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The value of $\underset{0}{\overset{15}{\int }}\{3x+4\}dx$ is

(where $\{\cdot \}$ is fractional part function)

Tangent to a curve $y=f\left(x\right)$ intersects the $y-$axis at a point $P.$ A line perpendicular to this tangent through $P$ passes through another point $(1,0).$ The differential equation of the curve is

If the co-ordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is

The angle of intersection of the curves $y=2si{n}^{2}xandy=cos2xatx=\frac{\pi }{6}$ is

Find the modulus and the argument of the complex number

If cos 2 B =

$\frac{cos(A+C)}{cos(A-C)}$, then tan A, tan B, tan C are in

Which of the following is the correct graph of the function $f\left(x\right)=\cos (3x-\frac{3\pi }{2})?$

Let $a_n$ denote the number of all $n-$digit positive integers formed by the digits $0,1$ or both such that no

consecutive digits in them are $0$. Let $b_n=$ the number of such $n-$digit integers ending with digit $1$ and

$c_n=$ the number of such n-digit integers ending with digit $0$.

The value of $b_6$ is

The sum of $(11{)}^2+(12{)}^2+(13{)}^2+\dots +(20{)}^2$ is

Cards are drawn one by one at random from a well-shuffled pack of $52$ playing cards until $2$ aces are obtained for the first time. The probability that $18$ draws are required for this, is

If the function f defined by f(x) = x^2 + 3x +a, x≤1 bx+2, x>1

Is derivable, then find the values of a and b.

If $f\left(x\right)=\{\begin{array}{cc}\frac{(4^x-1{)}^3}{\sin \left(\frac{x}{a}\right)\ln (1+\frac{x^2}{3})},& x\ne 0\\ 9(\ln 4{)}^3,& x=0\end{array}$ is continuous at $x=0$, then the value of $a$ is

If the function $f\left(x\right)=\{\begin{array}{cc}\frac{\sqrt{ax+b}-2}{x},& x\ne 0\\ a^2,& x=0\end{array}$ is continuous at $x=0,$ then which of the following(s) is/are correct

There are $2n$ terms in an A.P., whose first term is $a$ and common difference is $d$. The sum of the odd terms is $24$ and the sum of the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$, then which of the following is (are) CORRECT?

The number of solutions of the equation $2\cos x=2x^2+1$ in $x\in [-\frac{\pi }{2},\frac{\pi }{2}]$ is

The mean of $6$ distinct observations is $6.5$ and their variance is $\mathrm{10.25.}$ If $4$ out of $6$ observations are $2,4,5$ and $7,$ then the remaining two observations are

If $\overrightarrow{F_1},\overrightarrow{F_2}$ makes an angle of ${30}^{\circ }\text{and}{45}^{\circ }$ respectively with $\overrightarrow{F_3}$ as shown in the figure, and magnitude of $\overrightarrow{F_3}$ is $5\text{N}$, then the magnitude of $\overrightarrow{F_1},\text{and}\overrightarrow{F_2}$ respectively are $(\text{Given}\overrightarrow{F_1}+\overrightarrow{F_2}=\overrightarrow{F_3})$

The value of $(1-i{)}^4$ is

Let $f\left(x\right)={\sin }^{-1}x$ and $g\left(x\right)=\frac{x^2-x-2}{2x^2-x-6}$. If $g\left(2\right)=\underset{x\to 2}{lim}g\left(x\right)$, then the domain of the function $fog$ is :

A committee consists of 5 students 3 girls and 2 boys. If the team is to be formed out of 7 boys and 5 girls, then how many ways this selection can be made?

Which
of the given values of x
and y make
the following pair of matrices equal

(A)

(B) Not
possible to find

(C)

(D)

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

Let $f\left(x\right)=x^2$ and $g\left(x\right)=\sin x$ for all $x\in R$. Then the set of all $x$ satifying $(f\circ g\circ g\circ f)\left(x\right)=(g\circ g\circ f)\left(x\right)$, where $(f\circ g)\left(x\right)=f\left(g\right(x\left)\right)$, is

If $\frac{1}{b-c}$, $\frac{1}{c-a}$, $\frac{1}{a-b}$ be consecutive terms of an A.P., then $(b-c{)}^2,(c-a{)}^2,(a-b{)}^2$ will be in ___.

If tan⁴θ + cot⁴θ = 47, where θ is an acute angle, then the value of sin⁴θ + cos⁴θ is



यदि tan⁴θ + cot⁴θ = 47, जहाँ θ न्यूनकोण है, तब sin⁴θ + cos⁴θ का मान है

The point $P$ is on the $y$-axis. If $P$ is equidistant from $(1,2,3)$ and $(2,3,4),$ then $P_y=$