List of practice Questions

Find the distance between the points $P(1, -3, 4)$ and $Q (-4,1,2)$.
Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.
Find the degree measure of the angle subtended at the centre of a circle of radius $100 \,cm$ by an arc of length $22 \,cm$ as shown in figure. [Use $\pi=\frac{22}{7}$]
Find the derivative of $\frac{cos\,x}{1+sin\,x}$.
Find the $C.V.$ of the following data :
Find the circular measure of the following angle $75^{\circ}$
Find the coordinates of the points which trisect the line segment $AB$ where $A(2,1, -3)$ and $B(5, -8,3)$.
Find the angle in radian through which a pendulum swings and its length is $75\, cm$ and tip describes an arc of length $21 \,cm$.
Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.
Find the area of the largest isosceles triangle having perimeter $18$ metres.
Find perpendicular distance of the line joining the points $(cos \,\theta, sin \,\theta)$ and $(cos\, \phi, sin \,\phi)$ from the origin.
Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2\%$.
Find corresponding velocity-time graph for given displacement time graph
Find maximum height upto which v will move on inclined plane. All surfaces are smooth
Find out the incorrect match.
Filtration slits are formed by
Find all the points of local maxima and local minima of the function $f(x) = (x - 1)^3 (x + 1)^2$
Fill in the blanks. (i) The standard deviation of a data is of any change in origin, Put is on the change of scale. (ii) The sum of squares of the deviations of the values of the variable is when taken about their arithmetic mean. (iii) The mean deviation of the data is when measured from the median. (iv) The standard deviation is to the mean deviation taken from the arithmetic mean.
Fill up the blanks by selecting the correct option (i) Biogas is a mixture of gases which predominantly contains________ and is used a s ________ (ii) Methanogens are commonly found in the_______during sewage treatment (iii) _______ species are free-living fungi and effective biocontrol agents of several plant pathogens
Fill up the blanks in the following paragraph by selecting the correct option. $(i)$ are the primary female sex organs that produce $(ii)$ and $(iii)$. Each primary sex organ is about $(iv)$. in length and is connected to the pelvic wall and uterus by $(v)$.
Fill in the blanks $ (i)$ In a $LPP$, the objective function is always $(ii)$ The feasible region for a $LPP$ is always a polygon. $(iii)$ A feasible region of a system of linear inequalities is said to be , if it can be enclosed within a circle. $(iv)$ In a $LPP$, if the objective function $Z = ax + by$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same value.
Fill in the blanks. (i) The length of the latus rectum of the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$ is . (ii) The equations of the hyperbola with vertices $\left(\pm 2, 0\right)$, foci $ \left(\pm3, 0\right)$ is . (iii) If the distance between the foci of a hyperbola is $16$ and its eccentricity is $2$, then equation of the hyperbola is .
Fill in the blanks. (i) The number of different words that can be formed from the letters of the word such that two vowels never come together is . (ii) Three balls are drawn from a bag containing $5$ red, $4$ white and $3$ black balls. The number of ways in which this can be done if atleast $2$ are red is . (iii) The total number of ways in which six $'+'$ and four $'-'$ signs can be arranged in a line such that no two signs $'-'$ occur together, is .
Figure shows $(x, t), (y, t)$ diagram of a particle moving in 2-dimensions.
If the particle has a mass of 500 g, the force acting on the particle is
Figure shows a man of mass $55\, kg$ standing stationary with respect to a horizontal conveyor belt that is accelerating with $1\,m$ $s^{-2}$. The net force acting on the man is