List of practice Questions

If sumᵣ=0ⁿ+2ⁿCᵣ=2⁸-1, then n=
All the words that can be formed using alphabets A, H, L, U and R are written in a dictionary (no alphabet is repeated). Rank of the word RAHUL is
If the sum of odd numbered terms and even numbered terms in the expansion of (x+a)ⁿ are A and B respectively, then the value of (x²-a²)ⁿ is
The length of the chord x+y=3 intercepted by the circle x²+y²-2x-2y-2=0 is
The locus of the point of intersection of two tangents to the parabola y²=4ax, which are at right angle to one another is
The lengths of the tangent 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
Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]: I. f(x) is continuous 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
A ray of light coming from the point (1,2) is reflected at a point A on the x-axis and then passes through the point (5,3). The coordinates of the point A are
The equation x²-2√(3)xy+3y²-3x+3√(3)y-4=0 represents
The line joining (5,0) to (10cosθ,10sinθ) is divided internally in the ratio 2:3 at P. If θ varies, the locus of P is
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 exceeds 5, is
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0 endcases then f(x) is
The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x/4-sin²x/4)+(a-1)x is decreasing 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
(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 % Codes (A)(a)1453 (b)1354 (c)5423 (d)5324
What is the x-coordinate of the point on the curve f(x)=√(x)(7x-6), where the tangent is parallel to the x-axis?
Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ x+alpha₂ y=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then
If \( [x] \) denotes the greatest integer less than or equal to \( x \), and \( -1 < x < 0 < y < 1 < z < 2 \), then the value of the determinant

\( \begin{vmatrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{vmatrix} \)
is
If α,β are the roots of the equation x²-2x-1=0, then the value of α²β²+α-α²β² is
If a,b,c are real numbers then the roots of (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
The number of points at which the function f(x)=(1)/(log|x|) is discontinuous is
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one. Then the common difference of the progression is
If log a,log b,log c are in A.P. and also log a-log 2b,log 2b-log 3c,log 3c-log a are in A.P., then
If the matrix beginpmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endpmatrix is singular, then λ=