Trigonometry (IPMAT/JIPMAT) - Free PYQs + Solutions | AfterBoards
IPMAT Indore Free Mocks Topic Tests

Trigonometry - Past Year Questions

Filter & Analyse PYQs (Topic-Wise) →
Past Year Papers with Solutions filter tool

Q1:

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, is
Answer options
Option: 4
Correct Answer
Explanation →

Q2:

If cosαcos \alpha + cosβcos \beta = 1 then the maximum value of sinα−sinβsin \alpha - sin \beta is
Answer options
Option: 3
Correct Answer
Explanation →

Q3:

Ayesha is standing atop a vertical tower 200m200 m high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be 45∘45^{\circ}. At 11:02 AM, she observes the angle of depression of the car to be 30∘30^{\circ}. The speed at which the car is moving is approximately
Answer options
Option: 4
Correct Answer
Explanation →

Q4:

For 0<θ<π40\lt\theta\lt\frac{\pi}{4}, let a=((sin⁡θ)sin⁡θ)(log⁡2cos⁡θ),b=((cos⁡θ)sin⁡θ)(log⁡2sin⁡θ),c=((sin⁡θ)cos⁡θ)(log⁡2cos⁡θ)a=\left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \cos \theta\right), b=\left((\cos \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right), c=\left((\sin \theta)^{\cos \theta}\right)\left(\log _{2} \cos \theta\right) and d=((sin⁡θ)sin⁡θ)(log⁡2sin⁡θ)d=\left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right). Then, the median value in the sequence a,b,c,da, b, c, d is
Answer options
Option: 2
Correct Answer
Explanation →

Q5:

If sin⁡α+sin⁡β=23\sin \alpha+\sin \beta=\frac{\sqrt{2}}{\sqrt{3}} and cos⁡α+cos⁡β=13\cos \alpha+\cos \beta=\frac{1}{\sqrt{3}}, then the value of (20cos⁡(α−β2))2\left(20 \cos \left(\frac{\alpha-\beta}{2}\right)\right)^{2} is _________.
100
Correct Answer
Explanation →

Q6:

The set of all real value of pp for which the equation 3sin⁡2x+12cos⁡x−3=p3 \sin^2x + 12 \cos x - 3 = p has at least one solution is
Answer options
Option: 3
Correct Answer
Explanation →

Q7:

If the angles A,B,CA, B, C of a triangle are in arithmetic progression such that sin⁡(2A+B)=1/2\sin(2A + B) = 1/2 then sin⁡(B+2C)\sin(B + 2C) is equal to
Answer options
Option: 1
Correct Answer
Explanation →

Q8:

The value of cos⁡2(π8)+cos⁡2(3π8)+cos⁡2(5π8)+cos⁡2(7π8)\cos^2\left(\frac{\pi}{8}\right) + \cos^2\left(\frac{3\pi}{8}\right) + \cos^2\left(\frac{5\pi}{8}\right) + \cos^2\left(\frac{7\pi}{8}\right) is
Answer options
Option: 3
Correct Answer
Explanation →

Q9:

Given that cos⁡x+cos⁡y=1\cos x + \cos y = 1, the range of sin⁡x−sin⁡y\sin x - \sin y is
Answer options
Option: 4
Correct Answer
Explanation →

Q10:

If sinθ+cosθ=msin \theta + cos \theta = m, then sin6θ+cos6θsin^6 \theta + cos^6 \theta equals
Answer options
Option: 4
Correct Answer
Explanation →

Q11:

The number of pairs (x,y)(x, y) satisfying the equation sin⁡x+sin⁡y=sin⁡(x+y)\sin x + \sin y = \sin(x + y) and ∣x∣+∣y∣=1|x| + |y| = 1 is
6
Correct Answer
Explanation →

Q12:

If sin⁡θ+cos⁡θ=72\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}, then (sin⁡θ−cos⁡θ)(\sin \theta-\cos \theta) is equal to :
Answer options
Option: 2
Correct Answer
Explanation →

Q13:

Given below are two statements:
Statement I: cot⁡30∘+1cot⁡30∘−1=2(cos⁡30∘+1)\frac{\cot 30^{\circ}+1}{\cot 30^{\circ}-1}=2\left(\cos 30^{\circ}+1\right)
Statement II : 2sin⁡45∘cos⁡45∘−tan⁡45∘cot⁡45∘=02 \sin 45^{\circ} \cos 45^{\circ}-\tan 45^{\circ} \cot 45^{\circ}=0
Answer options
Option: 1
Correct Answer
Explanation →

Q14:

In △ABC,∠B=90∘,BC=5 cm,AC−AB=1 cm\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{BC}=5 \ \mathrm{cm}, \mathrm{AC}-\mathrm{AB}=1 \mathrm{~cm}, then 1+sin⁡(c)1+cos⁡(c)\frac{1+\sin (\mathrm{c})}{1+\cos (\mathrm{c})} is
Answer options
Option: 4
Correct Answer
Explanation →

Q15:

If sin⁡(θ)−cos⁡(θ)=0\sin (θ) - \cos (θ) = 0, the value of sin4 (θ) + cos4 (θ) is:
Answer options
Option: 2
Correct Answer
Explanation →

Q16:

Given below are two statement:
Statement I: If sin⁡(θ)=513\sin (\theta)=\frac{5}{13}, then the value of tan⁡(θ)=512\tan (\theta)=\frac{5}{12}
Statement II: if cot⁡(θ)=125\cot (\theta)=\frac{12}{5}, then the value of sin⁡(θ)=512\sin (\theta)=\frac{5}{12}
In the light of the above statements, choose the correct answer form the question below:
Answer options
Option: 3
Correct Answer
Explanation →

Q17:

Which of the following trigonometric identities are true?
sin⁡2(41∘)+sin⁡2(49∘)=1sin⁡2(60∘)−2tan⁡(45∘)−cos⁡2(30∘)=−1sin⁡2(θ)+11+tan⁡2(θ)=1\begin{aligned} & \sin ^2\left(41^{\circ}\right)+\sin ^2\left(49^{\circ}\right)=1 \\ & \sin ^2\left(60^{\circ}\right)-2 \tan \left(45^{\circ}\right)-\cos ^2\left(30^{\circ}\right)=-1 \\ & \sin ^2(\theta)+\frac{1}{1+\tan ^2(\theta)}=1 \end{aligned}
Answer options
Option: 2
Correct Answer
Explanation →

Q18:

Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, then the distance between their tops is
Answer options
Option: 3
Correct Answer
Explanation →

Q19:

The minimum value of (2sin⁡2θ+3cos⁡2θ)(2 \sin^2\theta + 3 \cos^2\theta) is
Answer options
Option: 3
Correct Answer
Explanation →

Q20:

sin⁡(13π6)\sin(\frac{13\pi}{6})
Answer options
Option: 1
Correct Answer
Explanation →

Trigonometry - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Trigonometry Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!