Marathi
English
Hindi
Bengali

Question

Download Solution PDF

If  then what is the value of the determinant of m sinθ + n cosθ 

  1. 1
  2. -1
  3. 3
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2
Free Tests
View all Free tests >
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins
Start Now

Detailed Solution

Download Solution PDF

गणना: 

m sinθ + n cosθ = sin θ  + cos θ 

= +

= 

आता,

|m sinθ + n cosθ| = 

=  + 

= 2()

= 2

म्हणून, पर्याय (4) योग्य आहे.

Download Solution PDF
Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Exams Tests Super Practice

More Evaluation of Determinants Questions

Q1.If \(\rm D_n=\begin{vmatrix}n&20&30\\\ n^2&40&50\\\ n^3&60&70\end{vmatrix}\) then what is the value of \(\rm \Sigma_{n=1}^4D_n?\)
Q2.If \(\rm \omega=-\frac{1}{2}+i\frac{\sqrt3}{2}\) then what is \(\rm \begin{vmatrix}1+\omega &1+\omega^2&\omega+\omega^2\\\ 1&\omega\ & \omega^2\\\ \frac{1}{\omega}&\frac{1}{\omega^2}&1\end{vmatrix}\) equal to? 
Q3.If \(\rm A=\begin{bmatrix}1&2&3\\\ 3&4&5\\\ 5&6&7\end{bmatrix}\) and \(\rm B=\begin{bmatrix}1&1&1\\\ 2&2&2\\\ 3&3&3\end{bmatrix}\), then det(A + B) = ?
Q4.If |z1| = |z2| and amp z1 + amp z2 = 0, then z1 and z2 are two complex numbers such that they are:
Q5.If \(\begin{vmatrix} x-4& 2x&2x\\\ 2x &x-4&2x\\\ 2x&2x & x-4 \end{vmatrix} =(A+Bx)(x-A)^2\) then the ordered pair (A, B) is equal to :
Q6.If a, b, c are positive and unequal, then the value of Δ = \(\begin{vmatrix} a& b&c\\\ b&c&a\\\ c&a&b \end{vmatrix}\) is: 
Q7.If \(\begin{vmatrix}(1+\alpha)^2&(1+2\alpha)^2&(1+3\alpha)^2\\\ (2+\alpha)^2&(2+2\alpha)^2&(2+3\alpha)^2\\\ (3+\alpha)^2&(3+2\alpha)^2&(3+3\alpha)^2 \end{vmatrix}=-648\alpha\) then the value of α is 
Q8.If α, β ≠ 0 and f(n) = αn + βn and \(\begin{vmatrix}3&1+f(1)&1+f(2)\\\ 1+f(1)&1+f(2)&1+f(3)\\\ 1+f(2)&1+f(3)&1+f(4) \end{vmatrix}\) = K(1 - α)2 (1 - β)2 (α - β)2 then K is equal to:
Q9.The number of 3 × 3 non-singular matrices with four entries as 1 and all other entries as 0 is
Q10.If a, b, c are different and \(\left|\begin{array}{ccc} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{array}\right|=0\) then x is equal to

More Determinants Questions

Q1.If P is a skew-symmetric matrix of order 3, then what is det(P) equal to? 
Q2.If \(\rm D_n=\begin{vmatrix}n&20&30\\\ n^2&40&50\\\ n^3&60&70\end{vmatrix}\) then what is the value of \(\rm \Sigma_{n=1}^4D_n?\)
Q3.If \(\rm \omega=-\frac{1}{2}+i\frac{\sqrt3}{2}\) then what is \(\rm \begin{vmatrix}1+\omega &1+\omega^2&\omega+\omega^2\\\ 1&\omega\ & \omega^2\\\ \frac{1}{\omega}&\frac{1}{\omega^2}&1\end{vmatrix}\) equal to? 
Q4.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q5.If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, where a, b, c ∈ R are non-zero and distinct; has non-zero solution, then
Q6.Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |AT A(adj(2A))–1 (adj(4B))(adj(AB))–1AAT | is equal to : 
Q7.If the system of equations  11x + y + λz = –5 2x + 3y + 5z = 3 8x – 19y – 39z = µ has infinitely many solutions, then λ4 – µ is equal to :
Q8.Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: 
Q9.Which one of the following options is incorrect?  For a square matrix A in the matrix equation AX = B. 
Q10.The area of the triangle (in unit2) whose vertices are A(4, 8),B(-6, 2) and C(5, 4) is: 
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 1 Free Tests
Start Free Test
Current Affairs (CA) 2024 Mega Pack for SSC/Railways/State Exam Mock Test
427 Total Tests with   1 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti king teen patti boss online teen patti