List of practice Questions

Assertion (A): 16th group elements have higher ionization enthalpy values than 15th group elements in the corresponding periods.
Reason (R): 15th group elements have half-filled stable electronic configuration.
If $ AX = D $ represents the system of simultaneous linear equations: $$ \begin{aligned} x + y + z &= 6 \\ 5x - y + 2z &= 3 \\ 2x + y - z &= -5 \end{aligned} $$ Then compute: $ (\text{Adj } A) D $
In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is
If the equation of the tangent to the circle \(x^2+y^2=a^2\) at \(P(x_1, y_1)\) is \(x x_1 + y y_1 = K\), then K =
The normal to the curve y = f(x) at the points (3, 4) makes an angle \( \frac{3\pi}{4} \) with positive x-axis then \(f'(3) = \)
Arrange the following species in the decreasing order of their bond orders. NO \quad NO$^+$ \quad NO$^-$ (I) \quad (II) \quad (III)
If \( b \) and \( c \) are non-zero real numbers, and \[ A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}, \] then \( \det(A + B) = \) ?
A body cools down from \(75^\circ C\) to \(65^\circ C\) in 10 minutes. It will cool down from \(65^\circ C\) to \(55^\circ C\) in a time
Consider a disc of radius \( R \) and mass \( M \). A hole of radius \( \frac{R}{3} \) is created in the disk such that the center of the hole is \( \frac{R}{3} \) away from the center of the disc. The moment of inertia of the remaining system about the axis perpendicular to the disc and passing through the original center is:
The number of radial nodes and angular nodes in a 4f orbital are respectively:
Evaluate \( \int_{-\pi}^{\pi} \frac{\cos^{2022}x}{1 + (2022)^x} \, dx \).
If \( \frac{a}{a_1} = \frac{b}{b_1} \), then the substitution used to solve the differential equation \(\frac{dy}{dx} = \frac{ax + by + c}{a_1x + b_1y + c_1} \) using separation of variables is:
A reaction gas mixture contains 50%, 30%, 20% of A, B and C by volume respectively. The mixture undergoes the following reactions: \[ \text{(i) } A + 2B \rightarrow P_1 \\ \text{(ii) } 2P_1 + 3C \rightarrow P_2 \] Choose the correct answer if the reaction completes.
If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$
A natural number $n$ such that $n!$ ends in exactly 1000 zeros is
Suppose $P$ and $Q$ are the midpoints of the sides $AB$ and $BC$ of a triangle where $A(1, 3)$, $B(3, 7)$ and $C(7, 15)$ are vertices. Then the locus of $R$ satisfying $AC^2 + QR^2 = PR^2$ is
How many grams of Mg is required to completely reduce 100 mL, 0.1 M $\mathrm{NO}_3^-$ solution using the following reaction? $\mathrm{NO}_3^- + \mathrm{Mg} \to \mathrm{Mg}^{2+} + \mathrm{NH}_3$
In the reaction of phosphorous with conc. HNO3, the oxidized and reduced products respectively are
Three vectors of magnitudes $ a, 2a, 3a $ are along the diagonals of three adjacent faces of a cube that meet at a point. Find the magnitude of the sum of these vectors.
Let $ \vec{a}, \vec{b}, \vec{c} $ be unit vectors such that: - $ \vec{a} \perp \text{plane of } \vec{b}, \vec{c} $ - Angle between $ \vec{b} $ and $ \vec{c} $ is $ \frac{\pi}{3} $ Find: $$ |\vec{a} + \vec{b} + \vec{c}| $$
If two vectors $ \vec{A} $ and $ \vec{B} $ are mutually perpendicular, then the component of $ \vec{A} \cdot \vec{B} $ along the direction of $ \vec{A} + \vec{B} $ is
Identify the correct statements from the following: (a) Alkali metals are strong reducing agents. (b) KO$_2$ is a diamagnetic oxide. (c) Lithium chloride exists as LiCl . 2H$_2$O
The product formed in the given reaction is Phenylmagnesium bromide (C$_6$H$_5$-MgBr) reacting with D$_2$O, leading to product ?.
There are 4 hotels in a town. If 3 men check into the hotels in a day, what is the probability that each checks into a different hotel?
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), the locus of the point of intersection of the tangents at the endpoints of normal chords is: