CUET · MATHS · PYQ PAPER 2023
The value of \(\lim _{x \rightarrow 0} \frac{1-\cos x}{2 x^2}\) is:
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0} \frac{1-\cos x}{2 x^2} = \frac{1}{2} \lim _{x \rightarrow 0} \frac{1-\cos x}{x^2} \) \( = \frac{1}{2} \cdot \frac{1}{2} \) \( = \frac{1}{4} \)
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
- Match List-I with List-II
Choose the correct answer from the options given below:List-I (Function f(x)) List-II (Interval) (A) \(f(x)=x|x|\) (I) Decreases on \((0, \infty)\) (B) \(f(x)=x^2+2 x-5\) (II) Increases on \((3, \infty)\) (C) \(f(x)=x^2-6 x+9\) (III) Decreases on \((-\infty,-1)\) (D) \(f(x)=-x^2\) (IV) Increases on \((-\infty, \infty)\) CUET 2025 Medium - If \(A\) and \(B\) are non singular square matrices of the same order,
then which of the statements are true ?
(A) \((\operatorname{adj} A)(\operatorname{adj} B)=(\operatorname{adj} B)(\operatorname{adj} A)\)
(B) \((A B)^T=A^T B^T\), if \(A^T\) denotes transpose of \(A\)
(C) \((A B)^{-1}=B^{-1} A^{-1}\)
(D) Multiplication of matrices is not commutativeCUET 2023 Medium - Probability that A speaks truth is \(\frac{4}{5}\). A coin is tossed. A reports that a head appears. The probability that actually there was head is:CUET 2023 Hard
- Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with \(|A|=2\) and let \(C=\left[C_{i j}\right]\), where \(C_{i j}\) is the cofactor of \(a_{i j}\) in \(A\). Then \(|C|\) is equal to :CUET 2025 Medium
- A and B are two students. Their chances of solving a problem correctly are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively.
If the probability of their making a common error is \(\frac{1}{20}\) and they obtain the same answer, then the probability that their answer is correct is:CUET 2023 Medium - The area (sq. units) bounded by the curve \(y=\sin x, \pi \leq x \leq 2 \pi\) and the \(x\)-axis isCUET 2025 Hard
More PYQs from CUET
- The physical quantity which is reciprocal of resistance is-CUET 2025 Hard
- Choose the incorrect statement from the following:CUET 2023 Easy
- Match List I with List II
List I
(Technique/term)List II
(Features)(A) Amniocentesis (I) Ligation of fallopian tube (B) Maternal mortality rate (II) Ligation of vas deferens (C) Vasectomy (III) Death rate (D) Tubectomy (IV) Testing of sex
Choose the correct options:CUET 2025 Easy - Which of the following methyl halide will have the highest value of dipole moment?CUET 2025 Hard
- Colostrum secreted by mother is rich in:CUET 2023 Medium
- Darwin's finches are the example of :CUET 2023 Hard