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If the sum of first two terms of an infinite GP is 1 and every term is twice the sum of all the successive terms, then its first term is

If $f\left(x\right)=x^4+2,$ then which of the following denotes the equation of the tangent at $x=2$

The equation of tangent to the curve y = x³ + 2x + 6 which is perpendicular to the line x + 14y + 4 = 0 is :

Given ellipse $x^2+4y^2=16$ and parabola $y^2-4x-4=0.$

The quadratic equation whose roots are the slopes of the common tangents to the parabola and the ellipse, is

If $f\left(x\right)=|1-x|,$ then the number of points (excluding the boundary points if exist) where $g\left(x\right)={\sin }^{-1}\left(f\right(|x|\left)\right)$ is non-differentiable, is

In $\Delta ABC,$ if $a=(b-c)\sec \theta ,$ then $\frac{2\sqrt{bc}}{|b-c|}\sin \frac{A}{2}=$

Input: 86 open shut door 31 49 always 45

How many steps will be required to complete the rearrangement?

The five sentences (labelled 1, 2, 3, 4, 5) given in this question, when properly sequenced, fu, in a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer. ___

If sin $\alpha sin\beta cos\beta +1=0$, prove that 1 + cot $\alpha tan\beta =0$.

What will be the next number in the following sequence?



6, 12, 18, 24, 30, 36, __

If $(1,5,35),(7,5,5),(1,\lambda ,7)$ and $(2\lambda ,1,2)$ are coplanar, then the sum of all possible values of $\lambda$ is :

Find the angle between the line joining the points (2, 0), (0, 3) and the line $x+y=1$

Under what name does Tauqir operate?

For what values of x,
the numbers
are
in G.P?

If matrix $A$ is non-singular and satisfies $A^2-A+I=O,$ then the inverse of $A$ is equal to

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non coplanar vectors and a vector $\overrightarrow{\alpha }$ is such that $\overrightarrow{\alpha }=p(\overrightarrow{b}\times \overrightarrow{c})+q(\overrightarrow{c}\times \overrightarrow{a})+r(\overrightarrow{a}\times \overrightarrow{b})\text{and}\overrightarrow{\alpha }\cdot (\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})=1$ $,\text{then}\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$ is equal to

The value of the integral $\int \frac{\sin \theta .\sin 2\theta ({\sin }^6\theta +{\sin }^4\theta +{\sin }^2\theta )\sqrt{2{\sin }^4\theta +3{\sin }^2\theta +6}}{1-\cos 2\theta }d\theta$ is
$($where $c$ is a constant of integration$)$

Equation of the curve passing through $(2,1)$ which has constant sub-tangent of length $k$, is:

Give the proforma of a Bills Receivable Book.

If three six faced die each marked with numbers 1 to 6 on six faces, the thrown find the total number of possible outcomes.

The line y = x + 1 is a tangent to the curve y²
= 4x at the point

(A) (1,
2) (B) (2, 1) (C) (1, −2) (D) (−1, 2)

The value of $sin\left(co{t}^{-1}\right(cos\left(ta{n}^{-1}x\right)\left)\right)$ is equal to

The number of integral value(s) of $x$ satisfying $||x-\pi |-|\pi x-1||=(x-1)(1+\pi ),$ is

If the normal at P on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ cuts the major and minor axes in Q and R respectively then PQ:PR =

If $A=\{1,2,3\},B=\{4,5,6\},$ then $A\cup B=$

Let the line

$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$

lies in the plane $x+3y-\alpha z+\beta =0.$ Then $(\alpha ,\beta )$ equals

A function f(x) defined on [a,b] will have a local maximum at x = b if

[ h is a positive quantity tending to zero]