List of practice Questions

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 cannot exceed 5, is
The lengths of the tangents 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 of
The length of the chord x+y=3 intercepted by the circle x²+y²-2x-2y-2=0 is
Match List I with List II and select the correct answer using the code given below the lists. List I • [(A)] f(x)=cos x • [(B)] f(x)=ln x • [(C)] f(x)=x²-5x+4.3 • [(D)] f(x)=eˣ List II • [1.] The graph cuts y-axis in infinite number of points • [2.] The graph cuts x-axis in two points • [3.] The graph cuts y-axis in only one point • [4.] The graph cuts x-axis in only one point • [5.] The graph cuts x-axis in infinite number of points
What is the x-coordinate of the point on the curve f(x)=√(x)(7x-6), where the tangent is parallel to x-axis?
A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90^∘. What is the maximum area which can be enclosed inside the quadrilateral?
Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]. I. f(x) is increasing in [-1,1] II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?
At an extreme point of a function f(x), the tangent to the curve is
The curve y=xeˣ has minimum value equal to
If a,b,c are real numbers then the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
Evaluate limₙtₒᵢₙfty(aⁿ+bⁿ)/(aⁿ-bⁿ), where a>b>1
The number of points at which the function f(x)=(1)/(log|x|) is discontinuous is
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x≠0
0, & x=0 endcases then f(x) is
For any differentiable function y of x, (d²x)/(dy²)((dy)/(dx))³+(d²y)/(dx²)=
The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x-4sin²x/4)+(a-1)x+sin x does not possess critical points is
Evaluate (x+\frac1x)²+(x²+\frac1x²)²+(x³+\frac1x³)² up to n terms is
If z₁=\sqrt3+i\sqrt3 and z₂=\sqrt3+i, then the complex number ((z₁)/(z₂))⁵0 lies in the
If the matrix beginbmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endbmatrix is singular, then λ=
Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ y+alpha₂ z=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then
If [x] denotes the greatest integer ≤ x and -1≤ x<0, 0≤ y<1, 1≤ z<2, then the value of the determinant beginvmatrix [x]+1 & [y] & [z]
[x] & [y]+1 & [z]
[x] & [y] & [z]+1 endvmatrix is
If α,β are the roots of x²-2x-1=0, then the value of α²β²-α²-β² is
In a △ ABC, if (cos A)/(a)=(cos B)/(b)=(cos C)/(c), and the side a=2, then area of the triangle is:
If sin⁻1((2a)/(1+a²)) -cos⁻1((1-b²)/(1+b²)) =tan⁻1((2x)/(1-x²)), then what is the value of x?
The arithmetic mean of numbers a,b,c,d,e is M. What is the value of (a-M)+(b-M)+(c-M)+(d-M)+(e-M)?
The fourth term of an A.P. is three times the first term and the seventh term exceeds twice the third term by one. Then the common difference of the progression is