Download App

Model Paper 8 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 81 Mark
MCQ
If $\frac{3 \pi}{4}<\alpha<\pi$, then $\sqrt{2 \cot \alpha+\frac{1}{\sin ^2 \alpha}}$ is equal to
  • A
    $-1+\cot \alpha$
  • B
    $-1-\cot \alpha$
  • C
    $1-\cot \alpha$
  • D
    $1+\cot \alpha$
✓

Answer

(b) - 1 - cot
Explanation: We have:
$\begin{array}{l}\sqrt{2 \cot \alpha+\frac{1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \cos \alpha}{\sin \alpha}+\frac{1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \sin \alpha \cos \alpha+1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \sin \alpha \cos \alpha+\sin ^2 \alpha+\cos ^2 \alpha}{\sin ^2 \alpha}} \\ =\sqrt{\frac{(\sin \alpha+\cos \alpha)^2}{\sin ^2 \alpha}} \\ =\sqrt{(1+\cot \alpha)^2} \\ =|1+\cot \alpha| \\ =-(1+\cot \alpha)\left[\text { When } \frac{3 \pi}{4}<\alpha<\pi, \cot \alpha<-1 \Rightarrow \cot \alpha+1<0\right] \\ =-1-\cot \alpha\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Model Paper 8→Model Paper 8 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y - 5 = 0 is:

  1. 1 : 2
  2. 3 : 7
  3. 2 : 3
  4. 2 : 5
→
a + i b > c + idcan be explained only when:
→
If D, G and R denote respectively the number of degrees, grades and radians in an angle, then:
→
If $1,\omega ,{{\omega }^{2}}$ are three cube roots of unity, then ${{(a+b\omega +c{{\omega }^{2}})}^{3}}$ + ${{(a+b{{\omega }^{2}}+c\omega )}^{3}}$ is equal to, if $a+b+c=0$ [West Bengal JEE 1992]
→
How many words can be made from the letters of the word GARDEN so that the vowels are in alphabetical order?
→

If the sum of n terms of an A.P. is given by

Sn = 3n + 2n2, then the common difference of the A.P. is:

  1. 3.
  2. 2.
  3. 6.
  4. 4.
→
Total number of divisors of 5880 is equal to:
→

If $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:

  1. $\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$ 

  2. $\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$ 

  3. $\frac{1-\text{x}^{2}}{4\text{x}}$ 

  4. $\frac{4\text{x}}{\text{x}^{2}-1}$

→
The directrix of the parabola x2 - 4x - 8y + 12 = 0 is
→
The number of values of ​x in $[0,\ 2\pi]$ that satisfy the equation $\sin^2\text{x}-\cos\text{x}=\frac{1}{4}$
→