List of practice Questions

Domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-[x]-6}}\) where [x] is greatest integer ≤ x is

The function f(x) = \(\sqrt3\) sin2x - cos2x + 4 is one-one in the interval

Let A = { x : x ∈ R; x is not a positive integer } Define f : A → R as f(x) = \(\frac{2x}{x-1}\), then f is

f : R → R defined by f(x) = \(\left\{ \begin{aligned}     & 2x;x>3 \\     &x^2;1<x≤3\\     & 3x;x≤1 \end{aligned} \right.\) then f(-2) + f(3) + f(4) is

If P(A) = 0.59, P(B) = 0.30 and P(A ∩ B) = 0.21 then P( A' ∩ B') =

The Standard Deviation of the numbers 31, 32, 33……. 46, 47 is

If a and b are fixed non-zero constants, then the derivative of \(\frac{a}{x^4}-\frac{b}{x^2}\) + cos x is ma + nb - p where

Consider the following statements :
Statement 1 : \(\lim\limits_{x\rightarrow1}\frac{ax^2+bx+c}{cx^2+bx+a}\) is 1 (where a + b + c ≠ 0)
Statement 2 : \(\lim\limits_{x\rightarrow-2}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is \(\frac{1}{4}\)

The mid points of the sides of triangle are (1, 5, -1) (0, 4, -2) and (2, 3, 4) then centroid of the triangle

The equation of straight line which passes through the point (a cos³θ, a sin³θ) and perpendicular to x secθ+y cosecθ = a is

If the middle term of the A.P is 300 then the sum of its first 51 terms is

A student has to answer 10 questions, choosing at least 4 from each of the parts A and B. If there are 6 questions in part A and 7 in part B, then the number of ways can the student choose 10 questions is

The cost and revenue functions of a product are given by c(x) = 20x + 4000 and R(x) = 60x + 2000 respectively where x is the number of items produced and sold. The value of x to earn profit is

If \((\frac{1+i}{1-i})^x=1\) then

The value of tan 1° tan 2° tan 3° ………. tan 89° is

A pure compound contains 2.4g of C, 1.2 × 10²³ atoms of H, 0.2 moles of oxygen atoms. Its empirical formula is

The value of cos 1200° + tan 1485° is

Henry’s law constant for the solubility of N₂ gas in water at 298K is 1.0 × 10⁵ atm. The mole fraction of N₂ in air is 0.8. The number of moles of N₂ from air dissolved in 10 moles of water at 298K and 5 atm pressure is

Domain of f(x) = \(\frac{x}{|-|x|}\) is

A and B are non-singleton sets and n(A × B) = 35. If B ⊂ A then ^n(A)C_n(B) =

A metal crystallises in BCC lattice with unit cell edge length of 300 pm and density 6.15 g cm^-3. The molar mass of the metal is

In a certain two 65% families own cell phones, 15000 families own scooter and 15% families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

Match the hormones of Column I with its functions in Column II.

Column I		Column II
1.	Catecholamines	p.	Diurnal rhythm
2.	MSH	q.	Immune response
3.	Thymosins	r.	Pigmentation
4.	Melatonin	s.	Stress hormone

In a standard ECG, one of the following functions of its components is not correctly interpreted.