Inequality

Q.

Find the ratio of the areas of the incircle and circumcircle of a square.

1. 1:1

2. 1:2

3. 1:3

4. 1:4

Q.

What is the semi perimeter of the triangle?

Q.

Question 69

A rule for finding the approximate length of diagonal of a square is to multiply the length of a side of the square by 1.414. find the length of the diagonal when:
(a) the length of a side of the square is 8.3 cm.
(b) the length of a side of the square is exactly 7.875 cm.

Q.

The number of all possible triplets $(a_1,a_2,a_3)$ such that $a_1+a_{2}cos\left(2x\right)+a_{3}si{n}^2\left(x\right)=0$ for all $x$ is

1. Zero

2. One

3. Three

4. Infinite

Q. How to plot irrational no. on number line like pie

Q. Question 5
If $cos(\alpha +\beta )=0$, then $sin(\alpha -\beta )$ can be reduced to

(A) $cos\beta$
(B) $cos2\beta$
(C) $sin\alpha$
(D) $sin2\alpha$

Q. If A, B, C are the angles of a triangle such that C is an obtuse angle, then

1. $tanA.tanB<1$
2. $tanA.tanB>1$
3. $tanA.tanB=1$
4. None

Q.

Evaluate the exponential expression $(-b{)}^4\times (-b{)}^5$, for $b=4$. [2 MARKS]

Q. How many numbers between 200 and 600 are divisible by 14?

1. 28
2. 27
3. 29
4. None of these

Q. Express the relation {(x, y) : 3x + y = 10 ; x, y $\in$ W} as the set of ordered pairs.

1. {(0, 10), (1, 7), (2, 4), (3, 1)}
2. {(0, 10), (1, 7), (2, 4), (3, 0)}
3. {(0, 10), (1, 6), (2, 3), (3, 1)}
4. {(0, 10), (1, 7), (4, 2), (1, 3)}

Q. Express as a single logarithm:
$\log 3+\log 4+\log 5$

Q.

Fill appropriate sign $\left(<,=,>\right)$

$\frac{3}{4}\square \frac{7}{8}$

Q. If $y=3^{x-1}+3^{-x-1}$ (x real), then the least value of y is

1. None of these
2. 2
3. 6
4. $\frac{2}{3}$

Q. What is the least value of x possible if -1 < x ≤ 1 and x is a real number?

1. 1
2. -0.99
3. None of these
4. -1

Q.

The largest interval for which $x^{22}-x^{19}+x^{14}-x^5+1>0$ is

1. (0, 1)

2. $(-\infty ,\infty )$

3. $(-\infty ,1]$

4. $[1,\infty )$

Q. If a, b, c are positive real numbers, then prove that ${\left[(1+a)(1+b)(1+c)\right]}^7>7^7{a}^4{b}^4{c}^4$.

Q.

f(x)=$x^2$ for x < 2

g(x)= $x^2$ for x > -1

Range of f(x)= range of g(x)

1. True

2. False

Q. If x, y, z are three + ive real numbers, then minimum value of $\frac{y+z}{x}+\frac{z+x}{y}+\frac{x+y}{z}$ is

1. 2
2. 1
3. 3
4. 6

Q. If $x_i>1\forall iϵN$, then
$lo{g}_{x_2}{x}_1+lo{g}_{x_3}{x}_2+\dots \dots +lo{g}_{x_n}{x}_{n-1}+lo{g}_{x_1}{x}_n$
has the minimum value

1. 1
2. None
3. 2
4. 0

Q. If a, b, c are the sides of a triangle then which of the following hold good?

1. $a^2+b^2+c^2>ab+bc+ca$
2. $\frac{a^2+b^2+c^2}{ab+bc+ca}$ lies between 1 and 2
3. $a^3+b^3+c^3>3abc$
4. $3(ab+bc+ca)\le (a+b+c{)}^2\le 4(bc+ca+ab)$

Q. Represent root x on number line

Q. If A, B, C be the angles of a triangle, then which of the following hold good?

1. $cotA.cotB.cotC\le \frac{1}{3\sqrt{3}}$
2. $cot\frac{A}{2}cot\frac{B}{2}cot\frac{C}{2}\ge 3\sqrt{\left(3\right)}$
3. $cosA+cosB+cosC<\frac{3}{2}$
4. $sin\left(\frac{A}{2}\right)sin\left(\frac{B}{2}\right)sin\left(\frac{C}{2}\right)\le \frac{1}{8}$

Q.

Show that the semiperimeter of the triangle is also doubled when each side of the triangle is doubled.

Q. For real a, b and x $-\sqrt{(a^2+b^2)}\le asinx+bcosx\le \sqrt{(a^2+b^2)}$

Q. $(a_1^2+a_2^2+\dots \dots a_n^2)(b_1^2+b_2^2+\dots \dots +b_n^2)\ge (a_1{b}_1+a_2{b}_2+\dots \dots +a_n{b}_n{)}^2$

Q. $lo{g}_{e}4+lo{g}_{4}e>2$

Q. Write the sets A and B such that A is finite, B is finite, A and B are disjoint sets.

Q. Between $1$ and $31$ are inserted m arithmetic means so that the ratio of the 7th and $(m-1)$ th means is $5:9$. Find the value of $m$.

Q. A.M. of the square root of products taken two together of n +ive quantities is less than A.M. of the n quantities itself.

Q. $cos{75}^0=?$

1. $\frac{(\sqrt{3}+1)}{2\sqrt{2}}$
2. $\frac{(\sqrt{3}-1)}{2\sqrt{2}}$
3. $\frac{(\sqrt{2}-1)}{2\sqrt{2}}$
4. $\frac{(\sqrt{2}+1)}{2\sqrt{2}}$