List of practice Questions

If
\[ \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \cdot A \cdot \begin{pmatrix} -3 & 2 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \]
then \(A\) is:
Let \[ f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2 \sin x & x^3 & 2x \\ \tan x & x & 1 \end{vmatrix}, \] then \[ \lim_{x \to 0} \frac{f(x)}{x^2} = ? \]
In \(\mathbb{R}\), a relation \(p\) is defined as follows: For \(a, b \in \mathbb{R}\), \(apb\) holds if \(a^2 - 4ab + 3b^2 = 0\).
Then:
Let \(f : \mathbb{R} \to \mathbb{R}\) be a function defined by \(f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}}\), then:
Let A be the set of even natural numbers that are<8 and B be the set of prime integers that are<7. The number of relations from A to B is:
If \((1 + x + x^2 + x^3)^5 = \sum_{k=0}^{15} a_k x^k\), then \(\sum_{k=0}^{7} (-1)^k \cdot a_{2k}\) is equal to:
If \(z_1\) and \(z_2\) be two roots of the equation \(z^2 + az + b = 0, \, a^2 < 4b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle if:
If \((x^2 \log x) \log_9 x = x + 4\), then the value of \(x\) is:
Let N be the number of quadratic equations with coefficients from {0,1,2,...,9} such that 0 is a solution of each equation. Then the value of N is:
Let \(y = f(x)\) be any curve on the X-Y plane and \(P\) be a point on the curve. Let \(C\) be a fixed point not on the curve. The length \(PC\) is either a maximum or a minimum. Then:
If a particle moves in a straight line according to the law \(x = a \sin(\sqrt{t} + b)\), then the particle will come to rest at two points whose distance is:
If for the series \(a_1, a_2, a_3, \ldots\), etc., \(a_{n+1} - a_n\) bears a constant ratio with \(a_n + a_{n+1}\), then \(a_1, a_2, a_3, \ldots\) are in:
The value of the surface integral
\(\displaystyle\oiint_{s}zdxdy\)
where S is the external surface of the sphere x2 + y2 + z2 = R2 is
An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30Β° with respect to horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m3 and 10 kN/m3, respectively.
The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is _____ (rounded off to the nearest integer).
The compound(s) which on reaction with CH3MgBr followed by treatment with aqueous NH4Cl would produce 1-methyl-1-phenylethanol as the major product is/are
The suitable synthetic route(s) for the following transformation
synthetic route(s)-transformation
is/are
B2 and C2, respectively, are
Zn–C bond polarity in the compounds below
Zn–C bond
follows the order
The number and nature of dβˆ’d transition(s) in the case of Sc2+ in an octahedral crystal field, respectively, are
[Ignore spin-orbit coupling and Jahn-Teller distortion.]
A system undergoes one clockwise cycle from point X back to point X as shown in the figure below:
clockwise cycle-point X back to point X
The correct statement about this process is
If nitrogen and oxygen gases are at the same temperature, the correct statement according to the kinetic theory of gases is
Consider photoelectric effect. The number of incident photons is the same for all frequencies. The plot that best describes the dependence of the number of photoelectrons (n) emitted as a function of the incident light frequency (Ξ½) is
In the cell reaction
P+(π‘Žπ‘ž)+Q(𝑠)β†’P(𝑠)+Q+(π‘Žπ‘ž) 
the EMF of the cell, 𝐸𝑐𝑒𝑙𝑙 is zero. The standard EMF of the cell, πΈπ‘œπ‘π‘’π‘™π‘™ is 
[Given: 
Activities of all solids are unity. 
Activity of P+(π‘Žπ‘ž) is 2 M. Activity of Q+(π‘Žπ‘ž) is 1 M. 
𝑅 = universal gas constant; 𝑇 = temperature; 𝐹 = Faraday constant]
The major product formed in the following reaction
Reaction-Br2 aq KOH
is
The major product formed in the following reaction
|HgSo4
is