List of practice Questions

Let $f:(-\frac{\pi}{4}, \frac{\pi}{4}) \rightarrow R$ be defined as 

If f is continuous at $x=0$, then the value of $6a+b^2$ is equal to : 
 

Let $\alpha, \beta$ be two roots of the equation $x^2 + (20)^{1/4}x + (5)^{1/2} = 0$. Then $\alpha^8 + \beta^8$ is equal to :
Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to :

$PCl_5 \rightleftharpoons PCl_3 + Cl_2 K_c = 1.844$
3.0 moles of $PCl_5$ is introduced in a 1 L closed reaction vessel at 380 K. The number of moles of $PCl_5$ at equilibrium is _________ $\times 10^{-3}$. (Round off to the Nearest Integer)

Match List - I with List - II : 

Choose the most appropriate match : 
 

Match List - I with List - II : 

Choose the most appropriate answer from the options given 
 

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is : 

 

Choose the correct answer from the options given below : 

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (which is $\perp$ to the plane of the disc and passing through its centre) to MI of smaller disc around one of its diameters lying on its plane ? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia) 

 

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that $|\vec{AB}| = |\vec{BC}| = |\vec{CD}|$, then $\vec{AB} + \vec{AC} + \vec{AD} = 4\vec{AO} + \vec{OB} + \vec{OC}$ 
Reason R : Polygon law of vector addition yields $\vec{AB} + \vec{BC} + \vec{CD} = \vec{AD} = 2\vec{AO}$ 

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a << A) : 

 

The value of $\lim_{n \to \infty} \frac{1}{n}\sum_{j=1}^{n}\frac{(2j-1)+8n}{(2j-1)+4n}$ is equal to :
The value of the definite integral $\int_{-\pi/4}^{\pi/4} \frac{dx}{(1+e^{x\cos x})(\sin^4 x + \cos^4 x)}$ is equal to :
Let the domain of the function $f(x) = \log_4(\log_5(\log_3(18x-x^2-77)))$ be $(a, b)$. Then the value of the integral $\int_a^b \frac{\sin^3 x}{\sin^3 x + \sin^3(a+b-x)} dx$ is equal to _________.
If $\log_3 2, \log_3(2^x-5), \log_3(2^x-\frac{7}{2})$ are in an arithmetic progression, then the value of x is equal to _________.
If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $\frac{37}{4}$ respectively, then $(a-b)^2$ is equal to :
If $\sin\theta + \cos\theta = \frac{1}{2}$, then $16(\sin(2\theta) + \cos(4\theta) + \sin(6\theta))$ is equal to :
The compound statement $(P \lor Q) \land (\sim P) \Rightarrow Q$ is equivalent to :
Let $f:R \rightarrow R$ be a function such that $f(2)=4$ and $f'(2)=1$. Then, the value of $\lim_{x\to 2}\frac{x^2f(2) - 4f(x)}{x-2}$ is equal to :
If the area of the bounded region $R = \left\{(x, y) : \max\{0, \log_e x\} \le y \le 2^x, \frac{1}{2} \le x \le 2\right\}$ is, $\alpha(\log_e 2)^{-1} + \beta(\log_e 2) + \gamma$, then the value of $(\alpha + \beta - 2\gamma)^2$ is equal to :
Let C be the set of all complex numbers. Let $S_1 = \{z \in C : |z-3-2i|^2 = 8\}$, $S_2 = \{z \in C : \text{Re}(z) \ge 5\}$ and $S_3 = \{z \in C : |z - \bar{z}| \ge 8\}$. Then the number of elements in $S_1 \cap S_2 \cap S_3$ is equal to :
$CO_2$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of $CO_2$ adsorbed becomes 64 times when the pressure of $CO_2$ is doubled. The value of n in the Freundlich isotherm equation is _________ $\times 10^{-2}$. (Round off to the Nearest Integer)
The oxidation states of 'P' in $H_4P_2O_7$, $H_4P_2O_5$ and $H_4P_2O_6$, respectively, are :
Which one of the following statements is NOT correct ?