# 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

Contents

## 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 ________ .

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

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

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

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

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

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

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 ….

Q143) Sum of the cube roots of the equation x4-3x3-2x2+3x +1 =0 is equal to
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

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

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 ______