CUET · MATHS · PYQ PAPER 2025
Match List-I with List-II
Consider two vectors \(\vec{a}=\hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=-3 \hat{i}-6 \hat{j}+3 \hat{k}\).
| List-I | List-II |
| (A) Angle between \(\vec{a}\) and \(\vec{b}\) | (I) \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\) |
| (B) Angle between \(\vec{a}\) and \(x\)-axis | (II) \(\cos ^{-1}\left(\frac{2}{\sqrt{6}}\right)\) |
| (C) Angle between \(\vec{b}\) and \(x\)-axis | (III) \(\pi\) |
| (D) Angle between \(\vec{a}\) and \(y\)-axis | (IV) \(\cos ^{-1}\left(-\frac{1}{\sqrt{6}}\right)\) |
- A \((A)-(I I I),(B)-(I V),(C)-(I),(D)-(I I)\)
- B \((A)-(I I I),(B)-(I),(C)-(I V),(D)-(I I)\)
- C \((A)-(I I I),(B)-(I I),(C)-(I),(D)-(I V)\)
- D \((A)-(I I),(B)-(I I I),(C)-(I),(D)-(I V)\)
Answer & Solution
Correct Answer
(B) \((A)-(I I I),(B)-(I),(C)-(I V),(D)-(I I)\)
Step-by-step Solution
Detailed explanation
\( |\vec{a}| = \sqrt{1^2+2^2+(-1)^2} = \sqrt{6} \) \( |\vec{b}| = \sqrt{(-3)^2+(-6)^2+3^2} = \sqrt{9+36+9} = \sqrt{54} = 3\sqrt{6} \)…
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
- Two biased dice are thrown together. For the first die \(P(6)=1 / 2\), other scores are equally likely. While for the second die, \(P (1)=2 / 5\) and other scores are equally likely then the mean for the probability distribution of 'the number of ones seen', will beCUET 2023 Easy
- If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=7,|\vec{b}|=3\) and \(|\vec{c}|=5\), then angle between \(\vec{b}\) and \(\vec{c}\) isCUET 2025 Hard
- If |\(\vec{a}\)| = 8, |\(\vec{b}\)| = 3, and |\(\vec{a} \times \vec{b}\)| = 12, then the value of \(\vec{a} \cdot \vec{b}\) is:CUET 2023 Medium
- If the feasible region of an LPP is bounded and the corresponding objective function is \(Z =5 x -9 y\), then the objective
function attains :CUET 2025 Hard - \(\int \frac{\sqrt{1-x}}{\sqrt{1+x}} d x=\alpha \sqrt{1-x^2}+\beta \sin ^{-1} x+C\), where \(C\) is an arbitrary constant, then which of the following are TRUE?
(A) \(\alpha=1\)
(B) \(\alpha=-1\)
(C) \(\beta=1\)
(D) \(\beta=-1\)
Choose the correct answer from the options given below :CUET 2025 Hard - The value of p so that the lines \(\frac{x-1}{-3}=\frac{2 y-2}{2 p}=\frac{z-3}{2}\) and \(\frac{x-1}{-3 p}=\frac{y-1}{4}=\frac{6-z}{5}\) are at right angles isCUET 2025 Hard
More PYQs from CUET
- An ordinary light of intensity \(I_0\) is passed through a polaroid \(P_1\) which is crossed with another polaroid \(P _{ 2 }\). Now a third polaroid is placed in between \(P _1\) and \(P _2\) with its pass aris making an angle \(\beta\) with the pass axis of \(P_1\). The value of \(\beta\) for which the intensity of light from \(P_2\) is \(\frac{I_0}{8}\) is :CUET 2023 Easy
- Aspartame is used in cold foods and soft drinks even though it is roughly 100 times as sweet as cane sugar and can pose a health hazard because:CUET 2023 Medium
- The brain size of Neanderthal man was :CUET 2023 Medium
- Read the paragraph given below and answer the question.
If a person is born with a hereditary disease, can a corrective therapy be taken for such a disease? Gene therapy is an attempt to do this. Gene therapy is a collection of methods that allows correction of a gene defect that has been diagnosed in a child/embryo. Here genes are inserted into a person's cells and tissues to treat disease.
ADA enzyme is crucial for the functioning ofCUET 2023 Hard - Answer the question on basis of passage given below :
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
Structure of \(\text{XeO}_3\) is:CUET 2023 Easy - Lack of Vitamin B1 causes:CUET 2025 Medium