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Four fair dice $D_1,D_2,D_3$ and $D_4$ each having six faces numberd $1,2,3,4,5$ and $6,$ are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1,D_2$ and $D_3$ is

If $C_0,C_1,C_2,\dots ,C_n$ denote the binomial coefficients respectively in $(1+x{)}^{2020},$ then

A square with each side equal to $a$ lies above the $x$-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle $\alpha (0<\alpha <\frac{\pi }{4})$ with the positive direction of the $x$-axis. Equation of a diagonal of the square is

The derivative of $\frac{7x^2}{4e^x-x}$ will be

The integral value of $x,$ for $\left|\begin{array}{ccc}{x}^2& x& 1\\ 0& 2& 1\\ 3& 1& 4\end{array}\right|=28$ is

If,
find A⁻¹. Using A⁻¹ solve
the system of equations

The value of ${\int }_{-2}^2(a{x}^3+bx+c)$ depends on [MNR 1988; UPSEAT 2000]

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If $9^7+7^9$ is divided by $64$, then the remainder is

If $y=1+\frac{x}{1!}+\frac{x^2}{2!}+\cdots \infty ,$ then which of the following is/are true

The value of $cot(\frac{\pi }{4}-2co{t}^{-1}3)$ is equal to

Solution set of the inequality $(x-2{)}^{x^2-6x+8}>1$, where $x>2$ is

The exhaustive set of values of $a^2$such that there exists a tangent to the ellipse$x^2+a^2{y}^2=a^2$such that the portion of the tangent intercepted by the hyperbola $a^2{x}^2-y^2=1$ subtends a right angle at the origin.

The sum of the squares of the lengths of the chords intercepted on the circle, $x^2+y^2=16$ by the lines, $x+y=n;n\in N$, where $N$ is the set of all the natural numbers, is :

If $y=\sin \theta +\cos \theta ,$ then the value of $\frac{d^{2}y}{d{x}^2}+y$ is

A line cuts the x-axis at A(4, 0) and the y-axis at B(0, 8). A variable line PQ is drawn perpendicular to AB cutting the x-axis in P and the y-axis in Q. If AQ and BP intersect at R, find the locus of R.

$2^{\frac{1}{4}}$. $4^{\frac{1}{8}}$. $8^{\frac{1}{16}}$. ${16}^{\frac{1}{32}}$................ is equal to

The area covered inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$ is

The middle term in the expansion of $(3a+\frac{1}{3}{)}^8$ is 1120,where a is a real number.

Find the value of a.

An ellipse has OB as semi-minor axis, F and F’ its foci and the angle FBF’ is a right angle. Then the eccentricity of the ellipse is

• Fill in the blanks with the words given in the brackets - (sail, bark, sing, play, ring)

• Write the names of the days of the week. You can begin with Sunday.

• Haldi wrote her name at school in this way -

• Haldi wrote - i met a giraffe

In a
hurdle race, a player has to cross 10 hurdles. The probability that
he will clear each hurdle is.
What is the probability that he will knock down fewer than 2 hurdles?

Find
the range of each of the following
functions.

(i) f(x)
= 2 – 3x,
x ∈
R, x
> 0.

(ii) f(x)
= x²
+ 2, x, is
a real number.

(iii) f(x)
= x, x
is a real number

Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$

In a triangle $ABC,$ if $\frac{a^2+b^2}{a^2-b^2}\sin (A-B)=1$ and the triangle is not right angled, then $\cos (A-B)=$

Find

and,
when

In the interval $x\in [0,1]$ the value of ${\cos }^{-1}\sqrt{1-x}+{\sin }^{-1}\sqrt{1-x}$ is

The locus of point $P$ when three normals drawn from it to parabola $y^2=4ax$ are such that two of them make complementary angles is