List of practice Questions

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex (3, 4, 5). Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing through O or P is :

In the expansion of $(2^\frac{1}{4}+3^{-\frac{1}{4}})^n$, the ratio of $5^{th}$ term from start and $5^{th}$ term form end is $\sqrt 6 : 1$ , then find $3^{rd}$ term

Equivalent statement to (p$\to$q) $\vee$ (r$\to$q) will be

Let $A=$ [$a_{ij}$]$_{2\times2}$ be a matrix and $A^2 = I$ where $a_{ij} \neq0$. If a sum of diagonal elements and b=det(A), then $3a^2+4b^2$ is

Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.

If [x+6]+[x+3] ≤ 7 and let call its solution as set A and set B is the solution of inequality 3^5x-8 < 3^-3x.

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

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 circle passing through the point P$( \alpha , \beta )$ in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of $( \alpha \beta )$ is ___

The figure represents the momentum time (p-t) curve for a particle moving along an axis under the influence of the force Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ?If $\left(t_3-t_2\right) < t_1$

Given below are two statements :

Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable

Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed

In the light of the above statements, choose the correct answer from the options given below:

'$A$' in the given reaction is

A pair of dice is rolled 5 times. let getting a total of 5 in a single throw is considered as success. If probability of getting atleast four success is $\frac{x}{3}$ then x is equal to

$I(x) = \int \frac{x^2(xsec^2x + tanx)}{(xtanx+1)^2} dx$. If $I(0)=1$ then $I(\frac{\pi}{4})$ is equal to

If $a_1,a_2,.......a_n$ are in arithmetic progression with common difference $d>n$, then find limit $\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})$ is____.

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 weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

Out of 18g of glucose only 4.5 g is dissolved in water to obtain 40 mL of its aqueous solution. Find the molarity of this glucose solution

Which of the following is the correct statement?
A. The solubility of gases in liquids incresses with a decrease of pressure.
B. If the dissolution process is endothermic, the solubility should increase with a rise in temperature.
C. If the dissolution process is endothermic, the solubility should decrease with a rise in temperature.
D. If the dissolution process is exothermic, solubility will not change with a increase in temperature.
E. If the dissolution process is exothermic, solubility should increase with an increase in temperature.
Choose the correct answer from the options given below:

Choose the correct option on the basis of the following statements and conclusions.
Statement: Morning walks are good for health.
Conclusion I: All healthy people go for morning walks.
II: Evening walks are harmful.

10 resistors, each of resistance R are connected in series to a battery of emf E and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased n times. The value of n is:

If a copper wire carries a direct current, the magnetic field associated with the current would be:

A wire is bent as shown in figure is placed in a uniform field B that emerges from the plane of the paper, outward as shown. The magnitude of force on the given wire is :

Which one of the following cannot be polarised?

Two thin lenses of power +3D and -1D are held in contact with each other. Focal length of the combination would be: