1
A-II, B-III, C-I, D-IV 2
A-III, B-IV, C-II, D-I 3
A-IV, B-III, C-II, D-I 4
A-IV, B-III, C-I, D-II Go to Discussion
Phrases Previous Year PYQ Phrases CUET 2023 PYQ
Solution Dog causes Rabies, Mosquito causes Malaria → A-IV
Amnesia affects Memory, Paralysis affects Movement → B-III
Meningitis affects Brain, Cirrhosis affects Liver → C-II
Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I
Correct matching: A-IV, B-III, C-II, D-I
Qus : 2
Phrases PYQ
1
Given below are two statements:
Statement I:
$\displaystyle \int_{-a}^{a} f(x),dx = \int_{0}^{a} [f(x)+f(-x)],dx$
Statement II:
$\displaystyle \int_{0}^{1} \sqrt{(1+x)(1+x^3)},dx \le \dfrac{15}{8}$
In the light of the above statements, choose the most appropriate answer from the options given below:
1
Both Statement I and Statement II are true 2
Both Statement I and Statement II are false 3
Statement I is true but Statement II is false 4
Statement I is false but Statement II is true Go to Discussion
Phrases Previous Year PYQ Phrases CUET 2023 PYQ
Solution Statement I:
This is a standard property of definite integrals.
So Statement I is true.
Statement II:
Using AM ≥ GM:
$(1+x)(1+x^3) \le \left(\dfrac{(1+x)+(1+x^3)}{2}\right)^2$
So,
$\sqrt{(1+x)(1+x^3)} \le \dfrac{2 + x + x^3}{2}$
Integrating from $0$ to $1$:
$\displaystyle \int_0^1 \sqrt{(1+x)(1+x^3)},dx \le \dfrac{15}{8}$
Statement II is true.
Qus : 3
Phrases PYQ
3
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A:
$\displaystyle \int_{-3}^{3} (x^3+5),dx = 30$
Reason R:
$f(x)=x^3+5$ is an odd function.
In the light of the above statements, choose the correct answer from the options given below:
1
Both A and R are true and R is the correct explanation of A 2
Both A and R are true but R is not the correct explanation of A 3
A is true but R is false 4
A is false but R is true Go to Discussion
Phrases Previous Year PYQ Phrases CUET 2023 PYQ
Solution
Qus : 5
Phrases PYQ
1
If $f(a+b-x)=f(x)$ then $\int ^b_axf(x)dx$ is equal to
1
$$\frac{a+b}{2}\int ^b_af(x)dx$$
2
$$\frac{b-a}{2}\int ^b_af(x)dx$$
3
$$\frac{a+b}{2}\int ^b_af(a+x)dx$$
4
$$\frac{a+b}{2}\int ^b_axf(x)dx$$
Go to Discussion
Phrases Previous Year PYQ Phrases CUET 2024 PYQ
Solution
We are asked to evaluate
\(\displaystyle I = \int_a^b x f(x)\, dx \quad \text{given } f(a+b-x)=f(x).\)
Step 1: Put substitution \(t=a+b-x\). Then \(dx=-dt\).
When \(x=a \Rightarrow t=b\),
when \(x=b \Rightarrow t=a\).
So,
\[
I = \int_a^b x f(x)\, dx = \int_b^a (a+b-t) f(t)(-dt)
= \int_a^b (a+b-t) f(t)\, dt.
\]
Step 2: Add both forms of \(I\):
\[
2I = \int_a^b [x f(x) + (a+b-x) f(x)] dx
= \int_a^b (a+b) f(x)\, dx.
\]
Step 3: Simplify:
\[
I = \frac{a+b}{2} \int_a^b f(x)\, dx.
\]
Final Answer:
\(\displaystyle \frac{a+b}{2}\int_a^b f(x)\, dx\)
→ matches Option 1 .
Qus : 6
Phrases PYQ
2
Match List – I with List – II
List - I List - II (A) $$\int ^{\pi/2}_0\frac{{\sin }^4x}{{\sin }^4x+{\cos }^4x}dx$$ (I) 0 (B) $$\int ^{\pi/3}_{\pi/6}\frac{1}{1+\sqrt[]{\tan x}}dx$$ (II) 0 (C) $$\int ^1_0x{e}^xdx$$ (III) $\frac{\pi}{12}$ (D) $$\int ^1_{-1}{x}^{109}{\cos }^{88}xdx$$ (IV) $\frac{\pi}{4}$
Choose the correct answer from the options given below:
1
(A – IV); (B – III); (C – I); (D – II)
2
(A – IV); (B – III); (C – II); (D – I)
3
(A – III); (B – IV); (C – II); (D – I)
4
(A – III); (B – IV); (C – I); (D – II)
Go to Discussion
Phrases Previous Year PYQ Phrases CUET 2024 PYQ
Solution [{"qus_id":"11693","year":"2024"},{"qus_id":"11703","year":"2024"},{"qus_id":"16713","year":"2023"},{"qus_id":"16693","year":"2023"},{"qus_id":"16658","year":"2023"},{"qus_id":"16713","year":"2023"},{"qus_id":"17320","year":"2026"}]
Phrases Online Test Series,
Click Here to
Phrases Online Test Series,
Click Here to
Are you sure to delete this comment ?
Please provide more information - at least 10 characters
