List of practice Questions

For a first-order reaction, the time required to reduce the concentration of the reactant to half its initial value is:
Find the area bounded between the parabola \( y^2 = 4x \) and the line \( y = 2x - 3 \).
The EAN of cobalt in the complex \([Co(NH_3)_6]^{3+\) is:}
The value of \[ \int_1^4 \log(\lfloor x \rfloor) \, dx \] where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \), is equal to:
A population \( P(t) \) of 1000 bacteria introduced to a nutrient medium grows according to the relation \[ P(t) = \frac{1000t + 1000t}{100 + t^2} \] The maximum size of this bacterial population is:
Let \[ f(x) = (\cos x + \sin x) \cdot \cos(3x + i \sin x) \cdot \left[ (2n - 1)x + i \sin((2n - 1)x) \right], \] where \( n \in \mathbb{N} \), and \( i = \sqrt{-1} \). Then: \[ f''(x) = \, ? \]
If \[ [2\vec{p} - 3\vec{q} \ \vec{q} \ \vec{s}] + [3\vec{p} + 2\vec{q} \ \vec{r} \ \vec{s}] = m[\vec{p} \ \vec{r} \ \vec{s}] + n[\vec{q} \ \vec{r} \ \vec{s}] + l[\vec{p} \ \vec{q} \ \vec{s}], \] then the values of \( m, n, l \) respectively are:
A box contains 9 tickets numbered from 1 to 9 inclusive. 3 tickets are drawn from the box one at a time. What is the probability that they are alternatively either (odd, even, odd) or (even, odd, even)?
A plane passes through the point \( (1, -2, 1) \) and is perpendicular to both the planes \[ 2x - 2y - 2z = 5 \quad \text{and} \quad x - y + 2z = 24 \] Then, the distance of the point \( (1, 2, 2) \) from this plane is:
An ellipse has \( OB \) as the semi-minor axis, and \( S \), \( S' \) as the foci. If \( \angle SBS' \) is a right angle, then the eccentricity \( e \) of the ellipse is:
In a triangle \( ABC \), with usual notation, if \[ \frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13} \] then the ratio \( \cos A : \cos B : \cos C \) is:
Smallest angle of a triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{54} \) is:
The ratio of areas bounded by curves \( y = \cos x \) and \( y = 0 \) between \( x = 0 \) to \( x = \frac{\pi}{3} \) and \( x = \frac{\pi}{3} \) to \( x = \frac{2\pi}{3} \), with the x-axis is:
Which institution declares ‘Domestic Systemically Important Banks (D-SIBs)’ in India?
The World Economic Forum (WEF) has chosen which city for establishing its Centre for the Fourth Industrial Revolution?
Which District in India has become the country’s first Constitution literate district?
National Cadet Corps (NCC) signed MoU with which institution to tackle the issue of plastic pollution?
As per Central Pollution Control Board (CPCB) data, which city was the most polluted place in India in 2022?
Which of the following teams has won Women’s Premier League (WPL) 2023 final?
Which country signed a deal with India to relocate dozens of Cheetahs?
Which country's population has dropped by 850,000, declining for the first time since the Great Famine of 1961?
Which country's first underground Air Force Base is Eagle 44 (Oghab 44)?
Which country has launched pilot project called ‘Welcome Corps’ for refugees?
Which of the following became the first Indian Union Territory to completely shift to e-governance mode?
US Food and Drug Administration (FDA) has approved ‘Lecanemab’ medication to treat which disease?