List of practice Questions

Let N be the foot of perpendicular from the point P (1, –2, 3) on the line passing through the points (4, 5, 8) and (1, –7, 5). Then the distance of N from the plane 2x – 2y + z + 5 = 0 is

Let the centre of a circle C be (α, β) and its radius r < 8. Let 3x + 4y = 24 and 3x – 4y = 32 be two tangents and 4x + 3y =1 be a normal to C. Then (α – β + r) is equal to

A child of mass 5 kg is going round a merry-goround that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

Identify $X , Y$ and $Z$ in the following reaction (Equation not balanced) $ClO + NO _2 \rightarrow \underline{ X } \stackrel{ H _2 O }{\longrightarrow} \underline{ Y }+\underline{Z}$

The random valuable X follows binomial distribution B (n, p) for which the difference of the mean and the variance is 1. If 2P(X = 2) = 3P(X = 1), then n²P(X > 1) is equal to

Which one of the following statements is correct for electrolysis of brine solution?

The value of $\frac{e^{-\frac{\pi}{4}}+\int^{\frac{\pi}{4}}_{0}e^{-x}\tan^{50}x\ dx}{\int^{\frac{\pi}{4}}_{0}e^{-x}(\tan^{49}x+\tan^{51}x)dx}$ is

As shown in the figure, a particle is moving with constant speed π m/s. Considering its motion from A to B, the magnitude of the average velocity is

Let$ |\vec{a}|=2, |\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{π}{4}$. Then $|(\vec{a}+2\vec{b})×(2\vec{a}-3\vec{b})|^2$ is equal to

A protein ' $X$ ' with molecular weight of $70,000 u$, on hydrolysis gives amino acids One of these amino acid is

A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and lm mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the estimation of focal length is

Let $S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}$. Then $\sum\limits_{z∈S}|z|^2$ is equal to

The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to

If the system of equations
2x + y - z = 5
2x -5y + λz = μ
x + 2y - 5z = 7
has infinitely many solutions, then (λ + μ)² + (λ - μ)²is equal to

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be $\frac{1}{9}$ .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

The methods NOT involved in concentration of ore are
A Liquation
B Leaching
C Electrolysis
D Hydraulic washing
E Froth floatation
Choose the correct answer from the options given below :

Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar?

Let for A = $\begin{bmatrix} 1 & 2 & 3 \\ \alpha & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix}$, |A| = 2. If |2adj (2adj (2A))| = 32ⁿ , then 3n + α is equal to

Let for a triangle ABC,
$\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} $
$\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} $
$\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} $
If $δ>0$ and the area of the triangle ABC is $5\sqrt6$, then $\vec{CB}.\vec{CA}$ is equal to

The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parellel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point

The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$ is

The correct order of basicity of oxides of vanadium is

If $\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17$ ,then 5a² + b² is equal to

The area of the region $\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}$ is

A network of four resistances is connected to 9V battery, as shown in figure. The magnitude of voltage difference between the points A and B is ______V.