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The equation of straight line passing through the point(a, b, c) and parallel to z- axis, is
[MP PET 1995; Pb. CET 2000]

To find the general solution of $si{n}^{-1}\left(\frac{dy}{dx}\right)=x+y$ using variable separable method, the substitution to be used is .

The lines joining the points of intersection of the curve $(x-h{)}^2+(y-k{)}^2-c^2=0$ and the line kx + hy = 2hk to the origin are perpendicular, then

If A is a matrix of order 3 and |A| = 8, then |Adj A| =

The condition on $a$ and $b$, such that the portion of the line $ax+by-1=0$, intercepted between the lines $ax+y=0$ and $x+by=0$, subtends a right angle at the origin is

If $x=e^{y+e^{y+e^{y+e^{y+\cdots \infty }}}}$

Identify the missing one.
Grandfather : Grandmother : : Father : ?

If a triangle is formed by any three tangents of the parabola $y^2=4ax$ whose two of its vertices lie on $x^2=4by$, then third vertex lie on

If the two equations $x^3+3p{x}^2+3qx+r=0$ and $x^2+2px+q=0$ have a common root, then the value of $4(p^2-q)(q^2-pr)$ is

The number of pairs of consecutive even natural numbers whose sum is less than $16$ is

The derivative of ${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=0$ is

A fan is rotating with angular velocity 100 $\frac{rev}{sec}$. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution made before it stops. (Assume uniform angular retardation) (ii)) Find the value of angular retardation (iii) Find the average angular velocity during this interval.

Ortho centre of the triangle whose vertices are (0,0), (3,0) and (4,0) is .....................

If a₁, a₂, a₃, . . . . . . , a_n . . . . . . .are in GP, then the value of the determinant

If x, y, z are different from zero and

then the value of the expression

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$ is .

Let $f\left(x\right)=\{\begin{array}{cc}ta{n}^{-1}x:& |x|\ge 1\\ \frac{x^2-1}{4}:& |x|<1.\end{array}$ Then domain of f'(x) is:

If $\alpha ,\beta$ are the roots of the equation $x^2-ax+b=0$ and roots of the eqaution $b{x}^2-4x+4=0$ are $\alpha +\frac{{\beta }^2}{\alpha }$ , $\beta +\frac{{\alpha }^2}{\beta }$ then$a+b$ can be -

The locus of the point of intersection of tangents to the parabola $y^2=4ax$ which includes an angle $\alpha$ is

${lim}_{x\to 1}\frac{x^2-\sqrt{x}}{\sqrt{x}-1}$

A car goes 5 km east, 3km south, 2km west and 1km north. The magnitude of the resultant displacement will be ___ km at an angle of $ta{n}^{-1}$(- / -) with the positive x-axis (where x axis is in the east direction) in the clock wise direction.

The negation of the statement $(p\wedge q)\to (\sim p\vee r)$ is

If the point of intersection of the lines $2px+3qy+r=0$ and $px–2qy–2r=0$ lies strictly in the fourth quadrant and is equidistant from the two axes, then

Identify the missing one.
Grandfather : Grandmother:: Father:?

If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is

For any two sets A and B , $A\cap (A\cup B)$ is equal to

By principle of mathematical Induction show that aⁿ​​​​​​-bⁿ is divisible by a+b when n is a positive integer.

The graph of the function $f\left(x\right)$ is shown in the figure

Then, which of the following is the graph of $g\left(x\right)=|f\left(|x|\right)|$?

If AD, BE and CF are the medians of a $△ABCthen(A{D}^2+B{E}^2+C{F}^2):(B{C}^2+C{A}^2+A{B}^2)$ is equal to

If a circle whose centre is (1,-3) touches the line 3x-4y-5=0, then the radius of the circle is

If $xϵR$, then $\frac{x^2-x+1}{x^2+x+1}$ takes values in the interval

${lim}_{x\to 0}\frac{3si{n}^{2}x-2sin{x}^2}{3x^2}$

Let $\overrightarrow{a},\overrightarrow{b},and\overrightarrow{c}$ be three unit vectors such that $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{\sqrt{3}}{2}(\overrightarrow{b}\times \overrightarrow{c}).If\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$, then the angle between $\overrightarrow{a}and\overrightarrow{b}$ is :

If $\alpha ,\beta$ are non real numbers satisfying $x^3-1=0$ then the value of $\left|\begin{array}{ccc}\lambda +1& \alpha & \beta \\ \alpha & \lambda +\beta & 1\\ \beta & 1& \lambda +\alpha \end{array}\right|$ is equal to

Choose the correct answer
The area bounded by the Y-axis, y = cos x and y = sin x, $0\le x\le \frac{\pi }{2}$ is
(a) $2(\sqrt{2}-1)$ (b) $\sqrt{2}-1$
(c) $\sqrt{2}+1$ (d) $\sqrt{2}$

There are $3$ coplanar (non-concurrent) lines $A,B$ and $C$, from these lines $10,12,11$ points are chosen respectively, such that no points other than points lying on the same line are collinear, then the total number of triangles that can be formed using these points are

The total number of terms in the expansion of $(x+a{)}^{47}-(x-a{)}^{47}$ after simplification is

In a self there are $2$ different physics books and $3$ different chemistry books. The number of ways in which a student can select a physics book or chemistry book is:

The interval(s) of $x$ which satisfies the inequality $\frac{1}{x+2}<\frac{1}{3x+7}$ is/are

The ordinates of the foot of normal(s) to the parabola $y^2=4ax$ from the point $(6a,0)$ is/are