List of practice Questions

Which of the following is not a natural polymer?

If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky – 5z = 1 and 3kx – ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

If the circle
x2+y2-2gx+6y-19c = 0,g,c∈R
passes through the point (6, 1) and its centre lies on the line x – 2cy = 8, then the length of intercept made by the circle on x-axis is

Compound ‘A’ undergoes following sequence of reactions to give compound ‘B’. The correct structure and chirality of compound ‘B’ is
[where Et is –C2H5]
sequence of reactions to give compound
The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is 
Let the solution curve \(y = y(x)\) of the differential equation \((1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1\) pass through the point \((0, \frac{\pi}{2})\). Then, \(\lim_{{x \to \infty}} e^x y(x)\) is equal to
The number of elements in the set S= {x∈R : 2cos⁡\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}
If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :
A metal wire of length 0.5 m and cross-sectional area 10–4 m2 has breaking stress 5 × 108 Nm–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms–1
The statement (p∧q) ⇒ (p∧r) is equivalent to :
Given below are two statements.
Statement-I: Stannane is an example of a molecular hydride.
Statement-II: Stannane is a planar molecule
In the light of the above statement, choose the most appropriate answer from the options given below.
In liquation process used for tin (Sn), the metal
When ethanol is heated with conc. H2SO4, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is
Let 
\(\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}\)
Then which of the following statements are true? 
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f 
R : f ′ is increasing for x > √2
Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?
Let \(\vec{a} = 3\hat{i} + \hat{j}\) and \(\vec{b} = \hat{i} + 2\hat{j} + \hat{k}\).
Let \(\vec{c}\) be a vector satisfying \(\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}\)
If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(λ\) is
Which of the following compounds is an example of hypnotic drug?
Two identical thin metal plates has charge q1 and q2 respectively such that q1 > q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is
A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.
The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10–4 N. The value of x is _______. [use g = 10 m/s2]
A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.
The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is \(\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)\)
If the distance of the point B from the tower is 15 units, then cot α is equal to :

Let a1, a2, a3,…. be an A.P. If
\(\begin{array}{l} \displaystyle\sum\limits_{r=1}^\infty\frac{a_r}{2^r}=4,\end{array}\)
then 4a2 is equal to ________.

\(\sum_{r=1}^{20}\)(r2+1)(r!) is equal to
Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of (\(\frac{\sqrt{24}+1}{\sqrt{34}}\))n, in the increasing powers of 134 be 64:1.If the sixth term from the beginning is \(\frac{\alpha}{\sqrt{34}}\), then α is equal to ___________.