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2(2y + 3) = 3x - 5 ;
-2x = 4y + 6
Consider the above system of equations. Which of the following solutions satisfy the sytem ?

The correct expresssion among the following is :

A variable takes value x with frequency ${}^{n+x-1}{C}_x,x$ = 0, 1, 2, . . . n. The mode of the variable is ___.

If the ratio of the roots of the equation $x^2$+px+q=0 be equal to the ratio of the roots of $x^2$+lx+m=0. Then

If $a_1,a_2,a_3...$ are in A.P, then $a_p,a_q,a_r$ are in A.P if p, q, r are in

If $f\left(x\right)=\{\begin{array}{cc}\frac{sin2x}{5x},& whenx\ne 0\\ k,& whenx=0\end{array}$ is continuous at x = 0, then the value of k will be

The equation of the circle passing through the points (4,1),(6,5) whose centre lies on the line 4x+y-16=0 is

​​​​​$\begin{array}{cccc}& \text{List 1}& & \text{List II}\\ \text{(1)}& \text{If PQ is a focal chord of the ellipse}& & \\ & \frac{x^2}{25}+\frac{y^2}{16}=1\text{which passes through S(3,0) \&}& & \\ & \text{PS=2, then the length of the focal chord PQ is}& \left(P\right)& 1\\ \text{(2)}& \text{The focal chord of}{y}^2=16x\text{is tangent to}& & \\ & (x-6{)}^2+y^2=2\text{. Then the possible values}& & \\ & \text{of the slopes of the chord is}& \left(Q\right)& 3\\ \text{(3)}& \text{A circle is described on the focal chord of}& & \\ & y^2=-12x\text{as a diameter such that it touches}& & \\ & \text{the line}x=a\text{. Then the value of}a\text{is}& \left(R\right)& 6\\ \text{(4)}& \text{If the eccentricity of the hyperbola is}\frac{5}{4}and& & \\ & \text{2x+3y-10=0 is a focal chord of the hyperbola}\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\text{,}& & \\ & \text{then the length of transverse axis is}& \left(S\right)& 8\\ & & \left(T\right)& 10\\ & & & \\ & & \left(U\right)& 4\end{array}$
Which of the following is only correct combination?

The number of ways in which ten candidates $A_1,A_2,A_3......A_{10}$ can be ranked if $A_1$ and $A_2$ are next to each other is

Find the number of fruits between Mango and Watermelon.

All possible values of $\theta \in [0,2\pi ]$ for which $\sin 2\theta +\tan 2\theta >0$ lie in :

Three houses are available in a locality. Three persons apply for the houses. Each applies for one houses without consulting others. The probability that all three apply for the same houses is

Let $b_i>1\text{for}i=1,2,...,101.$ Suppose ${\log }_e{b}_1,{\log }_e{b}_2,...,{\log }_e{b}_{101}$ are in Arithmetic Progression (A.P.) with the common difference ${\log }_{e}2.$ Suppose $a_1,a_2,...,a_{101}$ are in A.P. such that $a_1=b_1$ and $a_{51}=b_{51}.$ If $t=b_1+b_2+\cdots +b_{51}\text{and}s=a_1+a_2+\cdots +a_{51},$ then

If $11z^{10}+10i{z}^9+10iz-11=0then$

In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

The area bounded by the curve $y=x^3$, x-axis and two ordinates x=1 to x=2 equal to

Let f(x), g(x), h(x) be continous in [0, 2a] and satisfies $f(2a-x)=f\left(x\right),g(2a-x)=g\left(x\right),h\left(x\right)+h(2a-x)=3,f(2a-x)g(2a-x)=f\left(x\right)g\left(x\right)then{}^{}{\int }_0^{2a}f\left(x\right)g\left(x\right)h\left(x\right)dx=$

The maximum value of (cos ${\alpha }_1$) (cot ${\alpha }_2$) …….. (cot ${\alpha }_n$) = 1 is

If the equation $x^2+9y^2-4x+3=0$ is satisfied for real values of x and y then

If $A_1,A_2$ be two arithmetic means and $G_1,G_2$ be two geometric means between two positive numbers $a$ and $b,$ then$\left(\frac{A_1+A_2}{G_1{G}_2}\right)$ is equal to

If $V=\frac{4}{3}\pi r^3$,at what rate in cubic units is V increasing when r = 10 and $\frac{dr}{dt}=0.01$ ?

Let $F\left(x\right)=\int e^{si{n}^{-1}x}(1-\frac{x}{\sqrt{1-x^2}})dx,andF\left(0\right)=1,ifF\left(\frac{1}{2}\right)=\frac{k{\sqrt{3e}}^{\frac{x}{6}}}{\pi }$, then k =

If $Z_1,Z_2,Z_3$ are the vertices of the $\Delta$ ABC on the complex plane and are also the roots of the equation $Z^3–3\alpha Z^2+3\beta Z+x=0$, then the condition for the $△$ ABC to be equilateral triangle is

Which among the following can always represent a vector?

ind teh coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=6y$

The equation of the hyperbola whose transverse axis is 14 and whose vertex bisects the distance between centre and the focus is

The maximum value of $(se{c}^{-1}x{)}^2+(cose{c}^{-1}x{)}^2$ is equal to

For the given differential equation find the particular solution satisfying the given conditions.

$2xy+y^2-2x^2\frac{dy}{dx}=0,y=2whenx=1$

The value of $2tan\frac{\pi }{10}+3sec\frac{\pi }{10}-4cos\frac{\pi }{10}$ is

Cut off potentials for a metal in photo electric effect for light of wavelengths λ1, λ2 and λ3 is found to be V1, V2 and V3volts. If V1, V2 and V3 are in arithmetic progression then λ1, λ2 and λ3 will be in

${lim}_{x\to 0}\frac{cos\left(sinx\right)-cosx}{x^4}isequalto$

Solution of the differential equation $(x+2y^3)\frac{dy}{dx}=y$ is

Find the order and degree of the differential equation $\sqrt{1-{\left(\frac{dy}{dx}\right)}^2}=a{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}$ .