CUET · MATHS · PYQ PAPER 2023
\(\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)\) is valid for which values of \(\lambda\) ?
- A \(\lambda \in\left(-\frac{1}{3}, \frac{1}{3}\right)\)
- B \(\lambda>\frac{1}{3}\)
- C \(\lambda<\frac{1}{3}\)
- D All real values of \(\lambda\)
Answer & Solution
Correct Answer
(C) \(\lambda<\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-xy}\right)\) is valid if \(xy \(3 \cdot \lambda \(\lambda < \frac{1}{3}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- If \(\Delta_1=\left|\begin{array}{lll}x & b & b \\ a & x & b \\ a & a & x\end{array}\right|\) and \(\Delta_2=\left|\begin{array}{ll}x & b \\ a & x\end{array}\right|\) are determinants, then :CUET 2023 Easy
- The five month moving averages for the following data
is :Month (rth) 43 44 45 46 47 48 49 50 51 Actual Demand 105 106 110 110 114 121 130 128 137 CUET 2025 Hard - Match List-I with List-II
Choose the correct answer from the options given below :List-I List-II (A) If A is a non singular matrix of order n, then \(| A (\operatorname{adjA})|\) is equal to (I) \(|A|^{n-1}\) (B) If A is a non singular matrix of order n, then |adj(adj A)| is equal to (II) \(|A|^{n-2} A\) (C) If A is a non singular matrix of order n, then \(\operatorname{adj}(\operatorname{adj} A )\) is equal to (III) \(|A|^n\) (D) if A is a non singular matrix of order n, then \(|(\operatorname{adj} A)|\) is equal to (IV) \(|A|^{(n-1)^2}\) CUET 2025 Easy - The unit's digit of \(12^{12}\) is equal to :CUET 2025 Medium
- The minimum value of \(\left(x^2+\frac{250}{x}\right)\) is :CUET 2023 Hard
- The value of the integral \(\int \frac{\log x^3}{x} d x\) is :CUET 2023 Easy
More PYQs from CUET
- There are two values of a for which the determinant, \(\Delta = \begin{vmatrix} 1 & -2 & 5 \\ 0 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86\), then the sum of these values of a is:CUET 2023 Easy
- If \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]\) then product \(A B\) is :CUET 2023 Hard
- The number of all possible matrices of order \(2 \times 3\) with entries \(-1\) or \(1\) is:CUET 2025 Medium
- Glucose reacts with Tollen's reagent (ammoniacal silver nitrate) due to the presence ofCUET 2025 Medium
- Molar conductivity increases with......CUET 2025 Hard
- If a matrix has 12 elements, then the possible orders it can have, are
(A) \(1 \times 12\)
(B) \(4 \times 3\)
(C) \(6 \times 3\)
(D) \(6 \times 2\)
Choose the correct answer from the options given below :CUET 2025 Easy