Domain

Q. if (6x)^6=6^2^3 then find the value of x

Q.

If (2 + √5) ÷ (2 - √5) = x and (2 - √5) ÷ (2 + √5) = y; find the value of x^{​​​​​​2} - y^{​​​​​​2}

Q.

Assertion: The graph of the two linear equations x - 2y = 1 and 2x + 3y = 9 intersect at (3, 1).

Reason: Every point lying on x - 2y = 1 is a solution of 2x + 3y = 9

Now, choose the correct option.

1. Both the assertion and the reason are true and the reason is the correct explanation for the assertion.
2. Both the assertion and the reason are true but the reason is not the correct explanation for the assertion.
3. Assertion is true but the reason is false.
4. If assertion is false but reason is true.

Q.

If $\cos \theta =\left(\frac{1}{2}\right)\left(x+\frac{1}{x}\right)$, then $\left(\frac{1}{2}\right)\left(x^2+\frac{1}{x^2}\right)=?$

1. $\sin 2\theta$

2. $\cos 2\theta$

3. $\tan 2\theta$

4. $sec2\theta$

Q.

If $sec\left(\theta \right)$ is $\frac{5}{4}$ then write the value of $\cos \left(\theta \right)$?

Q.

The domain of the function $f\left(x\right)=\frac{1}{{\log }_{10}(1-x)}+\sqrt{x+2}$ is

1. $]0,1[$

2. $]-3,-2.5[\cup ]-2.5,-2[$

3. $[-2,0[\cup ]0,1[$

4. None of these

Q. Question 10
If $sin\theta +cos\theta =p$ and $sec\theta +cosec\theta =q$, then prove that $q(p^2-1)=2p$.

Q.

If, $f\left(x\right)=cos\left[{\pi }^2\right]x+cos[-{\pi }^2]x,$ where [x] stands for greatest integer function, then

1. $f\left(\frac{\pi }{2}\right)=1$

2. $f\left(\pi \right)=1$

3. $f(-\pi )=0$

4. $f\left(\frac{\pi }{4}\right)=2$

Q.

If $x$ satisfies $|x-1|+|x-2|+|x-3|\ge 6$, then

1. $0\le x\le 4$
   

2. $x\le -2$ or $x\ge 4$
   

3. $x\le 0$ or $x\ge 4$
   

4. none of these

Q.

The domain of the function $f\left(x\right)=e^{\left(\sqrt{5x-3-2x^2}\right)}$ is

1. 
2. 
3. 
4. 

Q. If $x>0$ and ${\log }_{2}x+{\log }_2\sqrt{x}+{\log }_2\sqrt[4]{4x}+{\log }_2\sqrt[8]{8x}+{\log }_2\sqrt[15]{15x}+....=4$, then $x=$______.

1. $4$
2. $2$
3. $\pm 3$
4. $\pm 48$

Q. 28. If graph ofxy=1 is reflected in y = 2x to give the graph 12x^2+rxy+sy^2+=0, then(a) r=7(c) r 25(b) s=-12(d) r + s =-192

Q. 64^1/3÷125^1/3=25

Q.

How many of the following pairs of function are identcal

(a) f (x) = $\frac{x^2}{x},g\left(x\right)=x$

(b) f(x) = $\frac{x^2-1}{x-1}$ g(x) = x + 1

(c) f(x) = $se{c}^{2}x-ta{n}^{2}x$ , g(x) = 1

(d) $f\left(x\right)=\frac{x}{x^2},g\left(x\right)=\frac{1}{x}$

__

Q. If $\sqrt{N}$ be converted into a continued fraction, and if the penultimate convergents in the first, second, ....$k^{th}$ recurring periods be denoted by $n_1,n_2,.....n_k$ respectively.Show that $\frac{n_k+\sqrt{N}}{n_k-\sqrt{N}}={\left(\frac{n_1+\sqrt{N}}{n_1-\sqrt{N}}\right)}^k$.

Q.

1. $\{-6,-\sqrt{4},0,1\}$
2. $\{-6,-\sqrt{4},0,\pi \}$
3. $\{-\sqrt{4},0,1\}$
4. Cannot be determined
   

Q.

The domain of f(x) is (0, 1). Then the domain of $f\left(e^x\right)+f\left(ln|x|\right)$ is

1. $(-1,e)$

2. $(1,e)$

3. $(-e,-1)$

4. $(-e,1)$

Q. If n(A) = 7 and n(A ∩ B) = 3, then n[(A ∩ B) ∩ A] is

Q. If A and B be two sets n (A)=15, n(B)=25, then number of possible values of n (A delta B) (symmetric difference of A and B is (1) 30 (2) 16 (3) 26 (4) 40

Q. If $\frac{x}{x^{1.5}}=8x^{-1}$ and x > 0, then x =

(a) $\frac{\sqrt{2}}{4}$

(b) $\sqrt[2]{2}$

(c) 4

(d) 64

Q. ${\int }_{-3}^3(\left|x\right|+|x-2|)dx+30=$

Q. The value of $x$ satisfying the logarithm ${\log }_{243}x=0.8$ is equal to

1. $81$
2. $2.43$
3. $1.8$
4. $27$

Q.

SHOW THAT 1 DIVIDED BY 1 + (ROOT)2

PLUS 1 DIVIDED BY (ROOT)2 +(ROOT)3 IS -1+(ROOT)3

Q. Solve:
$\log y\sqrt{x}.{\log }_z{y}^3.{\log }_x\sqrt{z^2}$

Q.

Let $f:(-1,1)\to R$ be such that $f\left(\cos 4\theta \right)=\frac{2}{2-se{c}^2\theta }$ for $\theta \in (0,\frac{\pi }{4})\cup \left(\frac{\pi }{4}\frac{\pi }{2}\right)$.Then the value (s) of $f\left(\frac{1}{3}\right)$ is (are)

1. $1-\sqrt{\frac{3}{2}}$

2. $1+\sqrt{\frac{3}{2}}$

3. $1-\sqrt{\frac{2}{3}}$

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