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2026 session1_23jan_shift1

11 maths questions

Q2 SUVAT in 2D & Gravity View

A particle is projected from the ground with an initial velocity making an angle of $60 ^ { \circ }$ with the horizontal. If its kinetic energy at the point of projection is $\mathrm { k } _ { 0 }$ and the kinetic energy at the highest point of the trajectory is $k _ { 1 }$, then find the value of $\frac { k _ { 0 } - k _ { 1 } } { k _ { 0 } }$\ (A) $\frac { 1 } { 2 }$\ (B) $\frac { 2 } { 3 }$\ (c) $\frac { 3 } { 4 }$\ (D) $\frac { 1 } { 5 }$

Q23 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View

A rectangle is formed by lines $x = 0 , y = 0 , x = 3 , y = 4$. A line perpendicular to $3 x + 4 y + 6 = 0$ divides the rectangle into two equal parts, then the distance of the line from ( $- 1 , \frac { 3 } { 2 }$ ) is\ (A) 2\ (B) $\frac { 8 } { 5 }$\ (C) $\frac { 6 } { 5 }$\ (D) $\frac { 17 } { 10 }$

Q24 Permutations & Arrangements Word Permutations with Repeated Letters View

Number of 4 letters words with or without meaning formed from the letters of the word PQRSSSTTUVV is\ (A) 1232\ (B) 1422\ (C) 1400\ (D) 1162

Q25 Probability Definitions Combinatorial Counting (Non-Probability) View

Let $\mathrm { A } = \{ - 2 , - 1,0,1,2,3,4 \}$ and R be a relation R , such that $\mathbf { R } = \{ ( \mathbf { x } , \mathbf { y } ) : ( \mathbf { 2 x } + \mathbf { y } ) \leq - \mathbf { 2 } , \mathbf { x } \in \mathbf { A } , \mathbf { y } \in \mathbf { A } \}$.\
Let $\boldsymbol { l } =$ number of elements in $\mathbf { R }$\ $\mathrm { m } =$ minimum number of elements to be added in R to make it reflexive.\ $\mathrm { n } =$ minimum number of elements to be added in R to make it symmetric, then $( 1 + m + n )$ is\ (A) 17\ (B) 10\ (C) 11\ (D) 14

Q26 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View

In the expansion of $\left( \left( 1 + x ^ { 2 } \right) ^ { 2 } ( 1 + x ) ^ { n } \right.$, coefficients of $x , x ^ { 2 }$ and $x ^ { 3 }$ are in A.P, then find sum of all possible values of $n \in N$.

Q27 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View

Let the area bounded by the curve $\mathrm { f } ( \mathrm { x } ) = \max \{ \sin x , \cos x \}$ and x -axis is\ $A$ where $x \in \left[ 0 , \frac { 3 \pi } { 2 } \right]$. Find $A + A ^ { 2 }$

Q28 Vectors Introduction & 2D Dot Product Computation View

For given vectors $\vec { a } = - \hat { i } + \hat { j } + 2 \hat { k }$ and $\vec { b } = 2 \hat { i } - \hat { j } + \hat { k }$ where $\vec { c } = \vec { a } \times \vec { b }$ and $\vec { d } = \vec { c } \times \vec { b }$. Then the value of $( \vec { a } - \vec { b } ) \cdot \vec { d }$ is:\ (A) 35\ (B) -35\ (C) 30\ (D) -30

Q29 Circles Area and Geometric Measurement Involving Circles View

The line $y = x + 1$ intersects the ellipse $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 1 } = 1$ at $A$ and $B$. Find the angle sub-stained by segment AB and centre of ellipse is\ (A) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 2 } \right)$\ (B) $\frac { \pi } { 2 } + 2 \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$\ (C) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$\ (D) $\frac { \pi } { 2 } - \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$

Q30 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View

The value of $\frac { { } ^ { 100 } C _ { 50 } } { 51 } + \frac { { } ^ { 100 } C _ { 51 } } { 52 } + \ldots \ldots \frac { { } ^ { 100 } C _ { 100 } } { 101 }$ is $\sum _ { \gamma = 50 } ^ { 100 } \frac { { } ^ { 100 } C _ { \gamma } } { \gamma + 1 }$\ (A) $\frac { 2 ^ { 100 } } { 100 }$\ (B) $\frac { 2 ^ { 101 } } { 101 }$\ (C) $\frac { 2 ^ { 100 } } { 101 }$\ (D) $\frac { 2 ^ { 101 } } { 100 }$

Q31 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View

If person A and person B can finish together whole work in 22.5 days. If B alone takes 24 days more to complete the work than A alone, find the number of days taken by A alone to finish the given work.\ (A) 18\ (B) 36\ (C) 60\ (D) 24

Q32 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View

Find $\int _ { \frac { \pi } { 24 } } ^ { \frac { 5 \pi } { 24 } } \frac { 1 + ( \tan 2 \mathrm { x } ) ^ { 1 / 3 } } { 1 + ( \tan 2 x ) ^ { 1 / 3 } } \mathrm { dx }$\ (A) $\frac { \pi } { 24 }$\ (B) $\frac { \pi } { 12 }$\ (C) $\frac { \pi } { 48 }$\ (D) $\frac { \pi } { 6 }$

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2026 session1_23jan_shift1