List of practice Questions

Solution of the equation $x^2 dy + y (x + y) dx = 0$ is
For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
(b) – 100 is to the right of – 50 on a number line.
(c) Smallest negative integer is – 1.
(d) – 26 is greater than – 25.
A body sliding on a frictionless track which terminates in a straight horizontal section CD. The body starts slipping from A and reaches point D. If h1 = 1 m, then how far from point D, will the body hit the ground?Take, g = 10 ms-2.
One end of a cylindrical glass rod ($\mu$ = 1.5) is given the shape of a concave refracting surface of radius 10 cm. An air bubble is situated in the glass rod at.a .point on its axis such that it appears to be at distance 10 cm from the surface and inside glass when seen from the other medium. The actual location of air bubble is
Two particles $ A $ and $ B $ are projected with same speed so that the ratio of their maximum heights reached is $ 3:1 $ . If the speed of $ A $ is doubled without altering other parameters, the ratio of the horizontal ranges attained by $ A $ and $ B $ is
If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to
If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to
If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are
The domain and range of relation $R = \{ (x , y ) /x , y \in N , x + 2y = 5\}$ is
Let f : R $\rightarrow$ R be function defined by f(x) = sin (2x -3), then f is
Order of $\left(3x + 2y\right) \left(\frac{dy}{dx}\right)^{2} +5x \frac{d^{2}y}{dx^{2}} = 0 $ is
An electric charge $10^{-3} \mu C$ is placed at the origin $(0,0)$ of $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points $A$ and $B$ will be
The electron affinity of Be is almost similar to that of
By using the properties of definite integrals, evaluate the integral: \(∫_0^π log(1+cosx)dx\)
In the metal carbonyls of the general formula M(CO)x where M = metal x = 4, EAN rule is satisfied for atomic number of M equal to:
The circle x2+y2+4x−7y+12=0 cuts an intercept on y -axis of length
The derivative of sec-1 12x2-1 with respect to 1-x2 at x=12 is:
The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is:
If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
The number of terms of an AP is even. The sum of the odd terms is 24 and of the even terms is 30. The last term exceeds the first by 1012. Then the number of terms in the series is ______.
In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
Phenol on reduction with H2 in the presence of Ni catalyst gives:
Which substance is produced when alcohol is added with petrol and used as a fuel?
The shapes of the compounds XeF2, XeF4, XeO3 and XeO4 respectively are: