = G.I.F.

Question 13 :
If for a function f, |f(x) - f(y)| &le; (x - y)² " x, y &isin; R, then f is -

Question 14 :
Let f(x) be a polyomial in x. Then the second order derivative of f(e^x), is -

Question 15 :
The number of critical points of f (x) = max (sin x, cos x) for x &isin; (0, 2&pi;)

Question 16 :
Let x &isin;<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e74bfab023ac44295581bd5' height='41' width='41' >, f(x) = x tan(sin x), g(x) = xsin(tanx) and h(x) = sinx tanx. Which one is greatest ?

Question 17 :
Let f(x) be a polynomial of degree 3 such that f(3) = 1, f &prime;(3) = -1. f &prime;&prime;(3) = 0 and f &prime;&prime;&prime;(3) =12. Then the value of f &prime;(1) is-

Question 18 :
In (-4, 4) the function f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e74c03cf511820358e69038' height='49' width='56' >e^-4t dt has -

Question 19 :
If y = x - x², then the derivative of y² w.r.t. x² is-

Question 20 :
The value of the function f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e74c02df511820358e69026' height='49' width='176' > is minimum at -