List of practice Questions

If ‘n’ and ‘a’ are positive integers such that nn = 3324 and n3 + 3n is an integral multiple of 3a, then find the largest possible value of a.
A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.
In the figure below, AB and AC are two tangents of the circle from the same external point A touching at points B and C, respectively. If ∠BAC = 2z° and ∠BDC = 5z°, then find the value of ∠BOC + ∠BAC in degrees.
AB and AC are two tangents of the circle from the same external point A
The correct order of ionisation enthalpy for Li, Na, Cl, F is:
The letter ?$D$? in $D$-carbohydrates represents
Complexes formed in the cyanide process are:
A solution of colourless unknown salt (X) on boiling with excess of NaOH produces non-flammable gas. The gas evolution ceases after some time. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt (X) is (are)
If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to
Which of the drawings (a) to (d) show : 
\((a)\)

\((b)\)

\((c)\)

\((d)\)

(i) 2 × \(\frac{1}{5}\)
(ii) 2 × \(\frac{1}{2}\)
(iii) 3 × \(\frac{2}{3}\)
(iv) 3 × \(\frac{1}{4}\)
The vapour pressure of water at room temperature is 23.8 mm Hg. The vapour pressure of an aqueous solution of sucrose with mole fraction 0.1 is equal to
The area of the region bounded by the curve y=x2 and the line y=16 is:
The solution of the differential equation dydx=sec⁡(yx)+yx is:
Order of [274310][543] is:
Find z1z2, when z1=6+2i and z2=2−i.
If $ {{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z, $ then modulus of the complex number $z$ is equal to
The minute hand of a clock is 10 cm long. How far does the tip of the hand move in 20 minutes
If B is the mid-point of AC and C is the mid-point of BD, where A, B, C, D lie on a straight line, say why AB = CD?
A small aperture is illuminated with a parallel beam of $\lambda$ = 628nm . The emergent beam has an angular divergence of 2$^\circ$ . The size of the aperture is.
The longest wavelength in Ao in the Balmer series of singly ionised helium ion, He+ is
∫02[x2]dx∣ is equal to

Indicate the steps in the preparation of: 

  1.  K2Cr2O7 from chromite ore. 
  2.  KMnO4 from pyrolusite ore.
Fill in the blanks:
  1. Burning of wood and coal causes ___ of air.
  2. A liquid fuel, used in homes is ___.
  3. Fuel must be heated to its ___   ___ before it starts burning.
  4. Fire produced by oil cannot be controlled by ___.
Which additives are used for the purpose of restoring nutrients lost or degraded during production?
The middleman between blood and tissues is:
Absence of oxygen in earth, made the atmosphere reducing. But it later became oxidizing in nature due to the emergence of ________.