JEE Mains 26 June 2022 Shift 1 Answer Key Question Paper

The first shift of the Day 4 of the JEE Main Exam 2022 is held on 26 june in morning from 9:00A.M. to 12:00 P.M. Here is the answers to questions of the JEE Mains 26 June Shift 1 Examination

JEE Mains Exam 26 June 2022 Exam Shift 1

Maths (Shift 1)

Q1. In how many ways a team of 3 boys and 3 girls can be formed from 10 boys and 5 girls , if two particular boys B1 and B2 are not in team together ?
Options –
A) 1120
B ) 1220
C ) 1115
D ) 1280

Answer : Option ( A ) 1120.

Q2. If ( 2021 ) 2023 is divided by 7, then remainder is equal to ________ .
Answer : Remainder = 5

Q3. Solve : \( \frac{48}{\pi^4}\ \int_{0}^{\pi}{\left(\frac{3\pi}{2}\ x^2-\ x^3\right)\ \frac{\sin{x}}{1+\ \cos^2{x}}\ \bullet d\ x} \)
Answer : 6

Q4. The function \( f \left(x\right)=\frac{x\ -\ 1}{x+1} \) , R – { -1,0,-1 } and fn+1 = f(fn(x)), then the value of f6(6) +f7(7) is equal to
Options –
A) -1/2
B) 3/2
C) -3/2
D) 1/2
Answer : C) -3/2

Q5) If F(x) = max( |x+1|, |x+2|, |x + 3|, …. |x +5| ) , then find the value of \( \int_{-6}^{0}{f(x)\ .\ dx} \)
Answer : 21

Q6) If the line \( \frac{x}{a}\ +\ \frac{y}{b}\ =\ 2 \) is tangent to the curve \( \left(\frac{x}{a}\right)^n+\ \left(\frac{y}{b}\right)^n=\ 2 \) at point ( a,b) , then the value of n
Options –
A) n \( \in \) N
B) ϕ
C) Singleton Set
D) Even
Answer : Option A) A) n \( \in \) N

Q7) If a biased coin is tossed 5 times and if the probability of getting exactly 4 heads is equal to probability of getting 5 heads , then the probability of getting at most 2 heads is
Options-
A) \( \frac{275}{6^5} \)
B) \( \frac{46}{6^4} \)
C) \( \frac{41}{5^5} \)
D) \( \frac{24}{648} \)
Answer : Option B \( \frac{46}{6^4} \)

Q8) Evaluate lim x→1/√2 \( {\left(\frac{\sin{{(\cos}^{-1}{x})\ }-\ x}{1\ -\ \tan{\cos^{-1}{x}}}\right)} \)
Options –
A) 1
B) 1/√2
C) -1
D) -1/√2
Answer : Option D) -1/√2

Q9) A normal is drawn from P(5,8) to the parabola y2=6x meeting it at Q. Tangent at Q to y2 = 6x meet point R on the directrix, then ordinate of point R is
Options-
A) 6/2
B) 9/4
C) 9/2
D) 3/2
Answer : Option B) 9/4

Q10) Let A be a matrix of Order 3*3 and is |adj (24A)| = |adj( 3 adj 2A) |, then |A|2 is equal to :
Options –
A) 26
B) 66
C) 212
D) 1
Answer : Option A ) 26

Q11) Triangle ABC is a equilateral triangle with vertex A(3,7) and B,C lie on the line x+y=5. Area of ∆ABC is
Options-
A) \( \frac{25}{2√3} \)
B) \( \frac{25}{√6} \)
C)
D) 25
Answer : Option A) \( \frac{25}{2√3} \) .

Q12) If A = \( \sum_{j=1}^{10}\sum_{i\ =\ 1}^{10}{min\left(i,j\right),B\ }=\ \sum_{i\ =\ 1}^{10}\sum_{j\ =\ 1}^{10}max\left(i,j\right) \) , then A+B is equal to
Options-
A) 1190
B) 1000
C) 1100
D) 1200
Answer : Option C) 1100

Q13) If Five observations a,b,5,8,10 has mean and variance as 6 and 6.8 respectively, then the value of (mean deviation about mean) * 25 is ….
Answer : 60

Q143) Sum of the cube roots of the equation x4-3x3-2x2+3x +1 =0 is equal to
Answer : 36
Hint : Divide by x on both sides and then solve.

Q15) If \( \vec{a}\ .\vec{b}\ =\ 1 \) , \( \vec{b}\ . \vec{c}\ = 2 \) , \( \vec{c}\ . \vec{a} = 3 \) , then the value of \( [ \vec{a}\ \times \ ( \vec{b}\ \times \vec{c} ), \vec{b}\ \times \ ( \vec{a}\ \times \vec{c} ) , \vec{c}\ \times \ ( \vec{a}\ \times \vec{b} ) ] \) is
Answer : 0

Q16) Area bounded by between the curves y = |x2 – 9| and y = 3 is equal to
Options-
A) 4(4√3 + 2√6 – 9)
B) 8(4√3 + 2√6 – 9)
C) 8(2√6 +4√3 – 9)
D) 8(4√3 -2√6 -9)
Answer : Option B) 8(4√3 + 2√6 – 9)

Q17) Let common tangent to x2 +y2 = 9/4 and y2=4x meet x-axis at point Q. If an ellipse with length of major axis equal to 6 and minor axis is length ‘OQ’ is drawn , then the value of l/e2 is (where l is the length of latus rectum and ‘e’ is eccentricity of the ellipse and O is origin)
Option-
A) 5
B) 2
C) 7
D) 8
Answer : Option B) 2

Q18) if f(x) = 2cos-1x + 4cot-1x – 3x2 -2x + 10 then the range of f9x) is [a,b] ,then the value of 4a-b is
Options-
A) 11
B) π
C) 11 + π
D) 11 – π
Answer : Option D) 11 – π

Q19) If Sin210° sin 20° sin40°sin50°sin70° = a-1/16sin10° , then the value of a is ______
Answer : 1/64

Physics (Shift 1)

Q1) A ball is thrown vertically upward. At the maximum heights. Which one the following is zero ?
Options-
A) Force
B) P.E.
C) Acceleration
D) Momentum
Answer : Momentum
Hint : Momentum is zero at the top position