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In the figure given below, ∠ACB = 90^o, ∠BDC = 90^o, CD = 4 cm, BD = 3 cm, AC = 12 cm. cos A - sin A is equal to:

If ${\log }_{4}5=a$ and ${\log }_{5}6=b$, then ${\log }_{3}2$ equal to

The values of $x$ which satisfies the equation $(x-1{)}^3+8=0$ are

Let $S$ be the set of all functions $f:[0,1]\to R$, which are continuous on $[0,1]$ and differentiable on $(0,1)$. Then for every $f$ in $S$, there exists a $c\in (0,1)$, depending on $f$, such that:

If $A$ and $B$ are two mutually exclusive events, then

Evaluate $\underset{0}{\overset{1}{\int }}\ln \left(x\right)dx$

The distance of the plane passing through (1, 1, 1) and perpendicular to the line $\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}$ from the origin is

If $x,y,z$ are in G.P. and $x+y,y+z,z+x$ are in A.P., where $x\ne y\ne z$, then common ratio of the G.P. is

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

The negation of the conditional statement ‘If it rains, I shall go to school’ is___.

If sum of n terms of an A.P. is 3$n^2$+5n and $T_m$= 164, m=?

If $r:R:r_1=2:5:12,$ then $\angle A=$

With respect to position of two circles which of the following statements is/are correct?

1. If one circle lies completely outside the other circle,

Number of direct common tangents = 2

Number of transverse common tangents = 2

2. If two circles touch each other externally

Number of direct common tangents = 2

Number of transverse common tangents = 1

3. If two circles touch each other internally

Number of direct common tangents = 1

Number of transverse common tangents = 0

4. If two circles intersect each other at two points

Number of direct common tangents = 2

Number of transverse common tangents = 0

5. If one circle lies completely inside the other circle

Number of direct common tangents = 0

Number of transverse common tangents = 0

The general solution of $\sin 4x\cos 2x=\cos 5x\sin x$ is

Let $I_1=\underset{-2}{\overset{2}{\int }}\frac{x^6+3x^5+7x^4}{x^4+2}dx$ and $I_2=\underset{-3}{\overset{1}{\int }}\frac{2(x+1{)}^2+11(x+1)+14}{(x+1{)}^4+2}dx$,

then the value of $I_1+I_2$ is

A box contains 30 bolts and 40 nuts. Half of the bolts and half of the nuts

are rusted. If two items are drawn at random, what is the probability that

either both are rusted or both are bolts?

A
source contains two phosphorous radio nuclides
(T_1/2
=
14.3d) and
(T_1/2
= 25.3d). Initially, 10% of the decays come from.
How long one must wait until 90% do so?

Solve the inequalities and represent the solution graphically on number line: 2(x – 1) < x + 5, 3(x + 2) > 2 – x

A region in $xy$-plane is bounded by $y=0$ and $y=\sqrt{25-x^2}$. If a point $(a,a+1)$ lies in the interior of the region, then :

$r{\cdot }^n{C}_r=$

The value of $\sum _{x=0}^4{\sin }^{-1}\left(\sin x\right)$ is equal to

${\int }_1^2\frac{dx}{\sqrt{(x-1)(2-x)}}$

Which of the following is true for a matrix A.

If $x^{\cos y}=4,$ then $\frac{dy}{dx}=$

1. 1

Two sides of a rhombus are along the lines, x - y + 1 = 0 and 7x - y - 5 = 0. If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus ?