List of practice Questions

If $\frac{x^{4} + 24 x^{2} + 28}{\left(x^{2} + 1\right)^{3}} = \frac{A }{\left(x^{2} + 1\right)} + \frac{B}{\left(x^{2} + 1\right)^{2}} + \frac{C}{\left(x^{2} + 1\right)^{3}} $ then $A + C = $
If osmotic pressure of 4% (w/v) solution of sucrose is same as 2% (w/v) solution of 'X' find molecular mass of X.
The maximum area of a rectangle inscribed in the circle $(x + 1)^2 + (y - 3)^2 = 64$ is
A straight line through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is:
Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :
For $1$ molal aqueous solution of the following compounds, which one will show the highest freezing point ?
The mass of a non-volatile, non-electrolyte solute (molar mass $= 50\, g\, mol^{-1}$) needed to be dissolved in $114\, g$ octane to reduce its vapour pressure to $75\%,$ is :
The trans-alkenes are formed by the reduction of alkynes with :
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12} / \sec$. What is the force constant of the bonds connecting one atom with the other ? ( Mole wt. of silver $= 108 $ and Avogadro number $= 6.02 \times 10^{23} \, gm \, mole^{-1} $ )
Given that, for the reaction,
\(\frac 12H_2+\frac 12Cl_2→HCl\)
△Hf (HCI) = -93 kJ/mol, B.E(H2) = 434 kJ/mol, B.E(Cl2) = 242 kJ/mol
The bond dissociation energy of HCl is
Who is leading the LTTE delegation for the peace process with Sri Lanka?
Who was the first UN Secretary General?
Which of the following sources yields the maximum revenue to the Union Government?
April 22 is observed every year as_____ 
The island of Perejil was recently in dispute between_____ 
What are the individual prices of three cameras?
I. The three cameras have an average price of $172.
II. Two are identical and sold for $332 together.
the following question consists of a question and two statements I and II
What is the numerical value of the ratio n/m ?
I. mn = 14
II. m = 6n
the following question consists of a question and two statements I and II
What is the area of a regular hexagon?
I. The length of one of the boundary lines of the hexagon is 36 cm.
II. The area of the hexagon is 6 times the area of an equilateral triangle formed on one of the sides.
the following question consists of a question and two statements I and II
What is the highest power of 5 that can completely divide n!
I. Precisely 2 integers between 1 and n, both inclusively are multiples of 50.
II. \(n < 200\)
the following question consists of a question and two statements I and II
Mr. Dhingra earns Rs. 8, 000 per month by working as a visiting lecturer in various colleges. What is his annual income?
I. During his entire free time, he gives free coaching to deserving students.
II. 40 students attend his free sessions.
the following question consists of a question and two statements I and II
A positive number is exactly divisible by both 3 and 7. What is that number?
I. It is greater than 20.
II. It is less than 25.
the following question consists of a question and two statements I and II
A radio is normally sold at a profit of 15%. At the annual sale, it is offered at a discount of 5%. What is its cost price?
I. The selling price after discount amounts to Rs. 150.
II. The discount given is Rs. 30.
the following question consists of a question and two statements I and II
A room 20 m x 10 m is to be painted. What will be the total cost?
I. The height of the room is 3 m.
II. Costing will be done on a square metre basis.
the following question consists of a question and two statements I and II
A train leaves from Delhi at 8.00 a.m. and reaches Agra 11.30 a.m. What is its speed?
I. It crosses a 400 metre-long bridge in 40 seconds.
II. It crosses a railway platform 800 metres long in 64 seconds.
Which of the following correctly constitutes the three organs of the government?