CUET · MATHS · PYQ PAPER 2025
Consider the line \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\)
Match List-I with List-II
| List-I | List-II |
| (A) A point on the given line | (I) \(\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)\) |
| (B) direction ratios of the line | (II) \((4,-2,-2)\) |
| (C) direction cosines of the line | (III) \((1,-2,4)\) |
| (D) direction ratios of a line perpendicular to given line | (IV) \((-1,2,-4)\) |
- A \((A) - (IV), (B) - (III), (C) - (II), (D) - (I)\)
- B \((A) - (III), (B) - (IV), (C) - (II), (D) - (I)\)
- C \((A) - (III), (B) - (IV), (C) - (I), (D) - (II)\)
- D \((A) - (IV), (B) - (III), (C) - (I), (D) - (II)\)
Answer & Solution
Correct Answer
(C) \((A) - (III), (B) - (IV), (C) - (I), (D) - (II)\)
Step-by-step Solution
Detailed explanation
Given line: \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\) A. Point on the line: \((1,-2,4)\) → (III) B. Direction ratios of the line: \((-1,2,-4)\) → (IV) C. Direction cosines of the line: \(|\vec{b}|=\sqrt{(-1)^2+2^2+(-4)^2}=\sqrt{21}\)…
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
- Suppose \(X\) has Poisson distribution such that \(3 P(X=1)=2 P(X=2)\) then \(P(X>0)\) is :CUET 2025 Medium
- If \(\int \frac{x^4}{x-2} d x=p x+q x^2+r x^3+s x^4+t \log |x-2|+C\), where \(C\) is an arbitrary constant and \(p, q, r, s, t\) are real numbers, then the correct arrangement of \(p, q, r, s, t\) isCUET 2025 Hard
- The solution of the differential equation \(\frac{d y}{d x}=\frac{a x+c}{b y+d}\) represents a circle whenCUET 2025 Hard
- If \(\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}, \vec{a} \times \vec{b}=\vec{a} \times \vec{c}\) and \(\vec{a} \neq \overrightarrow{0}\), then the vector \(\vec{b}\) is equal to:CUET 2025 Hard
- If \(A\) is a square matrix of order 3 such that \(|A|=3\) then \(|\operatorname{adj}(\operatorname{adj} A)|\) is equal to:CUET 2025 Hard
- If \(\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k},|\vec{b}|=5\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{6}\), then the area of the triangle formed by these two vectors as two sides is :CUET 2023 Easy
More PYQs from CUET
- Read the passage given below and answer the question.
Phenols and Alcohol have the same function group (-OH) but phenols are stronger acids than alcohol due the resonance stabilization of phenoxide ion than alkoxide ion (-RO\(^{-}\)). Electron withdrawing groups tend to increase the acidic strength while electron releasing groups tend to decrease it.
Compound 'A' on reaction with Conc. HCl and anhydrous \(ZnCl_2\), gives turbidity immediately.
Compound 'A' is :CUET 2023 Medium - Let \(X\) and \(Y\) be any two invertible square matrices of order \(n\). Then which of the statements are true?
(A) \((A B)^{-1}=A^{-1} B^{-1}\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=A^T B^T\), where \(A^T\) denotes transpose of A
(D) \((A B)^T=B^T A^T\), where \(A^T\) denotes transpose of A
Choose the correct answer from the options given below :CUET 2023 Easy - The general solution of \(\frac{d y}{d x}=1+x^2+y^2+x^2 y^2\) is:
(given that \(C\) is the constant of integration)CUET 2023 Hard - On the basis of following observations arrange the following compounds in increasing order of mol of AgCl precipitated per mol of the compound with excess of AgNO3
Choose the correct answer from the options given below:Formula Secondary valences Solution conductivity (A) PdCl2.4NH3 4 1:2 electrolyte (B) NICI4.2K 4 2:1 electrolyte (C) CoCl3.4NH3 6 1:1 electrolyte (D) CrCl3.6H2O 6 1:3 electrolyte CUET 2025 Medium - If \(A=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\) and \(A^2-8 A+K I=O\), then the value of \(K\) is:CUET 2023 Easy
- Which of the following statements are correct?
A. Electrical resistivity of copper is low.
B. Temperature coefficient of resistance for semiconductors is positive.
C. On carbon resistors, colour of the second strip indicates the multiplier.
D. During charging of a cell, the terminal potential difference becomes greater than the emf of the cell.
E. The cells are connected in series to get more voltage, than cells connected in parallel.
Choose the correct answer from the options given below:CUET 2023 Medium