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The circumcentre of the triangle formed by $(2,-5),$ $(2,7),$ $(4,7)$ is

The integral value(s) of
$x$ satisfying $\sqrt{-x^2+10x-16}<x-2$ is/are

A parallelogram is cut by two sets of m lines parallel to its sides. The number of parallelograms thus formed is

${lim}_{x\to 0}\frac{1-cos2x}{3ta{n}^{2}x}$

If a function f(x) is defined in x $ϵ$ [a, b], then f(x) is continuous at a if

In an experiment there are $20$ observation for which following results are given
$\sum x^2=8100,\sum x=214$
One observation that was $42$ was found to be wrong and it was replaced by the correct value $28$. Then the corrected standard deviation is

Current flows through uniform, square frames as shown. In which case is the magnetic field at the centre of the frame not zero ?

Given that the price of bananas is fixed at Rs 2 per banana in the following table. Calculate optimum level of consumption.

$\begin{array}{ccccccccc}\text{Number of}& 1& 2& 3& 4& 5& 6& 7& 8\\ \text{bananas}& & & & & & & & \\ \text{TU}& 5& 9.5& 13.5& 17& 20& 22.5& 24.5& 26\end{array}$

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in $c{m}^3/min$, when the radius is 2 cm and the height is 3 cm is

Let $T_r$ be the $r^{t}h$ term of an A.P. whose first term is a and common difference d. if for some positive integers m,
$n,m\ne n,T_m=\frac{1}{n},T_n=\frac{1}{m}$ then a – d =

If vertices of a quadrilateral are A (0,0), B(3,4), C(7,7) and D(4,3) then quadrilateral ABCD is

The value of $x$ for which the tangents to the curves $y=x\cos x,y=\frac{\sin x}{x}$ are parallel to the axis of $x$ are roots of

Let be a function with domain X and range Y. Let A, B $⊑$ X and C, D $⊑$ Y. Which of the following is not true?

The number of solutions of the equation $\cos x=\sqrt{1-\sin 2x}$ where $x\in [0,2\pi ]$ is

If $\tan A,\tan B$ are the roots of quadratic equation $a{x}^2+3x+4=0,a\ne 0$ and $\frac{\tan A}{\cot B-\tan A}=\frac{1}{3}$, then the value of $a$ is

The coordinates of the foot of perpendicular drawn from the point $(1,-2)$ on the line $y=2x+1$,is

The slope intercept form of the line $\frac{x}{2}+\frac{y}{4}=1$ is

$\int \frac{3x-1}{\sqrt{x^2+9}}dx=$

If f(x)=cos^2 x +sec^2 x, then

If y = 5 cos x -3 sin x, prove that $\frac{d^{2}y}{dx}+y=0$.

Prove

CosA to the power 4 - sinA to the power 4

Is =2CosA to the power 2

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0.

Two distinct chords of the parabola $y^2=4ax$ passing through $P(a,2a)$ are bisected by the line $x-y+1=0$. The possible length of the latus rectum of the parabola when $a>0$ is

The line $2x+3y=12$ meets the x-axis at A and y-axis at B. The line through $(5,5)$ perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.

If ${\sin }^{-1}(x-\frac{x^2}{2}+\frac{x^3}{4}-\frac{x^4}{8}+\cdots )=\frac{\pi }{6}$ where $|x|<2$, then the value of $x$ is

Find the equation of the straight line passing through (-2, 3) and inclined at an angle of ${45}^{\circ }$ with the x-axis.

$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are the edges of a cube of unit length and $\overrightarrow{r}$ be any unit vector inside the cube the ${|\overrightarrow{a}\times \overrightarrow{r}|}^2+{|\overrightarrow{b}\times \overrightarrow{r}|}^2+{|\overrightarrow{c}\times \overrightarrow{r}|}^2$ is

The locus represented by the equation , |z-1| + |z+1| = 2 is :

Find the inverse of the given matrix
$\left[\begin{array}{ccc}1& 0& 0\\ 0& cos\alpha & sin\alpha \\ 0& sin\alpha & -cos\alpha \end{array}\right]$

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student has opted NSS but not NCC.

If $sin2A=\lambda ,sin2B$, then write the value of $\frac{\lambda +1}{\lambda -1}$

Of the students in college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous years results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostler?

If one end of the diameter of a circle is (3, 4) which touches the x-axis then the locus of other end of the diameter of the circle is

The Rank of the following matrix is

$\left[\begin{array}{cccc}1& 0& 0& 3\\ 0& 1& 1& 2\\ 0& 0& 0& 0\\ 0& 0& 1& 1\end{array}\right]-----------$

If $\alpha ,\beta$ are roots of the equation $x^2-p(x+1)-c=0$, then

$(\alpha +1)(\beta +1)$=