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Practice Online Test Series for JEE Main 2018 & NEET 2018
Solution of `(x^2-2x^3y^3)dy=(3x^2y^4+2xy) dx` is
If A is the area given by `y>=e^(-x^2), x=1` and `y=1`, in the first quadrant then which is incorrect
If `int sqrt(cosec x) sqrt(sec^7x)dx= A sqrttan x + Bsqrt((f(x))^5)+C`; then; which is incorrect
If `alpha=|(int_0^(pi/2)(x cosx+1)e^(sinx)dx)/(int_0^(pi/2)(x sinx-1)e^(cosx)dx)|`,then `[alpha]=` (where [.] represents greatest integer function)
Let f(x) be a function satisfying `f(x) =f (100/x), AAx>0`, If `int_1^10(f(x))/xdx=5`, then value of `int_1^100(f(x))/xdx`
A, B, C, D are consecutive vertices of a rectangle, whose area is 6 and length of diagonal is `sqrt 13`. Area of ellipse passes through A and C and has foci at B and D is
If F(1,4) be a focus of a parabola and R(0,5) and S(3,5) be the point of intersection of tangents and perpendiculars drawn from F to same tangents at P & Q on the parabola respectively, then coordinate of P is
P is a point, whose distance from point (2, 0) and perpendicular distance from line `2x+alphay-4=0 (alpha in R)` are equal, the locus of P is
A line parallel to y-axis, cuts the circle `x^2+y^2=a^2` and parabola `y^2=-4a(x-a), a>0` at points P and Q respectively, in the first quadrant. If the locus of the middle point of P and Q is `y=sqrt(a(a-x)) +k/4sqrt(a^2-x^2)`, then value of K is
If the line `x+y=3` touches a hyperbola at (2,1) and intersects its asymptotes at A and B such that `AB=8sqrt2`, if hyperbola is centred at origin, then combined equation of asymptotes is
Let `x+alphay-1=0`, `alpha in R` be a variable chord of parabola `y^2=4x`. Which cuts the parabola at A and B. If normal at A and B meet at C, then locus of C may be
If `cot^(-1)((n^2-10n+21.6)/pi) > pi/6, n in N` then n can be
Two circles touching x-axis and the line `y-sqrt3x=0` intersects at two points and one of them is (1, 1), then other points is
If `sinA/sinB=sqrt3/2 and cosA/cosB =sqrt5/2`, `0<A,B<pi/2`, then `tan A +tan B` is equal to
The different equation whose general solution is given by, `y=(c_1 cos (x+c_2))- (c_3e^(-x+c_4))+ (c_5sin x)`, where `c_1, c_2, c_3, c_4, c_5` are arbitrary constants is
If A, B, C are three points on the hyperbola `xy=c^2` such that `/_ACB=90^o` and the tangent at C to `xy=c^2` is parallel to `x+3y+5=0`, then the slope of the chord joining AB
The area of the region containing the points satisfying `|y| +1/2<=e^(-|x|)` and max `(|x|, |y|) <= 2.` Is
If `x in [-1, 0)` then `cos^-1 (2x^2-1)-2 sin^-1 x=`
If `int ((x-1)(x-2)(x-3))/((x-4)(x-5)(x-6)) dx=ax+ b log|x-4|+ c log|x-5|+ d log |x-6| + e` then value of `a+b+c+d`
OA is the perpendicular drawn from center O of the ellipse `x^2/a^2+y^2/b^2=1`, to the tangent at any point P on the ellipse. If the normal drawn to the ellipse at the point P meets the x-axis at B, then (OA).(PB) is equal to
