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What is the sign of the sec θ and cosec θ in second quadrant respectively?

Which statement is true for the sentence?
The expert said that either method can be used to solve these problems.

The probability that a non leap year selected at random will have $53$ Sundays is

The middle term in the expansion of ${(ax-\frac{b}{x^2})}^{12}$ is:

The number of solutions of the equations $z^2+\overline{z}=0$, where $zϵC$ are

Let P be any point on the plane lx + my + nz = p and Q be a point on the line OP such that $OP\cdot OQ=p^2$. The locus of the point Q is

If f(x) = $|x-2|$, then

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is

Let $\overrightarrow{a}=4\overrightarrow{i}+3\overrightarrow{j}$ and $\overrightarrow{b}=3i+4j$. (a) Find the magitudes of (a) $\overrightarrow{a}$, (b) $\overrightarrow{b}$, (c) $\overrightarrow{a}+\overrightarrow{b}$ and (d) $\overrightarrow{a}-\overrightarrow{b}$.

If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+c=0and{S}_n={\alpha }^n+{\beta }^{n}thena{S}_{n+1}+b{S}_n+c{S}_{n-1}=(n\ge 2)$

A line through A (-5, -4) meets the lines x + 3y + 2 = 0, 2x + y + 4 = 0, 2x + y + 4 = 0 and x – y – 5 = 0 at B, C and D respectively. If ${\left(\frac{15}{AB}\right)}^2+{\left(\frac{10}{AC}\right)}^2={\left(\frac{6}{AD}\right)}^2,$, then the equation of the line is

Find the equation of the line passing through (- 2, 3) with slope - 4.

The equation sin x + x cos x = 0 has at least one root in the interval

Find the equation of the line passing through the point of intersection of the lines $4x-7y-3=0and2x-3y+1=0$ that has equal intercepts on the axes.

Image of a point P(2, -3, 1 ) with respect to line L is I. Find the coordinates of I, if foot of the perpendicular of P with respect to L is $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$

The sum of the squares of the eccentricites of $\frac{x^2}{4}+\frac{y^2}{3}=1$ and $\frac{x^2}{4}-\frac{y^2}{3}=1$ is

The negation of the Boolean expression $\sim s\vee (\sim r\wedge s)$ is equivalent to

The total number of irrartional terms in the binomial expansion of ${(7^{1/5}-3^{1/10})}^{60}$ is :

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls?
(ii) at least 3 girls?
(iii) almost 3 girls?

The area of the region above X-axis included between the parabola $y^2=x$ and the circle $x^2+y^2=2x$ in square units is

If P(n,5)=20.P(n,3), find n.

If 1+$\frac{1+2}{2}+\frac{1+2+3}{3}+....$to n terms is S. Then, S is equal to

Show that the point (x,y) given by $x=\frac{2at}{1+t^2}andy=a\left(\frac{1-t^2}{1+t^2}\right)$ lies on a circle for all real values of t such that $-1\le t\le 1$, where is any given real number.

8. Prove that :
(i) $\frac{sinA+sin3A+sin5A}{cosA+cos3A+cos5A}=tan3A$
(ii) $\left(ii\right)\frac{cos3A+2cos5A+cos7A}{cosA+2cos3A+cos5A}=\frac{cos5A}{cos3A}$
(iii) $\frac{cos4A+cos3A+cos2A}{cos4A+sin3A+sin2A}=cot3A$
(iv) $\frac{sin3A+sin5A+sin7A+sin9A}{cos3A+cos5A+cos7A+cos9A}=tan6A$
(v) $\frac{sin5A-sin7A+sin8A-sin4A}{cos4A+cos7A+cos7A-cos5A-cos8A}=cot6A$
(vi) $\frac{sin5A+cos2A-sin6AcosA}{sinAsin2A-cos2Acos3A}=tanA$
(vii) $\frac{sin11A+sinA+sin7A+sin3A}{cos11AsinA+cos7Asin3A}=tan8A$
(viii) $\frac{sin3Acos4A-sinAcos2A}{sin4AsinA+cos6AcosA}=tan2A$
(ix) $\frac{sinAsin2A+sin3Asin6A}{sinAcos2A+cos3Acos6A}=tan5A$
(x) $\frac{sinA+2sin3A+sin5A}{sin3A+2sin5A+sin7A}=\frac{sin3A}{sin5A}$
(xi) $\frac{sin(\theta +\varphi )-2sin\theta +sin(\theta +\varphi )}{cos(\theta +\varphi )-2cos\theta +cos(\theta +\varphi )}$

The centre of the circle passing through the point (0, 1) and touching the curve $y=x^2$ at (2, 4) is

All the letters of the word 'EAMCOT' are arranged in different possible ways. find the number of arrangement in which no two vowels are adjacent to each other.

Let f(x) be a function defined by $f\left(x\right)=\{\begin{array}{cc}\frac{3}{|x|+2x},& x\ne 0\\ 0,& x=0\end{array}$ Show that ${lim}_{x\to 0}$ f(x)does not exist.

If x+y+z=6, xy+xz+yz=11, xyz=6 thenequals

The graph for the linear function $y=4x+5$ is

Let I $=\int \frac{e^x}{e^{4x}+e^{2x}+1}dx.J=\int \frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx,$Then, for an arbitrary constant c, the value of J-I equals

The probability of a bomb hitting a bridge is 1/2 and two direct hits are needed to destroy it. Find the least number of bombs required so that the probability of the bridge being destroyed is greater than 0.9.___

The values of ‘a’ for which exactly one root of the equation $e^a{x}^2-e^{2a}x+e^a-1=0$ lies between 1 and 2 are given by

In a sequence of (4n+1) terms, the first (2n+1) terms are in A.P., whose common difference is 2, and the last (2n+1) terms are in G.P whose common ratio is 0.5 if the middle terms of the A.P and G.P are equal then the middle term of the sequence is

A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sun is just setting ? Refractive index of water $=\frac{4}{3}$.

The equations to the common tangents to the two hyperbolas $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ are

If $f\left(x\right)=\{\begin{array}{cc}{x}^k\sin \left(\frac{1}{x}\right),& x\ne 0\\ 0,& x=0\end{array}$ is differentiable at $x=0,$ then (where $k$ is an integer)

If n is even and the value of ${}^n{C}_r$ is maximum, then r =

The minor matrix of the matrix $\left[\begin{array}{ccc}1& -1& 2\\ 2& -1& 1\\ 1& 1& -1\end{array}\right]$ is

If ${\int }_0^{\alpha }\frac{dx}{1-cos\alpha cosx}=\frac{A}{sin\alpha }+B(\alpha \ne 0).$Then possible values of A and B are

If f(x) = x, x≤1, and f(x) =x² + bx + c, x>1, and f'(x) exists finitely for all x ϵ R, then

Let $f\left(\alpha \right)=\left[\begin{array}{ccc}cos\alpha & -sin\alpha & 0\\ sin\alpha & cos\alpha & 0\\ 0& 0& 1\end{array}\right]$, then $\left(f\right(\alpha ){)}^{-1}$ is equal to