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The verties of a triangle are O (0,0), A(a,0)andB(0,b). Write the coordinates of its circumcentre.

The order and the degree of the differential equation are

If the sets A and B are defined as

A = {(x, y) : y = $\frac{1}{x}$, x≠ 0 and x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

The negation of the compound statement $p\wedge (\sim p\vee q)$ is ___.

If α&β are zeros of the polynomial f(x)=x²+px+q,then find a polynomial having 1/α & 1/β as its zeros.

Let $a_n,nϵN$ is an A.P. with common difference ${}^{\prime }{d}^{\prime }$ and whose all terms are non-zero. If $n$ approaches infinity, then the sum $\frac{1}{a_1{a}_2}+\frac{1}{a_2{a}_3}+...+\frac{1}{a_n{a}_{n+1}}$ will approach

For any three sets $X,Y\&Z;(X\cup Y)\cup Z=$

If one end of focal chord $PQ$ of the parabola $y^2=8x$ is at $P(\frac{1}{2},-2),$ then the equation of tangent to it at $Q$ is

If f is a continuous function in the interval [a, b], then the value of ${\int }_0^{1}f\left(\left(b-a\right)x+a\right)\mathrm{dx}$ is equal to

₹20 is charged for parking initally and an additional charge of ₹10 is there for every hour.



The equation for total charge for x hours will be .

Let $p,q$ be integers and let $\alpha ,\beta$ be the roots of the equation, $x^2-x-1=0,$ where $\alpha \ne \beta .$ For $n=0,1,2,....,$ let $a_n=p{\alpha }^n+q{\beta }^n.$



FACT: If $a$ and $b$ are rational numbers and $a+b\sqrt{5}=0.$ then $a=0=b.$



If $a_4=28,$ then $p+2q=$

If the mean deviation of the numbers $1,1+d,1+2d,\cdot ,1+100d$ from their mean is 255, then $d$ is equal to:

If $\alpha ,\beta ,\gamma ,\delta$ are the roots of equation $2x^4+4x^3-3x^2+3x+1=0$, then value of $\frac{1}{2\alpha -1}+\frac{1}{2\beta -1}+\frac{1}{2\gamma -1}+\frac{1}{2\delta -1}$ is

If $x$ satisfies the inequality $(x^2-x-1)(x^2-x-7)<-5,$ then number of integral value(s) of $x$ satisfying the given inequality is

The number of ways a father can distribute $50$ different coins equally among his $5$ childrens is

Given two quadratic equations $x^2-1=-b^2-2bx\&x^2-1=-a^2-2ax$ have exactly one root in common then select the correct statements.

If $\cos B$ is the geometric mean of $\sin A$ and $\cos A$, where $0<A,B<\frac{\pi }{2}$, then the value(s) of $\cos 2B$ is/are

The condition for which the quadratic equation $(p^2-3p+2)x^2+(p^2-4)x+(p-1)=0$ will have a graph which is a downward opening parabola is

Let $[A{]}_{2\times 2}$ and $[B{]}_{3\times 3}$ be the two matrices such that $det\left(A\right)=2$ and $det\left(B\right)=3.$ Then the value of $det(det(A)\cdot B)+det(det(B)\cdot A)$ is

If $(2x-1{)}^{20}-(ax+b{)}^{20}=(x^2+px+q{)}^{10}$ holds true $\forall x\in R$ where $a,b,p$ and $q$ are real numbers, then which of the following is (are) TRUE ?

If the length of the subnormal at any point on the curve $x{y}^n=a^{n+1}(a\ne 0)$ is constant, then the value of $n$ is

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuciei will be:

Find C, when $\overline{\text{C}}=200,\text{MPC}=0.5$ and $\text{Y}=1,000$.

Direction(7-10): Answer the questions based on the directions given in the passage below:

The following scatter plot shows the details of the sales of cool drinks on 12 different days vs the noon temperature on that day.

Read the data carefully and answer the questions that follow.

Common Solution:

What was the median value of sales(in Rs.) of all the given days?

For the function $f\left(x\right)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$. The value of $f\left(\pi \right)$, so that $f\left(x\right)$ is continuous at $x=\pi$ is

Sum of the series $\sum _{r=0}^n(-1{)}^r{}^n{C}_r\cdot [i^{5r}+i^{6r}+i^{7r}+i^{8r}],$ is

Find the equation of the set of the points P such that its distances from the points A(3, 4, -5) and B(-2, 1, 4) are equal.

x + y = 7;
3x + 4y = 11
What value of (x , y) satisfies the above system of equations?