List of practice Questions

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.

Calculate the cardiac output of an individual having 70 heart beats/min with a stroke volume of 55 ml.

Identify the incorrect statement/s.
1. Kinetin is a derivative of Adenine which is a pyrimidine.
2. The technique of decapitation is widely used in tea plantations.
3. Ethylene is a gaseous plant hormone.
4. Use of GA₃ hastens the malting process in brewing industry.
5. ABA is a growth promoter.

Match the location of the cell given in Column I with its function in Column II.

Column I		Column II
1.	Mitochondrial matrix	p.	Kreb's cycle
2.	Cytoplasm	q.	ETC
3.	F0 and F1	r.	Glycolysis
4.	Inner mitochondrial membrane	s.	ATP synthesis

The enzyme that is not found in C₃ plants is

The correct statement regarding defects in solid is

The correct sequence of events in prophase I is

Match the compounds of Column I with their functions in Column II.

Column I		Column II
1.	Trypsin	p.	Fights infectious agents
2.	GLUT - 4	q.	Is an intercellular ground substance
3.	Collagen	r.	Works as an enzyme
4.	Antibody	s.	Enables glucose transport into cells

In Chrysoberyl, a compound containing Beryllium, Aluminium and oxygen, oxide ions form cubic close packed structure. Aluminium ions occupy \(\frac{1}{4}\)th of octahedral voids. The formula of the compound is