MARKS ALL Premium Mathematics dpps chapterwise with solutions For Jee mains and advanced 2026,2027

CHAPTER PG
1: Quadratic Equations 2
2: Complex Numbers 24
3: Permutation Combination 44
4: Sequences and Series 67
5: Binomial Theorem 88
6: Trigonometric Equations 108
7: Straight Lines 128
8: Circle 150
9: Parabola 174
10: Ellipse 195
11: Hyperbola 218

,Marks Premium DPPs - Math (11th)

Quadratic Equations

Easy Questions

Question 1

Let α, β be the roots of the equation ax 2 + bx + c = 0. A root of the equation
a 3 x 2 + abcx + c 3 = 0 is
A. A) α + β
B. B) α 2 + β
C. C) α 2 − β
D. D) α 2 β

Question 2

In △ABC, with tustal notations, m∠C = π2 , if tan ( A
2
) and tan ( B2 ) are the roots of the
equation. a 1 x 2 + b 1 x + c 1 = 0 (a 1 ≠ 0), then

A. A) a 1 + b 1 = c 1
B. B) b 1 + c 1 = a 1
C. C) a 1 + c 1 − b 1
D. D) b 1 = c 1

Question 3

If px 2 + qx + r = p(x − α)(x − β), and p 3 + pq + r = 0; p, q and r being real numbers,
then which of the following is not possible?

A. A) α = β = p
B. B) α ≠ β = p
C. C) α = β ≠ p
D. D) β ≠ α = p

Question 4

If (α + √β) and (α − √β) are the roots of the equation x 2 + px + q = 0, where α, β, p
and q are real, then the roots of the equation (p 2 − 4q) (p 2 x 2 + 4px) − 16q = 0 are

,A. A) ( α1 + 1 ) and ( α1 − 1 )
√β √β

B. B) ( 1 + β1 ) and ( 1 − β1 )
√α √α

C. C) ( 1 + 1 ) and ( 1 − 1 )
√α √β √α √β

D. D) (√α + √β) and (√α − √β)

Question 5

The number of real solutions of the equation ( 10
9
) = −3 + x − x 2 is
A. A) 0
B. B) 1
C. C) 2
D. D) None of these

Question 6

If m 1 and m 2 are slopes of the lines represented by
(sec 2 θ − sin 2 θ)x 2 − 2 tan θxy + sin 2 θy 2 = 0, then |m 1 − m 2 | =
A. A) 1
B. B) 2
C. C) 4
D. D) 3

Question 7

If x, y, z ∈ R, x + y + z = 5, x 2 + y 2 + z 2 = 9, then length of interval in which x lies is

A. A) 8/3
B. B) 4/3
C. C) 2/3
D. D) 1/3

Question 8

If the roots of the equation x 2 + ax + b = 0 are c and d, then one of the roots of the equation
x 2 + (2c + a)x + c 2 + ac + b = 0 is
A. A) c
B. B) d − c
C. C) 2d

, D. D) 2c

Question 9

The number of solutions for the equation x 2 − 5|x| + 6 = 0 is

A. A) 4
B. B) 3
C. C) 2
D. D) 1

Question 10

If α, β, γ are the roots of the equation x 3 + px + q = 0, then the value of the determinant
α β γ
β γ α is
γ α β
A. A) q
B. B) 0
C. C) p
D. D) p 2 − 2q

Question 11

If one root of the equation (l − m)x 2 + lx + 1 = 0 is double of the other and if l is real then
the greatest value of m is (l ≠ m) :

A. A) 3
1

B. B) 89
C. C) 98
D. D) 3





∣
Question 12

If α and β are the roots of the equation x 2 + x + 1 = 0, then the equation whose roots are α 19
and β 7 is

A. A) x 2 − x − 1 = 0
B. B) x 2 − x + 1 = 0
C. C) x 2 + x − 1 = 0
D. D) x 2 + x + 1 = 0

Question 13