CUET · MATHS · PYQ PAPER 2023
A line passes through two points A(2, -3, -1) and B(8, -1, 2). The co-ordinates of a point on this line at a distance of 14 units from A are:
Α. (14, 1, 5)
Β. (86, 25, 41)
C. (-10, -7, -7)
D. (-82, -31, -43)
E. (10, 7, 7)
Choose the correct answer from the options given below:
- A B and D only
- B A and D only
- C A and C only
- D C and E only
Answer & Solution
Correct Answer
(C) A and C only
Step-by-step Solution
Detailed explanation
\(\vec{AB} = (8-2, -1-(-3), 2-(-1)) = (6, 2, 3)\) \(|\vec{AB}| = \sqrt{6^2 + 2^2 + 3^2} = \sqrt{36+4+9} = \sqrt{49} = 7\) \(\vec{P} = \vec{A} \pm \frac{14}{|\vec{AB}|}\vec{AB} = (2, -3, -1) \pm \frac{14}{7}(6, 2, 3)\)…
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
- The projection vector of the vector \(2 \hat{i}+3 \hat{j}+\hat{k}\) on \(2 \hat{i}+\hat{j}-2 \hat{k}\) isCUET 2025 Medium
- Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is:CUET 2025 Medium
- If \(f(x)=|x|+|x-5|\), then which of the following statements are TRUE?
(A) \(f\) is a continuous function everywhere
(B) \(f\) is a continuous function except x = 5 and x = 0
(C) \(f\) is a continuous function except x = 0 but not differentiable at x = 5
(D) \(f\) is a continuous function everywhere but not differentiable at x = 0 and x = 5
Choose the correct answer from the options given below:CUET 2025 Medium - Match \(List - I\) with \(List - II\)
\(List - I\) \(List - II\) (A) \(\frac{d}{d x}\left(\sin x^2\right)\) (I) \(\frac{1}{5}\) (B) \(\frac{d}{d x}\left(e^{\sin x}\right)\) (II) 0 (C) \(f(x)=\tan ^{-1} x\) then \(f^{\prime}(2)\) (III) \(2 x \cos x^2\) (D) If \(y=3 \cos x-2 \sin x\), then \(\frac{d^2 y}{d x^2}+y\) (IV) \(e^{\sin x} \cos x\) CUET 2023 Medium - The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)CUET 2025 Easy - At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?CUET 2025 Hard
More PYQs from CUET
- The minimum value of \(a x+b y\), where \(x y=c^2\) and \(a, b, c\) are positive, is:CUET 2023 Easy
- If a copper wire carries a direct current, the magnetic field associated with the current would be:CUET 2023 Easy
- For the given five values 3.6, 4.3, 4.3, 3.4, 4.4, the three years moving averages are:CUET 2025 Medium
- Match List-I with List-II
List- I List- II (A) For a series LC circuit (I) Currents in L and C are 180° out of phase (B) For a parallel LC circuit (II) Power Factor=0 (C) For a purely capacitive circuit (III) Voltage across L and C are 180° out of phase (D) For a series LCR circuit at resonance (IV) Reactance is zero
Choose the correct answer from the options given below:CUET 2025 Hard - Identify one of the given factors which does not affect Hardy-Weinberg equilibrium.CUET 2025 Easy
- Magnetic moment of first series of transition metal complexes is determined by........CUET 2023 Medium