Aspire Faculty ID #15267 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

If $\cos\theta + \sec\theta = 3$, then $\cos^{2}\theta + \sec^{2}\theta$ is …

Solution

Let $\cos\theta = x \Rightarrow \sec\theta = \dfrac{1}{x}$. So, $x + \dfrac{1}{x} = 3 \Rightarrow x^{2} + \dfrac{1}{x^{2}} = (x + \dfrac{1}{x})^{2} - 2 = 9 - 2 = 7.$ Hence $\cos^{2}\theta + \sec^{2}\theta = 7.$
← Previous Next →

Previous 10 Questions — JAMIA MCA 2016

Nearest first
1
The value of $2\sin^{2}\theta \cdot \cos^{2}\theta (\sec^{2}\theta + \csc^{2}\theta)$ is …
Topic: JAMIA MCA 2016
 2
$\displaystyle \int \sqrt{x}e^{\sqrt{x}}dx$ is equal to …
Topic: JAMIA MCA 2016
 3
$\displaystyle \int_{0}^{1}\frac{x}{(1-x)^{1/2}}dx$ is equal to …
Topic: JAMIA MCA 2016
 4
$\displaystyle \int_{0}^{\frac{\pi}{4}}\sec^{2}x\sin x\,dx=a+\sqrt{2}$, find $a$
Topic: JAMIA MCA 2016
 5
If $x>0$, then $\displaystyle \int |x|^{3} dx$ is equal to …
Topic: JAMIA MCA 2016
 6
$\displaystyle \int_{1}^{x}(1+\log t)^{2}\,dt$ is equal to …
Topic: JAMIA MCA 2016
 7
$\displaystyle \lim_{x\to1}\frac{x+x^{2}+\ldots+x^{10}-10}{5x-5}$ is equal to …
Topic: JAMIA MCA 2016
 8
$\displaystyle \lim_{x\to a}\frac{x^{10}-a^{10}}{x^{2}-a^{2}}$ is equal to …
Topic: JAMIA MCA 2016
 9
If $\displaystyle \lim_{x \to a} \frac{x^{\alpha} - x^{a}}{x - a} = -1$, then $\alpha$ is equal to …
Topic: JAMIA MCA 2016
 10
$\displaystyle \lim_{h \to 0} \frac{\sqrt{x + h} - \sqrt{x}}{h}$ is equal to …
Topic: JAMIA MCA 2016

Next 10 Questions — JAMIA MCA 2016

Ascending by ID
1
The value of $\tan1^{\circ} \cdot \tan2^{\circ} \cdot \tan3^{\circ} \cdots \tan89^{\circ}$ is …
Topic: JAMIA MCA 2016
 2
If $\cos\theta + \cos^{3}\theta = \sin^{2}\theta$, then $\sin^{6}\theta - 4\sin^{4}\theta + 8\sin^{2}\theta$ is equal t…
Topic: JAMIA MCA 2016
 3
If $\cos^{2}\theta + \sec^{2}\theta = a$, then …
Topic: JAMIA MCA 2016
 4
The amplitude of $\dfrac{1+i\sqrt{3}}{\sqrt{3}+i}$ is equal to …
Topic: JAMIA MCA 2016
 5
If $z$ be a complex number and $\bar{z}$ be its conjugate, then the number of solutions of $z^{2} + 2\bar{z} = 0$ is …
Topic: JAMIA MCA 2016
 6
If $z$ be a complex number, then one of the solutions of the equation $z^{2} + |z|^{2} = 0$ is …
Topic: JAMIA MCA 2016
 7
If $\omega$ is a cube root of unity, then the value of $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is …
Topic: JAMIA MCA 2016
 8
Let cube roots of unity be $1, \omega, \omega^{2}$. Which of the following is a cube root of the equation $(x - 1)^{3} …
Topic: JAMIA MCA 2016
 9
If $m^{\text{th}}$ term of an A.P. is $n$ and $n^{\text{th}}$ term is $m$, then its $10^{\text{th}}$ term is …
Topic: JAMIA MCA 2016
 10
Let sum of $n$ terms of an A.P. be $S_n=3n^2+5$. If $T_n$ (the $n$th term) of this series is $159$, then $n$ is …
Topic: JAMIA MCA 2016
Ask Your Question or Put Your Review.

loading...