List of practice Questions

The distance of the point $(6,-2 \sqrt{2})$ from the common tangent $y=m x+c, m>$, of the curves $x=2 y^2$ and $x=1+y^2$ is :

The shortest distance between the lines $ x = y + 2 = 6z - 6 $ and $ x + 1 = 2y = -12z $ is:

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?

What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?

If equation of the plane that contains the point $(-2,3,5)$ and is perpendicular to each of the planes $ 2x + 4y + 5z = 8 $ and $ 3x - 2y + 3z = 5 $, is $ \alpha x + \beta y + \gamma z = 97 $, then $ \alpha + \beta + \gamma $ is:

Which of the following is material for deciding the jurisdiction of the Civil Court in the light of the Code of Civil Procedure, 1908?

The molar conductivities at infinite dilution for Na₂SO₄,K₂S0_4,KCl, HCl and HCOONa at 300K are 260, 308, 150, 426, and 105 S cm² mol^-1, respectively. What will be A⁺m for formic acid in the same unit?

A disc is rolling without slipping on a surface. The radius of the disc is $ R $. At $ t = 0 $, the topmost point on the disc is $ A $ as shown in the figure. When the disc completes half of its rotation, the displacement of point $ A $ from its initial position is:

What is biodiversity hotspot?

Minimise $z = 3x + 8y$ subject to: \[ 3x + 4y \geq 8, 5x + 2y \geq 11, x \geq 0,\; y \geq 0. \]

Let f(z) = u + iv be an analytic function, where u = x³-3xy² +3x² -3y², then the imaginary part v of f(z) is

Calculate the current flowing through two long parallel wires carrying equal currents and separated by a distance of 1.35 cm, experiencing a force per unit length of $ 4.76 \times 10^{-2} \, \text{N/m} $.

The ratio of wavelengths of proton and deuteron accelerated by potential $V_p$ and $V_d$ is $1: \sqrt{2}$ Then, the ratio of $V_p$ to $V_d$ will be

From the figure of column chromatography given below, identify incorrect statements

A. Compound 'c' is more polar than 'a' and 'b'
B. Compound 'a' is least polar
C. Compound 'b' comes out of the column before 'c' and after 'a'
D. Compound 'a' spends more time in the column
Choose the correct answer from the options given below

Compound A from the following reaction sequence is

Br2 , C S 2 0 − 5 ° C 0 − 5 ° 𝐶 → 𝐵 𝑟 2 , 𝐶 𝑆 2 B. N a N O 2 / H C l

Let a tangent to the curve $y^2=24 x$ meet the curve $x y=2$ at the points $A$ and $B$ Then the mid points of such line segments $A B$ lie on a parabola with the

If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______

If $m$ and $n$ respectively are the numbers of positive and negative values of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{99}{2}$, then $m n$ is equal to__

Two billiard balls of mass $005\, kg$ each moving in opposite directions with $10 \, ms ^{-1}$ collide and rebound with the same speed If the time duration of contact is $t =0005 \, s$, then what is the force exerted on the ball due to each other?

Major product of the following reaction is

Let $f(x)=\begin{cases}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\ 0 & , x=0\end{cases}$Then at $x=0$

Match the terms in Column-I with their description in Column-II and choose the correct option:

Column I (Chemical reactions)		Column II (Enzymes used)
(i)	Glucose → CO₂+ Ethanol	a	Pepsin
(ii)	Sucrose→Glucose + Fructose	b	Diastase
(iii)	Starch →Maltose	c	Zymase
(iv)	Protein→Amino acids	d	Invertase

If f(x) = [a+13 sinx] & x ε (0, $\pi$), then number of non-differentiable points of f(x) are [where 'a' is integer]

A solid sphere and a ring have equal masses and equal radius of gyration. If the sphere is rotating about its diameter and ring about an axis passing through and perpendicular to its plane, then the ratio of radius is $\sqrt{\frac{x}{2} }$ then find the value of x.

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] is