List of practice Questions

$$ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0 $$

What is 'C' in the given sequence of reactions?

An $\alpha$-particle of energy \( E \) is liberated during the decay of a nucleus of mass number 236. The total energy released in this process is 236. The total energy released in this process is
RUBISCO CO acts as

Review: 
You have recently read a famous book/magazine. Write a Review on the same with the help of the following points: 
- title, front page, back page 
- language, features, contents 
- Pictures, quality, presentation 
- Values, vision and variety 
 

Which of the following vitamins are water soluble?
Gutta percha is:
Pyrolusite ore is:
The banana bond in diborane is constituted by:
Formic acid on heating with concentrated H\(_2\)SO\(_4\) gives:
The following amines is the product of Gabriel phthalimide synthesis:
Which type of linkage is present in nucleic acids?
Which is prepared by peptisation?
What percentage of animals are invertebrates?
Area of the triangle bounded by the lines given by the equations: \[ 12x^2 - 20xy + 7y^2 = 0 \quad \text{and} \quad x + y - 1 = 0 \]
If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and the points \[ \lambda \vec{a} + 3\vec{b} - \vec{c}, \quad \vec{a} - \lambda \vec{b} + 3\vec{c}, \quad 3\vec{a} + 4\vec{b} - \lambda \vec{c}, \quad \vec{a} - 6\vec{b} + 6\vec{c} \] are coplanar, then one of the values of \( \lambda \) is:
0.592 g of copper is deposited in 60 minutes by passing 0.5 amperes current through a solution of copper (II) sulphate. The electro chemical equivalent of copper (II) in g/C is:

The system of simultaneous linear equations : 

 

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that the first three tosses resulted in 2 or more heads, is:
The slope of one of the pair of lines \(2x^2 + hxy + 6y^2 = 0\) is three times the slope of the other line, \(h = ?\)
If the quadratic equation \( 3x^2 + (2k + 1)x - 5k = 0 \) has real and equal roots, then the value of \( k \) such that \( -\frac{1}{2}<k<0 \) is:
Convex mirror is used as
The position vector of the point of intersection of the line joining the points \( \mathbf{i} - \mathbf{j} + \mathbf{k} \) and the line joining the points \( 2\mathbf{i} + \mathbf{j} - 6\mathbf{k} \), \( 3\mathbf{i} - \mathbf{j} - 7\mathbf{k} \) is:
P and Q are the points of trisection of the line segment AB. If the position vectors of A and B are \( 2\hat{i} - 5\hat{j} + 3\hat{k} \) and \( 4\hat{i} + \hat{j} - 6\hat{k} \) respectively, then the position vector of the point that divides PQ in the ratio 2:3 is:
The equation of the pair of transverse common tangents drawn to the circles \( x^2 + y^2 + 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is: